Time Series Forecasting with the Long Short-Term Memory Network in Python

The Long Short-Term Memory recurrent neural network has the promise of learning long sequences of observations.

It seems a perfect match for time series forecasting, and in fact, it may be.

In this tutorial, you will discover how to develop an LSTM forecast model for a one-step univariate time series forecasting problem.

After completing this tutorial, you will know:

  • How to develop a baseline of performance for a forecast problem.
  • How to design a robust test harness for one-step time series forecasting.
  • How to prepare data, develop, and evaluate an LSTM recurrent neural network for time series forecasting.

Kick-start your project with my new book Deep Learning for Time Series Forecasting, including step-by-step tutorials and the Python source code files for all examples.

Let’s get started.

  • Update May/2017: Fixed bug in invert_scale() function, thanks Max.
  • Updated Apr/2019: Updated the link to dataset.
Time Series Forecasting with the Long Short-Term Memory Network in Python

Time Series Forecasting with the Long Short-Term Memory Network in Python
Photo by Matt MacGillivray, some rights reserved.

Tutorial Overview

This is a big topic and we are going to cover a lot of ground. Strap in.

This tutorial is broken down into 9 parts; they are:

  1. Shampoo Sales Dataset
  2. Test Setup
  3. Persistence Model Forecast
  4. LSTM Data Preparation
  5. LSTM Model Development
  6. LSTM Forecast
  7. Complete LSTM Example
  8. Develop a Robust Result
  9. Tutorial Extensions

Python Environment

This tutorial assumes you have a Python SciPy environment installed. You can use either Python 2 or 3 with this tutorial.

You must have Keras (2.0 or higher) installed with either the TensorFlow or Theano backend.

The tutorial also assumes you have scikit-learn, Pandas, NumPy and Matplotlib installed.

If you need help with your environment, see this post:

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Shampoo Sales Dataset

This dataset describes the monthly number of sales of shampoo over a 3-year period.

The units are a sales count and there are 36 observations. The original dataset is credited to Makridakis, Wheelwright, and Hyndman (1998).

Download the dataset to your current working directory with the name “shampoo-sales.csv“.

The example below loads and creates a plot of the loaded dataset.

Running the example loads the dataset as a Pandas Series and prints the first 5 rows.

A line plot of the series is then created showing a clear increasing trend.

Line Plot of Monthly Shampoo Sales Dataset

Line Plot of Monthly Shampoo Sales Dataset

Experimental Test Setup

We will split the Shampoo Sales dataset into two parts: a training and a test set.

The first two years of data will be taken for the training dataset and the remaining one year of data will be used for the test set.

For example:

Models will be developed using the training dataset and will make predictions on the test dataset.

A rolling forecast scenario will be used, also called walk-forward model validation.

Each time step of the test dataset will be walked one at a time. A model will be used to make a forecast for the time step, then the actual expected value from the test set will be taken and made available to the model for the forecast on the next time step.

For example:

This mimics a real-world scenario where new Shampoo Sales observations would be available each month and used in the forecasting of the following month.

Finally, all forecasts on the test dataset will be collected and an error score calculated to summarize the skill of the model. The root mean squared error (RMSE) will be used as it punishes large errors and results in a score that is in the same units as the forecast data, namely monthly shampoo sales.

For example:

Persistence Model Forecast

A good baseline forecast for a time series with a linear increasing trend is a persistence forecast.

The persistence forecast is where the observation from the prior time step (t-1) is used to predict the observation at the current time step (t).

We can implement this by taking the last observation from the training data and history accumulated by walk-forward validation and using that to predict the current time step.

For example:

We will accumulate all predictions in an array so that they can be directly compared to the test dataset.

The complete example of the persistence forecast model on the Shampoo Sales dataset is listed below.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the RMSE of about 136 monthly shampoo sales for the forecasts on the test dataset.

A line plot of the test dataset (blue) compared to the predicted values (orange) is also created showing the persistence model forecast in context.

Persistence Forecast of Observed vs Predicted for Shampoo Sales Dataset

Persistence Forecast of Observed vs Predicted for Shampoo Sales Dataset

For more on the persistence model for time series forecasting, see this post:

Now that we have a baseline of performance on the dataset, we can get started developing an LSTM model for the data.

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LSTM Data Preparation

Before we can fit an LSTM model to the dataset, we must transform the data.

This section is broken down into three steps:

  1. Transform the time series into a supervised learning problem
  2. Transform the time series data so that it is stationary.
  3. Transform the observations to have a specific scale.

Transform Time Series to Supervised Learning

The LSTM model in Keras assumes that your data is divided into input (X) and output (y) components.

For a time series problem, we can achieve this by using the observation from the last time step (t-1) as the input and the observation at the current time step (t) as the output.

We can achieve this using the shift() function in Pandas that will push all values in a series down by a specified number places. We require a shift of 1 place, which will become the input variables. The time series as it stands will be the output variables.

We can then concatenate these two series together to create a DataFrame ready for supervised learning. The pushed-down series will have a new position at the top with no value. A NaN (not a number) value will be used in this position. We will replace these NaN values with 0 values, which the LSTM model will have to learn as “the start of the series” or “I have no data here,” as a month with zero sales on this dataset has not been observed.

The code below defines a helper function to do this called timeseries_to_supervised(). It takes a NumPy array of the raw time series data and a lag or number of shifted series to create and use as inputs.

We can test this function with our loaded Shampoo Sales dataset and convert it into a supervised learning problem.

Running the example prints the first 5 rows of the new supervised learning problem.

For more information on transforming a time series problem into a supervised learning problem, see the post:

Transform Time Series to Stationary

The Shampoo Sales dataset is not stationary.

This means that there is a structure in the data that is dependent on the time. Specifically, there is an increasing trend in the data.

Stationary data is easier to model and will very likely result in more skillful forecasts.

The trend can be removed from the observations, then added back to forecasts later to return the prediction to the original scale and calculate a comparable error score.

A standard way to remove a trend is by differencing the data. That is the observation from the previous time step (t-1) is subtracted from the current observation (t). This removes the trend and we are left with a difference series, or the changes to the observations from one time step to the next.

We can achieve this automatically using the diff() function in pandas. Alternatively, we can get finer grained control and write our own function to do this, which is preferred for its flexibility in this case.

Below is a function called difference() that calculates a differenced series. Note that the first observation in the series is skipped as there is no prior observation with which to calculate a differenced value.

We also need to invert this process in order to take forecasts made on the differenced series back into their original scale.

The function below, called inverse_difference(), inverts this operation.

We can test out these functions by differencing the whole series, then returning it to the original scale, as follows:

Running the example prints the first 5 rows of the loaded data, then the first 5 rows of the differenced series, then finally the first 5 rows with the difference operation inverted.

Note that the first observation in the original dataset was removed from the inverted difference data. Besides that, the last set of data matches the first as expected.

For more information on making the time series stationary and differencing, see the posts:

Transform Time Series to Scale

Like other neural networks, LSTMs expect data to be within the scale of the activation function used by the network.

The default activation function for LSTMs is the hyperbolic tangent (tanh), which outputs values between -1 and 1. This is the preferred range for the time series data.

To make the experiment fair, the scaling coefficients (min and max) values must be calculated on the training dataset and applied to scale the test dataset and any forecasts. This is to avoid contaminating the experiment with knowledge from the test dataset, which might give the model a small edge.

We can transform the dataset to the range [-1, 1] using the MinMaxScaler class. Like other scikit-learn transform classes, it requires data provided in a matrix format with rows and columns. Therefore, we must reshape our NumPy arrays before transforming.

For example:

Again, we must invert the scale on forecasts to return the values back to the original scale so that the results can be interpreted and a comparable error score can be calculated.

Putting all of this together, the example below transforms the scale of the Shampoo Sales data.

Running the example first prints the first 5 rows of the loaded data, then the first 5 rows of the scaled data, then the first 5 rows with the scale transform inverted, matching the original data.

Now that we know how to prepare data for the LSTM network, we can start developing our model.

LSTM Model Development

The Long Short-Term Memory network (LSTM) is a type of Recurrent Neural Network (RNN).

A benefit of this type of network is that it can learn and remember over long sequences and does not rely on a pre-specified window lagged observation as input.

In Keras, this is referred to as stateful, and involves setting the “stateful” argument to “True” when defining an LSTM layer.

By default, an LSTM layer in Keras maintains state between data within one batch. A batch of data is a fixed-sized number of rows from the training dataset that defines how many patterns to process before updating the weights of the network. State in the LSTM layer between batches is cleared by default, therefore we must make the LSTM stateful. This gives us fine-grained control over when state of the LSTM layer is cleared, by calling the reset_states() function.

The LSTM layer expects input to be in a matrix with the dimensions: [samples, time steps, features].

  • Samples: These are independent observations from the domain, typically rows of data.
  • Time steps: These are separate time steps of a given variable for a given observation.
  • Features: These are separate measures observed at the time of observation.

We have some flexibility in how the Shampoo Sales dataset is framed for the network. We will keep it simple and frame the problem as each time step in the original sequence is one separate sample, with one timestep and one feature.

Given that the training dataset is defined as X inputs and y outputs, it must be reshaped into the Samples/TimeSteps/Features format, for example:

The shape of the input data must be specified in the LSTM layer using the “batch_input_shape” argument as a tuple that specifies the expected number of observations to read each batch, the number of time steps, and the number of features.

The batch size is often much smaller than the total number of samples. It, along with the number of epochs, defines how quickly the network learns the data (how often the weights are updated).

The final import parameter in defining the LSTM layer is the number of neurons, also called the number of memory units or blocks. This is a reasonably simple problem and a number between 1 and 5 should be sufficient.

The line below creates a single LSTM hidden layer that also specifies the expectations of the input layer via the “batch_input_shape” argument.

The network requires a single neuron in the output layer with a linear activation to predict the number of shampoo sales at the next time step.

Once the network is specified, it must be compiled into an efficient symbolic representation using a backend mathematical library, such as TensorFlow or Theano.

In compiling the network, we must specify a loss function and optimization algorithm. We will use “mean_squared_error” as the loss function as it closely matches RMSE that we will are interested in, and the efficient ADAM optimization algorithm.

Using the Sequential Keras API to define the network, the below snippet creates and compiles the network.

Once compiled, it can be fit to the training data. Because the network is stateful, we must control when the internal state is reset. Therefore, we must manually manage the training process one epoch at a time across the desired number of epochs.

By default, the samples within an epoch are shuffled prior to being exposed to the network. Again, this is undesirable for the LSTM because we want the network to build up state as it learns across the sequence of observations. We can disable the shuffling of samples by setting “shuffle” to “False“.

Also by default, the network reports a lot of debug information about the learning progress and skill of the model at the end of each epoch. We can disable this by setting the “verbose” argument to the level of “0“.

We can then reset the internal state at the end of the training epoch, ready for the next training iteration.

Below is a loop that manually fits the network to the training data.

Putting this all together, we can define a function called fit_lstm() that trains and returns an LSTM model. As arguments, it takes the training dataset in a supervised learning format, a batch size, a number of epochs, and a number of neurons.

The batch_size must be set to 1. This is because it must be a factor of the size of the training and test datasets.

The predict() function on the model is also constrained by the batch size; there it must be set to 1 because we are interested in making one-step forecasts on the test data.

We will not tune the network parameters in this tutorial; instead we will use the following configuration, found with a little trial and error:

  • Batch Size: 1
  • Epochs: 3000
  • Neurons: 4

As an extension to this tutorial, you might like to explore different model parameters and see if you can improve performance.

  • Update: Consider trying 1500 epochs and 1 neuron, the performance may be better!

Next, we will look at how we can use a fit LSTM model to make a one-step forecast.

LSTM Forecast

Once the LSTM model is fit to the training data, it can be used to make forecasts.

Again, we have some flexibility. We can decide to fit the model once on all of the training data, then predict each new time step one at a time from the test data (we’ll call this the fixed approach), or we can re-fit the model or update the model each time step of the test data as new observations from the test data are made available (we’ll call this the dynamic approach).

In this tutorial, we will go with the fixed approach for its simplicity, although, we would expect the dynamic approach to result in better model skill.

To make a forecast, we can call the predict() function on the model. This requires a 3D NumPy array input as an argument. In this case, it will be an array of one value, the observation at the previous time step.

The predict() function returns an array of predictions, one for each input row provided. Because we are providing a single input, the output will be a 2D NumPy array with one value.

We can capture this behavior in a function named forecast() listed below. Given a fit model, a batch-size used when fitting the model (e.g. 1), and a row from the test data, the function will separate out the input data from the test row, reshape it, and return the prediction as a single floating point value.

During training, the internal state is reset after each epoch. While forecasting, we will not want to reset the internal state between forecasts. In fact, we would like the model to build up state as we forecast each time step in the test dataset.

This raises the question as to what would be a good initial state for the network prior to forecasting the test dataset.

In this tutorial, we will seed the state by making a prediction on all samples in the training dataset. In theory, the internal state should be set up ready to forecast the next time step.

We now have all of the pieces to fit an LSTM Network model for the Shampoo Sales dataset and evaluate its performance.

In the next section, we will put all of these pieces together.

Complete LSTM Example

In this section, we will fit an LSTM to the Shampoo Sales dataset and evaluate the model.

This will involve drawing together all of the elements from the prior sections. There are a lot of them, so let’s review:

  1. Load the dataset from CSV file.
  2. Transform the dataset to make it suitable for the LSTM model, including:
    1. Transforming the data to a supervised learning problem.
    2. Transforming the data to be stationary.
    3. Transforming the data so that it has the scale -1 to 1.
  3. Fitting a stateful LSTM network model to the training data.
  4. Evaluating the static LSTM model on the test data.
  5. Report the performance of the forecasts.

Some things to note about the example:

  • The scaling and inverse scaling behaviors have been moved to the functions scale() and invert_scale() for brevity.
  • The test data is scaled using the fit of the scaler on the training data, as is required to ensure the min/max values of the test data do not influence the model.
  • The order of data transforms was adjusted for convenience to first make the data stationary, then a supervised learning problem, then scaled.
  • Differencing was performed on the entire dataset prior to splitting into train and test sets for convenience. We could just as easily collect observations during the walk-forward validation and difference them as we go. I decided against it for readability.

The complete example is listed below.

Running the example prints the expected and predicted values for each of the 12 months in the test dataset.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

The example also prints the RMSE of all forecasts. The model shows an RMSE of 71.721 monthly shampoo sales, which is better than the persistence model that achieved an RMSE of 136.761 shampoo sales.

A line plot of the test data (blue) vs the predicted values (orange) is also created, providing context for the model skill.

Line Plot of LSTM Forecast vs Expected Values

Line Plot of LSTM Forecast vs Expected Values

As an afternote, you can do a quick experiment to build your trust in the test harness and all of the transforms and inverse transforms.

Comment out the line that fits the LSTM model in walk-forward validation:

And replace it with the following:

This should produce a model with perfect skill (e.g. a model that predicts the expected outcome as the model output).

The results should look as follows, showing that if the LSTM model could predict the series perfectly, the inverse transforms and error calculation would show it correctly.

Develop a Robust Result

A difficulty with neural networks is that they give different results with different starting conditions.

One approach might be to fix the random number seed used by Keras to ensure the results are reproducible. Another approach would be to control for the random initial conditions using a different experimental setup.

We can repeat the experiment from the previous section multiple times, then take the average RMSE as an indication of how well the configuration would be expected to perform on unseen data on average.

This is often called multiple repeats or multiple restarts.

We can wrap the model fitting and walk-forward validation in a loop of fixed number of repeats. Each iteration the RMSE of the run can be recorded. We can then summarize the distribution of RMSE scores.

The data preparation would be the same as before.

We will use 30 repeats as that is sufficient to provide a good distribution of RMSE scores.

The complete example is listed below.

Running the example prints the RMSE score each repeat. The end of the run provides summary statistics of the collected RMSE scores.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

We can see that the mean and standard deviation RMSE scores are 138.491905 and 46.313783 monthly shampoo sales respectively.

This is a very useful result as it suggests the result reported above was probably a statistical fluke. The experiment suggests that the model is probably about as good as the persistence model on average (136.761), if not slightly worse.

This indicates that, at the very least, further model tuning is required.

A box and whisker plot is created from the distribution shown below. This captures the middle of the data as well as the extents and outlier results.

LSTM Repeated Experiment Box and Whisker Plot

LSTM Repeated Experiment Box and Whisker Plot

This is an experimental setup that could be used to compare one configuration of the LSTM model or set up to another.

Tutorial Extensions

There are many extensions to this tutorial that we may consider.

Perhaps you could explore some of these yourself and post your discoveries in the comments below.

  • Multi-Step Forecast. The experimental setup could be changed to predict the next n-time steps rather than the next single time step. This would also permit a larger batch size and faster training. Note that we are basically performing a type of 12 one-step forecast in this tutorial given the model is not updated, although new observations are available and are used as input variables.
  • Tune LSTM model. The model was not tuned; instead, the configuration was found with some quick trial and error. I believe much better results could be achieved by tuning at least the number of neurons and number of training epochs. I also think early stopping via a callback might be useful during training.
  • Seed State Experiments. It is not clear whether seeding the system prior to forecasting by predicting all of the training data is beneficial. It seems like a good idea in theory, but this needs to be demonstrated. Also, perhaps other methods of seeding the model prior to forecasting would be beneficial.
  • Update Model. The model could be updated in each time step of the walk-forward validation. Experiments are needed to determine if it would be better to refit the model from scratch or update the weights with a few more training epochs including the new sample.
  • Input Time Steps. The LSTM input supports multiple time steps for a sample. Experiments are needed to see if including lag observations as time steps provides any benefit.
  • Input Lag Features. Lag observations may be included as input features. Experiments are needed to see if including lag features provide any benefit, not unlike an AR(k) linear model.
  • Input Error Series. An error series may be constructed (forecast error from a persistence model) and used as an additional input feature, not unlike an MA(k) linear model. Experiments are needed to see if this provides any benefit.
  • Learn Non-Stationary. The LSTM network may be able to learn the trend in the data and make reasonable predictions. Experiments are needed to see if temporal dependent structures, like trends and seasonality, left in data can be learned and effectively predicted by LSTMs.
  • Contrast Stateless. Stateful LSTMs were used in this tutorial. The results should be compared with stateless LSTM configurations.
  • Statistical Significance. The multiple repeats experimental protocol can be extended further to include statistical significance tests to demonstrate whether the difference between populations of RMSE results with different configurations are statistically significant.


In this tutorial, you discovered how to develop an LSTM model for time series forecasting.

Specifically, you learned:

  • How to prepare time series data for developing an LSTM model.
  • How to develop an LSTM model for time series forecasting.
  • How to evaluate an LSTM model using a robust test harness.

Can you get a better result?
Share your findings in the comments below.

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710 Responses to Time Series Forecasting with the Long Short-Term Memory Network in Python

  1. Avatar
    Chang April 7, 2017 at 4:42 pm #

    I’ve been working on multi-step-ahead forecast after reading your ebook and following one step ahead tutorials. But still struggling getting nothing. It seems that seq2seq model is used, but I want to configure simple lstm for multi step ahead prediction. Can you help me in getting basic idea to do this?

    • Avatar
      Jason Brownlee April 9, 2017 at 2:53 pm #

      Yes, I have some seq2seq examples scheduled to come out on the blog soon.

      • Avatar
        Shawn December 29, 2021 at 10:20 am #

        This is all fine and well but how do you do a true step ahead forecast BEYOND the dataset? Every blog I see just shows comparison graphs of actual and predicted. How do you use this model to simply look ahead x number of periods past the data, with no graphs? Thanks!

  2. Avatar
    Supriya April 9, 2017 at 9:49 am #

    Hi Jason,
    Thank you for this blog. I am working on multi-step-ahead forecast using recursive prediction technique and I have some difficulty. Blog on this particular topic would be really helpful.
    Also, is it possible to somehow implement recursive technique in ARIMA?.

    • Avatar
      Jason Brownlee April 9, 2017 at 3:01 pm #

      Absolutely, you can take the predictions as history and re-fit the ARIMA.

      Thanks for the suggestion, it would make a good blog post.

  3. Avatar
    Peter Marelas April 9, 2017 at 2:45 pm #

    Hi Jason,

    LSTM remember sequences but is there a way to encode calendar effects in the network so that it remembers or learns events that occur at different intervals within the sequence and each cycles? A concrete example would be a time series that exhibits specific events that repeat themselves on specific times in the year, example first Monday of every month and/or last day of every month. I am thinking whether we can label this data in advance to help the LSTM predict these events better?

    • Avatar
      Guillaume July 10, 2017 at 8:12 pm #

      Hello Peter,

      You might want to check out the X-11 method to separate trend, seasonal, and random change to your sequence. Then apply an algorithm to each part.

      You can look at the following article :
      Study of the Long-term Performance Prediction Methods Using the Spacecraft Telemetry Data
      from Hongzeng Fang
      (Sorry but I can’t find a free dl page anymore ..).

      • Avatar
        Jason Brownlee July 11, 2017 at 10:29 am #

        Thanks for the tip.

        • Avatar
          Yasmine Sayed May 18, 2018 at 11:58 pm #

          Hey Jason, in the case of taking the last observation in the dataset in order to predict the next future timestep (for which we don’t have current values for), does the model use only that 1 observation to predict the next??? Or because it’s an LSTM , does it use both the memory from all the preceding observations during training + the last observation in order to predict the next timestep?

          If it’s the latter – it would make more sense to me. Otherwise I can’t see the sense in using nothing but 1 observation to predict one ahead and guarantee any type of accuracy.

          • Avatar
            Jason Brownlee May 19, 2018 at 7:43 am #

            The way the model is defined, an input sequence is provided in order to predict one time step.

            You can define the mapping any way you wish for your problem though.

  4. Avatar
    Kunpeng Zhang April 10, 2017 at 5:04 am #

    Hi Jason,
    Nice post. Is there any tutorial available on multivariate time series forecasting problem?
    I got two sets of data: traffic flow data and weather data. I am thinking to predict the traffic flow using these two data sets.
    I’d like to learn if I get weather condition involved what will happen for my model.
    Could you kindly give me some advice?
    Thank you.

  5. Avatar
    Gabriel Beauplet April 13, 2017 at 12:21 am #

    You did a great job. This is very detailed ! Bravo 😉

  6. Avatar
    Hand April 19, 2017 at 1:39 pm #

    Great tutorial,

    How do we get a prediction on a currently not existing point in the future?

  7. Avatar
    Hans April 20, 2017 at 1:44 am #

    I mean without a y.

    Error measurements are cool, but I also want to make a prediction for a next step.
    That’s my main intention to read this tutorial.

    Since there are other tutorials out there, lacking the same issue, it would be great to have a complete example, with a real live ouput/result/value.

    I’m aware of the fact that every problem should have its own solution/model, but with a real result (or a comprehensible way to it), the code would be more practical/reusable- especially for python-ml beginners trying to predict some values in the future.

    • Avatar
      Jason Brownlee April 20, 2017 at 9:30 am #

      Fit your model on the entire training dataset then predict the next time step as:

      • Avatar
        Donna May 22, 2017 at 7:07 am #

        Hi Jason, thanks for your tutorial. But can you specify how to fit the model on the entire training set and do the prediction for future point? Thanks.

        • Avatar
          Jason Brownlee May 22, 2017 at 7:56 am #

          That is just a little too much hand holding Donna. What are you having trouble with exactly?

      • Avatar
        tuotuo October 16, 2018 at 8:57 pm #

        Hi, Jsson:
        yhat = model.predict(X):X means current values? and yhad means predict value?

        • Avatar
          Jason Brownlee October 17, 2018 at 6:49 am #

          Yes, X is the input required to make one or more predictions and yhat are the predictions.

          • Avatar
            Ran Xu July 2, 2019 at 4:59 pm #

            Hi, Jason, just got one question related to prediction. Since in your example, you own did prediction one test data,(known), where you have the row data to inverse the difference. What about the prediction for future unknown data, how can we do the difference inversion ?

          • Avatar
            Jason Brownlee July 3, 2019 at 8:21 am #

            Yes, inverting the difference for a prediction only requires the last known observation.

  8. Avatar
    Hans April 20, 2017 at 2:14 pm #

    Thank you Jason,

    I’m new to Python (mainly coding other languages) and just beginning to understand the code- thanks to your outstanding detailed descriptions.

    In the last weeks I tried out two other tutorials and failed exactly at this point (making a first own test-appliance with a result).

    A) Could you please suggest a location/row number in the code in one of the examples for that line?

    B) Is there a magic trick available to avoid the date conversion and work with real dates in own data sets?
    In the moment I would have to transform my data to that date format of the used raw data.

    I’m afraid to break the code logic.

    But I also try to research every crucial part of the code separately for example here:

    My current Python skills are on the level of this tutorial
    https://www.youtube.com/watch?v=N4mEzFDjqtA .

    • Avatar
      Jason Brownlee April 21, 2017 at 8:30 am #

      Hi Hans,

      What do you mean by “first own test-appliance with a result”. I don’t follow.

      Do you mean make a prediction? If so you can make a prediction by fitting the model no all of your data and calling model.predict(X).

      Pandas is really flexible when it comes to loading date data. A good approach for you might be to specify your own date parsing function to use when loading your data. See this post for an example that does this:

  9. Avatar
    Hans April 20, 2017 at 3:39 pm #

    Worth to mention (latest Windows-Info 4.2017):

    There is an issue with Keras/Anaconda on Windows.
    To run the last example above on Win, we have to manually reinstall Keras.
    Further informations can be found here:
    …otherwise it throws compiling errors.

      • Avatar
        Hans April 21, 2017 at 11:12 am #

        I already saw this tutorial written by you.

        On Windows (not a Mac) it’s a slightly different story to build such an environment, even with Anaconda.

        It begins with the fact that there is no Tensorflow with a version <= 3 for Windows and ends with the Keras-hint.

        We needed several days to discuss it on Github and find the right setup in the context of another RNN-script (see the link).

        I use virtual conda-environments and your scripts are running on windows if the keras-hint is implemented.
        Before I had the same issue with some of your scripts then with the discussed one on Github (compile error).

  10. Avatar
    Hans April 20, 2017 at 5:02 pm #

    Update, what I mean:

    I guess one could trigger “forecast_lstm(model, batch_size, X)” or “yhat = model.predict(X)” from the end of the last two example scripts.

    But how to do that in regard to the trained model?

    “Month=13, Predicted=???”

    Do I have to define a new “fictional” X? And if so how?

    • Avatar
      Jason Brownlee April 21, 2017 at 8:32 am #

      You must load the new input data for which a prediction is required as X and use your already fit model to make the prediction by calling the predict() function.

      I’m eager to help, but perhaps I don’t understand the difficulty exactly?

      • Avatar
        Christian C. Russo June 17, 2018 at 2:10 pm #

        Hi again Jason! brilliant tutorial once again,

        I believe many people is asking about the model.predict() because it’s not really working as expected.

        First problem is that doing:

        yhat = model.predict(X)

        with the code example previously given, returns:

        NameError: name ‘model’ is not defined

        As I understand, this is because the model is created under the name “lstm_model” instead of model, so using:

        yhat = lstm_model.predict(X)

        works, but returns:

        ValueError: Error when checking : expected lstm_1_input to have 3 dimensions, but got array with shape (1, 1)

        So, personally, what I have done, is using the “forecast_lstm” function, this way:

        yhat = forecast_lstm(lstm_model, 1, X)



        Which actually returns a value.

        Now the next problem is that the X, is nothing else than the last X of the example, as I never redefine it.

        I found that the amount of functions and filters applied to the training data is quite big, hence I need to replicate them to make the shape match.

        This is my original training data.

        series = read_sql_query(seleccion, conn, parse_dates=[‘creacion’], index_col=[‘creacion’])


        2018-06-17 03:56:11 0.0
        2018-06-17 03:54:03 2.0
        2018-06-17 03:52:11 4.0
        2018-06-17 03:50:05 6.0
        2018-06-17 03:48:17 4.0
        2018-06-17 03:46:04 4.0
        2018-06-17 03:44:01 4.0
        2018-06-17 03:43:05 1.0
        2018-06-17 03:40:12 2.0
        2018-06-17 03:38:12 0.0
        2018-06-17 03:36:21 4.0
        2018-06-17 03:34:32 4.0
        2018-06-17 03:32:05 3.0
        2018-06-17 03:30:01 2.0
        2018-06-17 03:28:23 1.0
        2018-06-17 03:26:17 3.0
        2018-06-17 03:24:04 0.0
        2018-06-17 03:22:34 4.0
        2018-06-17 03:20:04 2.0
        2018-06-17 03:18:18 2.0
        2018-06-17 03:16:00 3.0
        2018-06-17 03:14:06 6.0
        2018-06-17 03:12:06 4.0
        2018-06-17 03:10:04 2.0
        2018-06-17 03:08:02 0.0
        2018-06-17 03:06:02 4.0
        2018-06-17 03:04:02 4.0
        2018-06-17 03:02:10 3.0
        2018-06-17 03:00:22 4.0
        2018-06-17 02:59:13 3.0
        … …
        [7161 rows x 1 columns]

        Then, this process is applied to “series”:

        # transform data to be stationary
        raw_values = series.values
        diff_values = difference(raw_values, 1)

        # transform data to be supervised learning
        supervised = timeseries_to_supervised(diff_values, 1)
        supervised_values = supervised.values

        if you print “supervised_values” at that point, the original data has been transformed to:

        [[0 array([4.])]
        [array([4.]) array([-3.])]
        [array([-3.]) array([1.])]

        [array([2.]) array([4.])]
        [array([4.]) array([-3.])]
        [array([-3.]) array([-1.])]]

        which is clearly less and more condensed information…

        Therefore, if I try to apply

        yhat = forecast_lstm(lstm_model, 1, X)

        after the new data has been loaded:

        predecir = read_sql_query(seleccion, conn, parse_dates=[‘creacion’], index_col=[‘creacion’])

        #limpiamos la cache


        yhat = forecast_lstm(lstm_model, 1, X)
        #ynew = ynew[0]


        I get the following error:

        AttributeError: ‘DataFrame’ object has no attribute ‘reshape’


        So kinda lost in how to actually apply the same structure to the new data before being able to make the new prediction!

        I’ll paste the source my code in case someone needs it:

        You’ll see that I’m loading the data directly from MySQL, and also, splitting the training and test data with a different approach from a previous example given in the blog!

        I’m not sure either about how to make the next prediction!

        Thanks a lot for this blog once again… I wouldn’t be even trying this if it wasn’t for your help and explanations!!!

        My best wishes,

  11. Avatar
    Hans April 21, 2017 at 10:31 am #

    Hello Jason,

    I knew I shouldn’t mention the date conversion part :-). Meanwhile I managed it with “return datetime.strptime(x, ‘%Y-%m-%d’)”
    I have all of your example script parts in separate python file version. So I can test out modifications for specific requirements.

    python basic_data_loading.py
    python persistence_forecast_model.py
    python transform_time_series_to_supervised.py
    python transform_time_series_to_statonary_remove_trends.py
    python transform_scales.py
    python complete_example.py

    Own data loading is solved. That was a relatively easy task.

    • Avatar
      Hans April 21, 2017 at 10:56 am #

      Since the transforming and performance measurement parts are running (I guess they will do even with integer data)
      I now have to build a part lets call it:

      “python predict_one_value.py”

      Of course I have to load my own data that’s clear.

      The question is where to trigger the function

      yhat = model.predict(X)

      in the context of one of your example-scripts and finally say:
      print(yhat). That’s all.

      I guess a short example snippet could solve the problem.
      Could you provide an example- It would help a lot?

      Currently I also don’t understand the role of X completely.
      In the context of “datetime.strptime” it seems to be a date only, If I print it out.
      So if I would have training data of:
      – 01.12.1977
      – 02.12.1977
      – 03.12.1977
      I would guess I could say something like “yhat = model.predict(“1977-12-04″)”.
      The question is where and when in which code context.

      Thank you.

      • Avatar
        Hans April 21, 2017 at 12:06 pm #


        Currently I use the the code from “complete example” (“without robust result”).
        If I comment out from line 106 to line 127 and then at the end of the script say:

        # report one value in the future
        test = datetime.strptime('2017-04-15', '%Y-%m-%d')
        yhat = model.predict(test)

        I get the error message ‘model is not defined’. So trying…

        # report one value in the future
        test = datetime.strptime('2017-04-15', '%Y-%m-%d')
        yhat = lstm_model.predict(test)

        …throws the error “Data should be a Numby array”.

        I guess maybe I could also append a new date to the raw data (without a y),
        but I’m not sure If this would be right.

        The best way to get this running would be an example snipped in context.

        • Avatar
          Jason Brownlee April 22, 2017 at 9:22 am #

          This post will give you a clearer idea of how to use neural nets in Keras including making predictions:

          Yes, input data to making a prediction must be a 2D numpy array. It will not be date data, it will be past obs in the case of time series forecasting.

          • Avatar
            Hans April 22, 2017 at 11:41 am #

            Thank you,

            I will read it ;-).

          • Avatar
            Hans April 22, 2017 at 12:46 pm #

            I have read the tutorial and tried out the pima indians diabetes example.
            I guess I got it and understand the 5 steps (mostly).

            Unfortunately this does not answer my question. Or do I miss something?
            In my problem I have only one input like in the tutorial on this site.

            When you say:

            “yhat = model.predict(X)”

            would give a forecast for a next step.
            What about a step which is not in the training data nor in the test data?

            I have a SVM model which proves and predicts based on my raw data (realized in another environment).
            Lets say I have 100 items training data, 10 items test data.
            It will printout 10 predictions and additionally corresponding performance data.
            The last printed prediction is for a future step which lies in the future.

            How would this be archived in your example?
            Do I have to shift something?

          • Avatar
            Jason Brownlee April 23, 2017 at 5:14 am #

            To make predictions beyond your dataset, you must feed in the last few observations from your dataset as input (X) to predict what happens next (y).

            This post might clear up your thinking on X and y:

          • Avatar
            Hans April 23, 2017 at 1:27 pm #

            >To make predictions beyond your dataset, you must feed in the last few observations from your dataset as input (X) to >predict what happens next (y).

            Is there an example available where this is done?

          • Avatar
            Jason Brownlee April 24, 2017 at 5:32 am #

            Yes, the “LSTM Forecast” section of this very post.

          • Avatar
            Hans April 24, 2017 at 1:55 pm #

            Assuming that “X = row[0:-1]” is an observation,
            how do we sample/collect the last few observations, to make a forecast.?

          • Avatar
            Jason Brownlee April 25, 2017 at 7:43 am #

            It depends on your model, if your model expects the last one observation as input, then reframe that value as a 2d array and provide it as X to model.predict(X).

            If your model requires the last two lag obs as inputs, retrieve them, define them as a one row, two column matrix and provide them to model.predict().

            And so on. I hope that helps.

          • Avatar
            Arun July 13, 2017 at 10:37 am #

            HI Jason,

            Even i started with machine learning and have similar kind of doubt so in one step forecasting we can only get one time step future observation correct ? and to get the prediction i have provided last input observation and then the value obtained from model.predict(X) has to be again scaled and inversed correct ?

            PFB the code:
            X = test_scaled[3,-1:] (my last observation)
            yhat = forecast_lstm(lstm_model, 1, X)
            yhat = invert_scale(scaler, X, yhat)
            yhat = inverse_difference(raw_values, yhat, 1)

            Can you please guide me if i am going in a right way ?

          • Avatar
            Jason Brownlee July 13, 2017 at 4:53 pm #

            Yes, one step forecasting involves predicting the next time step.

            You can make multi-step forecasts, learn more in this post:

            Yes, to make use of the prediction you will need to invert any data transforms performed such as scaling and differencing.

          • Avatar
            Arun Menon July 13, 2017 at 11:32 pm #

            Thank you Jason ..

          • Avatar
            Arun Menon July 13, 2017 at 11:48 pm #

            Hi Jason,

            Being said that, i have another clarification , so when i forecast the next time step using this model , using the below code:
            X = test_scaled[3,-1:] (my last observation)
            yhat = forecast_lstm(lstm_model, 1, X)
            yhat = invert_scale(scaler, X, yhat)
            yhat = inverse_difference(raw_values, yhat, 1)

            in the above code, let yhat be the prediction of future time step, can i use the result of yhat and use the same model to predict one more step ahead in the future ? is this what we call as the recursive multistep forecast ?

          • Avatar
            Jason Brownlee July 14, 2017 at 8:30 am #

            Yes. This is recursive.

          • Avatar
            Arun Menon July 14, 2017 at 1:40 am #

            Hi Jason,

            Can i use the below code and use the recursive multistep forecast
            for eg :
            yhat value can be used as an input to the same model again to get the next future step and so on ?

            X = test_scaled[3,-1:] (my last observation)
            yhat = forecast_lstm(lstm_model, 1, X)
            yhat = invert_scale(scaler, X, yhat)
            yhat = inverse_difference(raw_values, yhat, 1)

          • Avatar
            Arun Menon July 14, 2017 at 11:59 am #

            Hi Jason,

            In predictive analytics using this ML technique, how many future steps should we able to predict , is there any ideal forecasting range in future for eg if i have a data for the last 10 days or so , and i want to forecast the future , the less the future time steps are set, the better the result as the error will be minimum right. Can i use the same code for predicting time series data in production for network traffic for future 3 days ? requirement given for me was to predict the network bandwidth for the next entire week given the data for past 1 year.

            Your comments and suggestions always welcome 🙂


          • Avatar
            Jason Brownlee July 15, 2017 at 9:37 am #

            It depends on the problem and the model.

            Generally, the further in the future you want to predict, the worse the performance of the model.

  12. Avatar
    Hans April 21, 2017 at 6:37 pm #


    can we normalize the RMSE-value(s)?
    And if so how?

    • Avatar
      Jason Brownlee April 22, 2017 at 9:24 am #

      Normalize the skill score?

      Yes, but you will need to know the largest possible error.

  13. Avatar
    Hans April 22, 2017 at 12:55 pm #

    I’m feeding your example with values ranged from 1 to 70.

    There is no increasing trend in my raw data.

    When it comes to predictions the script predicts values above 70.
    Regarding to the other tutorial (5 Step Life-Cycle) I think it has to do with the compile part (model.compile).
    But I’m not sure. Could you provide a comprehensible hint in regard of the example script on this site?

  14. Avatar
    Fabian April 23, 2017 at 10:33 am #

    Hi Jason,
    assuming you had multiple features (you can add one feature to the shampoo dataset) and wanted to use multiple timesteps, what would the dataset look like that I put into the model? Is it a 3 dimensional array, where the features are lists of values and each observation is a list of these features and the label(s) (which is also a list of values)?

    • Avatar
      Jason Brownlee April 24, 2017 at 5:31 am #

      Good question, it would be a 3D array with the dimensions [samples, timesteps, features].

  15. Avatar
    Rahul April 26, 2017 at 5:33 am #

    Right now the model gives only one step forecast. What if I wanted to create a model which gives forecast for next 60 months.

  16. Avatar
    Kunpeng Zhang April 27, 2017 at 1:07 am #

    Hi Jason, I have a question.
    raw_values = series.values
    diff_values = difference(raw_values, 1)
    print(len(raw_values)) 36
    print(len(diff_values)) 35

    So, after difference we lose the first value?

  17. Avatar
    Guido van Steen April 27, 2017 at 2:27 am #

    Dear Jason,

    Thank you very much for this extremely useful and interesting post.

    I may be missing something, but I think there is one omission: By differencing you loose the trend including its start and end level. Later on you try restore the trend again, but in your code it seems you fail to restore the end level. IMO the end level of the current observations should be added to all the predictions.

    Thanks again!

    • Avatar
      Jason Brownlee April 27, 2017 at 8:44 am #

      What do you mean by the end level? Sorry I don’t follow, perhaps you could restate your comment?

  18. Avatar
    Raul April 27, 2017 at 3:32 am #

    Great tutorial!
    Quick question: On the scaling section of the tutorial you say that

    “To make the experiment fair, the scaling coefficients (min and max) values must be calculated on the training dataset and applied to scale the test dataset and any forecasts. This is to avoid contaminating the experiment with knowledge from the test dataset, which might give the model a small edge.”

    However, if the max of your sample is on the test dataset the scaling with parameters from the training set will yield a number outside the [-1,1] range. How can one deal with that?


    • Avatar
      Jason Brownlee April 27, 2017 at 8:46 am #


      One good approach is to estimate the expected min and max values that are possible for the domain and use these to scale.

      If even then you see values out of range, you can clamp them to the bounds 0/1.

  19. Avatar
    Guido van Steen April 27, 2017 at 6:20 am #

    Dear Jason,

    To be more precise: you should add the difference between the start level and the end level of the train set. This is because the current code effectively replicates the train set. By this I means that it starts at the same level as the train set. However, it should start at the end level of the train set.

    Kind regards,


    • Avatar
      Guido van Steen April 27, 2017 at 3:11 pm #

      I will try to restate my comment:

      Currently the predictions (of your test set) start at the same level as the observations (in your train set). Therefore, there is a shift between the last observed value (in your train set) and the first predicted value (of your test set). The size of this shift is equal to: start level of the observations minus end level of the observations (in your train set). You should correct for this shift by adding it to the predicted values.

      • Avatar
        Jason Brownlee April 28, 2017 at 7:35 am #

        Isn’t this made moot by making the data stationary?

  20. Avatar
    Deeps April 28, 2017 at 4:59 am #


    1. can you please explain me the below 2 lines in detail.

    model.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape[1], X.shape[2]), stateful=True))

    2. I want to know the layer architecture. What are the number of neurons in hidden layer?
    3. If I want to add one more hidden layer, how the syntax looks like?
    4. What could be the reason for test rmse is less than train rmse?

  21. Avatar
    Fabio May 2, 2017 at 9:43 pm #

    Hallo Jason, thank you for this post! I bought the first version of your book and I have seen you have in the meantime deeper analysed this topic. Very good! 🙂 Something have I yet not clear.

    “Samples: These are independent observations from the domain, typically rows of data.
    Time steps: These are separate time steps of a given variable for a given observation.”

    I could understand the case where the time step parameter is 1 as in your book and in this example but I can’t figure out why and how it could be grater than 1…

    My hypothesys, sure wrong 🙂

    Perhaps when a timestep is made of n observations one could give the value n to it…but then I would expect when one in the model writes (pag. 192):

    “model.add(LSTM(4, input_shape=(1, look_back)))”

    the LSTM would use (look_back * timesteps) rows for every step to predict the next row…

    I cannot also understand why you say ‘of a given variable’…a row is normally built by the values of many variables, isn’t it?

    Could you give me an example with timesteps > 1? Thank you!

    • Avatar
      Jason Brownlee May 3, 2017 at 7:36 am #

      Hi Fabio,

      The structure of the input to the LSTM is [samples, timesteps, features]

      If you have multiple observations at one time step, then these are represented as features.

      Does that help?

      • Avatar
        Fabio May 7, 2017 at 10:28 pm #

        Hello Jason,

        unfortunately If don’t have a concrete example I cannot fully understand…The examples in your posts and your book are clear to me but they are always on timesteps=1…if I’m not wrong. For example how could be adapted the szenario described in this post in order to manage a timesteps>1?

        Thank you very much!

        PS. In the meantime I bought also your book on time series 🙂

  22. Avatar
    Nitin May 5, 2017 at 8:11 am #

    Thanks Jason for the wonderful tutorial!
    I am using your tutorial to apply LSTM network on some syslog/network log data.

    I have syslog data(a specific event) for each day for last 1 year and so I am using LSTM network for time series analysis.

    As I understand from your tutorial.
    1. A batch of data is a fixed-sized number of rows from the training dataset that defines how many patterns to process before updating the weights of the network. Based on the batch_size the Model takes random samples from the data for the analysis. For time series this is not desirable, hence the batch_size should always be 1.
    2. By default, the samples within an epoch are shuffled prior to being exposed to the network. This is undesirable for the LSTM because we want the network to build up state as it learns across the sequence of observations. We can disable the shuffling of samples by setting “shuffle” to “False“.

    Scenario1 –
    Using above two rules/guidelines – I ran several trials with different number of neurons, epoch size and different layers and got better results from the baseline model(persistence model).

    Without using above guidelines/rules – I ran several trials with different number of neurons, epoch size and different layers and got even better results than Scenario 1.

    Query – Setting shuffle to True and Batch_size values to 1 for time series. Is this a rule or a guideline?

    It seems logical reading your tutorial that the data for time series should not be shuffled as we do not want to change the sequence of data, but for my data the results are better if I let the data be shuffled.
    At the end what I think, what matters is how I get better predictions with my runs.
    I think I should try and put away “theory” over concrete evidence, such as metrics, elbows, RMSEs,etc.

    Kindly enlighten.

    • Avatar
      Jason Brownlee May 5, 2017 at 11:25 am #

      Random samples are not taken, LSTMs require sequence data to be ordered – they learn order dependence.

      The “shuffle” argument must be set to “False” on sequence prediction problems if sequence data is spread across samples.

  23. Avatar
    Masum May 7, 2017 at 12:44 am #

    Dear Jason,

    I have two hours time series data which consists of 120 observations, using LSTM RNN how can I predict next 30 observation while putting all my data to training section.

    We normally split the original data set in two data set ( test dataset and validation dataset) for checking our model performance. I would like to see that my model is only taking help from training dataset to produce an output that does match with validation data set. What I understand from several of your blogs that we are forecasting single value and using that single forecasting along with the help of validation dataset we are forecasting rest of values. I believe I getting lost there? How it is going to work when have only past and current data ( suppose no validation data) and we want to predict the next half an hour.

    For example, suppose I have data of a product price from 12 to 1:30pm which consists of 90 observations and using these past 90 observations can we forecast the price of that product during 1:31 to 2:00pm(otherwise next 30 observations) .

    Would you please help me to solve the confusion that I have? By the way I am going through your books time series forecasting with Python and deep learning with Python.

  24. Avatar
    masum May 7, 2017 at 5:57 am #

    Thanks for quick replay

    Looks like you sleep very less as you have provided feedback on early morning from your site.

    Thanks for being so kind to your students. May god bless you.

    By the way do you have any blog or example for second option that you have provided me(use the same model again and again and use predictions as inputs for subsequent predictions). Obviously I would like to see that I am not using any data from validation dataset or not getting any feedback from validation data. Model should only from past and current data along with current predictions. I hope you got this confused student.

    Thanking you

    • Avatar
      Jason Brownlee May 8, 2017 at 7:41 am #

      Sorry, I don’t have an example of using the model recursively. I believe you could adapt the above example.

      • Avatar
        masum May 9, 2017 at 9:10 am #

        would you please give me some hint where I have to change the code to make the model recursive as I am not very good at coding.

        • Avatar
          Jason Brownlee May 10, 2017 at 8:36 am #

          Predictions would be used as history (input) to make predictions on the subsequent time steps.

  25. Avatar
    Max May 9, 2017 at 11:10 am #

    Thanks Jason for the wonderful tutorial!
    A little problem here:

    def invert_scale(scaler, X, value):
    new_row = [x for x in X] + [yhat]

    Does it should be

    def invert_scale(scaler, X, value):
    new_row = [x for x in X] + [value]

  26. Avatar
    Charlie May 17, 2017 at 4:08 am #

    I’m getting the following error when running the first block of code you provide.

    TypeError: strptime() argument 1 must be str, not numpy.ndarray

    It seems like this a problem with how Python 3.6 handles byte strings.

    • Avatar
      Jason Brownlee May 17, 2017 at 8:42 am #

      I have only tested the code on Python 2.7 and Python 3.5, perhaps try one of those?

      Otherwise, you may need to adapt the example for your specific platform, if an API change is indeed the cause of your issue.

    • Avatar
      Sabih November 8, 2017 at 6:47 am #

      The issue was with the text in footer ‘Sales of shampoo over a three year period’.

      Either delete the footer OR

      Change the line:

      series = read_csv(‘shampoo-sales.csv’, header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)


      series = read_csv(‘shampoo-sales.csv’, header=0, parse_dates=[0], index_col=0, squeeze=True, date_parser=parser, skipfooter=2)

    • Avatar
      John Strong November 23, 2017 at 2:48 am #

      I think that error is caused by the line of descriptive text at the bottom of the shampoo sales data file. If you see this comment at the bottom of the data file, remove it:

      Sales of shampoo over a three year period

      The data file also has the dates enclosed in double quotes. A couple of times that bit me too. The date_parser callback is a little fickle.

  27. Avatar
    Logan May 18, 2017 at 10:28 am #

    Hello, Your examples are great, thanks.

    I have a question:

    1- What do we do with the array of predicted values when we use lstm_model.predict() with train data in the example? It seems like they are not being used. Is it important for the net?

    • Avatar
      Jason Brownlee May 19, 2017 at 8:10 am #

      Thanks Logan.

      What do you mean exactly? Is there a specific section and line of code you are referring to in the tutorial?

      • Avatar
        Logan May 27, 2017 at 2:47 am #

        Yes, line 101 lstm_model.predict(train_reshaped, batch_size=1) on section Complete LSTM Example.

        By the way, I have another question: When the differentiation is applied to the entire dataset, isn’t it giving information about the test dataset to the model?

        Thanks. You’ve been helping me a lot.

        • Avatar
          Jason Brownlee June 2, 2017 at 11:58 am #

          In this case yes, but in practice, we can apply the same method to the test data using data from training step-wise without cheating.

          • Avatar
            Long June 13, 2018 at 10:14 pm #

            Hi Jason, I’m also having the same question as Logan mentioned above. Line 101
            lstm_model.predict(train_reshaped, batch_size=1)
            do we need this line.
            I comment this line, and I see no difference. Could you explain a bit more why we need this line ?
            Thank you for the great tutor.
            Best, Long

          • Avatar
            Jason Brownlee June 14, 2018 at 6:07 am #

            It is supposed to seed the state on the training data.

            If it does not add value, remove it.

  28. Avatar
    Brandon May 19, 2017 at 12:34 pm #

    Hi Jason,

    Thanks so much for this helpful tutorial. Could you clarify which of all the parameters need to be updated to change the lag value? I haven’t been able to get it to work.


    • Avatar
      Jason Brownlee May 20, 2017 at 5:34 am #

      Great question.

      Change the parameters to the timeseries_to_supervised() function

      • Avatar
        John Strong February 10, 2018 at 9:28 am #

        I had to change the limits of the range() function to get the loop to work for lag values > 1.

        def timeseries_to_supervised(data, lag=1):
        df = DataFrame(data)
        columns = [df.shift(i) for i in range(lag, 0, -1)]
        df = concat(columns, axis=1)
        df.fillna(0, inplace=True)
        return df

  29. Avatar
    Nirikshith May 29, 2017 at 8:23 pm #

    Hi Jason,

    I have been following you for quite sometime now. Another great example for time series. I remember trying out sliding window approach in one of the earlier blogs. I am still waiting for you to write up a blog on involving external features(it can be as simple as (is_weekday =0/1 is_weekend=0/1) and see how its implemented.

    can you point out where we can add the above external variables in the above example and the format please for these features please. I will try it out. being new to python its very confusing with these reshapes and pre -format required for LSTM s

    #aspring data scientist, student

    • Avatar
      Jason Brownlee June 2, 2017 at 12:25 pm #

      You can add them as separate features.

      I am working on an example at the moment. I hope to post it when it gives good results.

  30. Avatar
    Donato June 1, 2017 at 10:00 pm #

    Hi Jason, nice example! I have your similar problem, but I don’t know how resolve. I have a two different class to predict, in different files. I have to training my neural network with this different files. The problem is that each file has different number of samples, and I have to use the same LSTM for each file.How I can generalize the number of input for each LSTM??
    This is my problem:

  31. Avatar
    Pengyuan Shao June 8, 2017 at 10:02 pm #

    Dear Jason:
    You did a great job!!
    Thank you for sharing the great post with us.
    I’m a beginner to machine learning, these days i am busy on doing a project to predict the movement of ship on the sea.
    I found this post is very usefull and easy to understand.
    I have one question that:
    if the number of neurons is the past steps used to predict next step?
    Thank you for answer in advance.

    Best wishes

    • Avatar
      Jason Brownlee June 9, 2017 at 6:24 am #

      I’m not sure what you mean.

      The number of neurons defines the size/complexity of the model. The model is used to make predictions.

      Perhaps you could reframe your question?

  32. Avatar
    Macarena June 10, 2017 at 7:19 pm #

    Congrats for the blog, and thanks! It helped me a lot.
    I have one question related to the data transformation. I understand the step to make that one input is the last output, so the LSTM can learn and save that info. But I have a different case (classification) and I don’t know how could I apply this.
    In my case my inputs are images (frames from a video) what have a temporal dependency, and my outputs are numbers (0,1 or 2). First I want to pass the images through a CNN network and then take the features and those would be my LSTM input. In that case, it is necessary to process the data as you have done here? I thought the LSTM would save that info by itself, but now I’m not so sure.

    Thank you in advance.

    • Avatar
      Jason Brownlee June 11, 2017 at 8:23 am #

      I don’t have an example of working with video data.

      Generally, the principles would be the same. As a classification problem, you would need to change the output layer to use one of the log loss activation functions. The input would be from a CNN or similar, e.g. [cnn]->[lstm]->[dense].

      Let me know how you go.

    • Avatar
      Phil June 22, 2021 at 1:51 pm #

      Hey did you ever get this working I have a similar problem I would like to address and would value your input!!

  33. Avatar
    Kim Miller June 15, 2017 at 6:14 am #

    In your ARIMA tutorial you also use the shampoo data set, but measure accuracy by MSE. Making the change to RMSE:

    rmse = sqrt(mean_squared_error(test, predictions))
    print('Test RMSE: %.3f' % rmse)

    I get:

    > Test RMSE: 83.417

    Can we conclude that ARIMA is far better than an LSTM for this problem so far in our research?

    • Avatar
      Jason Brownlee June 15, 2017 at 8:55 am #

      No, these are demonstrations. Both algorithms would require tuning to present the best version of themselves (“steel man” vs “straw man”) for model selection.

  34. Avatar
    Kim Miller June 15, 2017 at 12:28 pm #

    We are writing the timeseries_to_supervised function to accept a lag:

    def timeseries_to_supervised(data, lag=1):

    Is this feature to essentially the Window Method + reshaping described in your July 21, 2016 tutorial?

    But we don’t seem to use that parameter, always “timeseries_to_supervised(diff_values, 1)”

    Using lag values up to around 50 (on the airline data) and changing predict() like so:

    # forecast the entire training dataset to build up state for forecasting
    train_reshaped = train_scaled[:, 0:look_back].reshape(len(train_scaled), 1, look_back)
    # train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
    lstm_model.predict(train_reshaped, batch_size=1)

    seems to make good predictions with very low RMSE on test.

    Am I possibly breaking the model now so it’s cheating somehow?

    • Avatar
      Kim Miller June 16, 2017 at 5:27 am #

      look_back = 60
      epochs = 15

      Month=1, Predicted=321.813110, Expected=315.000000
      Month=2, Predicted=310.719757, Expected=301.000000
      Month=3, Predicted=363.746643, Expected=356.000000
      Month=46, Predicted=458.424683, Expected=461.000000
      Month=47, Predicted=418.427124, Expected=390.000000
      Month=48, Predicted=412.831085, Expected=432.000000
      Test RMSE: 18.078

      for test harness

      yhat = y
      Test RMSE: 0.000

      It seems there is contamination of training data in the test forecast in the sense that forecast_lstm(model, batch_size, X) is being given X observations, each with 60 historical past observations that overlap into training data. But so what, right? That’s history that training saw, and as it moves into the test data it adds history only seen in the test set. But that’s how real life observations work it seems: You always have all of the past to look at.

      Finally, you say, “In this tutorial, we will go with the fixed approach for its simplicity, although, we would expect the dynamic approach to result in better model skill.” For a small dataset like we have, a large lag seems as if it gives us a semi-dynamic approach in some ways?

      Solid model with a seemingly good RMSE?
      Full code: http://tinyurl.com/y74ypvde
      Prediction v. Actual Plot: http://tinyurl.com/y9ouajdm

  35. Avatar
    Pedro June 15, 2017 at 5:22 pm #

    Hi Jason,

    You’re doing a great job helping people to learn how to apply machine learning. One week ago, I didn’t know anything about time series, but now I’m able to play a little bit with it. Thanks you!

    Regarding this post, I’ve a doubt. When we say

    ‘To make the experiment fair, the scaling coefficients (min and max) values must be calculated on the training dataset and applied to scale the test dataset and any forecasts. This is to avoid contaminating the experiment with knowledge from the test dataset, which might give the model a small edge.’

    shouldn’t we do

    scaler = scaler.fit(X[:-12])

    instead of

    scaler = scaler.fit(X) ?

    If we use X we are using data from the test set, no?

    Thanks for your attention and keep up with the good work!

    • Avatar
      Jason Brownlee June 16, 2017 at 7:51 am #

      Correct. Ideally, we would use domain knowledge to estimate the expected min/max of values that could ever be observed.

  36. Avatar
    Eric June 20, 2017 at 6:57 pm #

    Hello Jason,

    After using the robust code (last one) I got theses results

    1) Test RMSE: 180.438
    2) Test RMSE: 110.352
    3) Test RMSE: 119.655
    4) Test RMSE: 170.720
    5) Test RMSE: 211.877
    6) Test RMSE: 101.453
    7) Test RMSE: 105.532
    8) Test RMSE: 149.351
    9) Test RMSE: 88.118
    10) Test RMSE: 138.013
    11) Test RMSE: 265.045
    12) Test RMSE: 135.861
    13) Test RMSE: 167.766 … (rest is omitted, it was taking too long).
    Being a beginner in machine learning and using your tutorial to learn about it could you tell me if theses results are normal (being so different from what you have) while everything before was ok. If theses are not, could you tell my what could be the reason of such difference?

    Thank you for your attention and please do continue making tutorial like that, it’s really helpful!

  37. Avatar
    Dhineshkumar June 30, 2017 at 7:18 pm #

    Hi Jason,

    Thank you so much for the tutorial.

    I have few doubts though.

    1. I am working on a problem where the autocorrelation plot of the detrended data show me that the value at time t is significantly correlated to around past 100 values in the series. Is it ideal to take the batch size of 100 to model the series?

    2. You mentioned that less than 5 memory units is sufficient for this example. Can you please give me some idea on how to choose the number of memory units for a particular problem like the above? On what other factors does this number depend on?

    Kindly clarify.

    • Avatar
      Jason Brownlee July 1, 2017 at 6:33 am #

      Try passing in 100-200 time steps and see how you go.

      Systematically test a suite of different memory units to see what works best.

  38. Avatar
    Sophie July 4, 2017 at 3:04 pm #

    Hey Jason! Thanks a lot for this tutorial, it really helped.

    I used this tutorial as is for predicting the cost of an item which is of the the range of a dollar and few cents.

    My dataset has 262 rows, i.e 0 to 261.

    When I run the model, the graph captures even the most intricate trends beautifully, BUT there seems to be a lag of 1 time step in the predicted data.

    The predicted values of this month almost exactly matches the expected value of the previous month. And this trend is followed throughout.

    The indexing is the only thing I’ve changed,

    train, test = supervised_values[0:200], supervised_values[200:]
    rmse = sqrt(mean_squared_error(raw_values[200:], predictions))

    are the only lines of code I’ve really changed

  39. Avatar
    Viorel Emilian Teodorescu July 9, 2017 at 2:09 am #

    Hi, Jason

    Doesn’t LSTM have a squashing gate at input? With outputs in between (-1, 1)? Then why do we need to prepare the input data to be between (-1, 1) if the first input gate will do this for us?

    Am I missing something?

  40. Avatar
    Hans July 9, 2017 at 2:58 am #


    unseenPredict = lstm_model.predict(X)

    …how do we structure X to get a one step forward prediction of unseen data?

    Or can we change some offsets in script “Complete LSTM Example” to get the same effect, and if so how?

  41. Avatar
    Paba July 10, 2017 at 8:45 pm #

    Hi Jason,
    Thanks for the excellent tutorial. I tried to modify the above code to include multiple timesteps and multiple lags in the model. I run give these parameters as input and paralleling run the script for different configurations to select the most accurate model. What do you think of the modifications I have done to the following functions? I am especially concerned about the time_steps included in the model, is that correct?

    def timeseries_to_supervised(data, lag=1, time_steps=0):
    df = DataFrame(data)
    columns = [df.shift(i) for i in range(1, lag+1)]
    #considers the number of time_steps, t, involved and
    #add next t x columns next to each x columnn
    #question?? if time_steps = 3, does that mean y should start from y_4 and
    #we trim the last 3 values from the dataset?
    if time_steps > 0 :
    columns_df = concat(columns,axis=1)
    #note that I have multipled i by -1 to perform left shift rather than right shift
    timestep_columns = [columns_df.shift(i*-1) for i in range(1, time_steps+1)]
    timestep_columns_df =concat(timestep_columns, axis=1)
    df = concat(columns, axis=1)
    df.fillna(0, inplace=True)
    return df

    def fit_lstm(train, batch_size, nb_epoch, neurons, lag, time_steps):
    X, y = train[:, 0:-1], train[:, -1]
    X = X.reshape(X.shape[0], time_steps+1, lag)
    model = Sequential()
    model.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape[1] , X.shape[2]), stateful=True, return_sequences=True))
    model.add(LSTM(neurons, stateful=True))
    model.compile(loss=’mean_squared_error’ optimizer=’adam’)
    for i in range(nb_epoch):
    model.fit(X, y, epochs=1, batch_size=batch_size, verbose=1, shuffle=False)
    return model

    def forecast_lstm(model, batch_size, X, lag,time_steps):

    X = X.reshape(1,time_steps+1,lag)
    pad = np.zeros(shape=(batch_size-1, time_steps+1, lag))
    padded = np.vstack((X, pad))
    yhat = model.predict(padded, batch_size=batch_size)
    return yhat[0,0]

  42. Avatar
    Kim Miller July 13, 2017 at 9:01 am #

    I want to extend this idea to several features x the lag values for each x time observations. Does it seem reasonable to give MinMaxScaler that 3D object? How does the y truth fit in what I give MinMaxScaler, since it’s only 2D?

    • Avatar
      Jason Brownlee July 13, 2017 at 10:04 am #

      No, I would recommend scaling each series separately.

      • Avatar
        Kim Miller July 13, 2017 at 11:51 am #

        Above you seem to scale y along with X. But with multiple features, the rest of which are not just a time-shifted copy of y, I assume we could fit y_train by itself before transforming y_train and y_val? Then that’s actually the only scaler object we need to save for later inversion?

        • Avatar
          Jason Brownlee July 13, 2017 at 4:58 pm #

          I would recommend scaling each series before any shifting of the series to make it a supervised learning problem.

          I hope that answers your question, please shout if I misunderstood.

          • Avatar
            Kim Miller July 14, 2017 at 2:17 am #

            I think the words “each series separately” threw me. I assume we can still scale all incoming values (all X’s and the time series that will later become y and shifted, one of the X’s) using a single scaler object. Then we create the lag values from scaled values. Finally, that single scaler object is used to invert y predictions. I have that right?

          • Avatar
            Jason Brownlee July 14, 2017 at 8:33 am #

            Each series being a different “feature” or “column” or “time series” or whatever we call it.

            The coefficients (min/max or mean/stdev) used in the scaling of each series will need to be kept to reverse the operation on predictions and apply the operation to input data later. You can save the coefficients or the objects that wrap them.

  43. Avatar
    Sasha July 13, 2017 at 4:15 pm #

    Jason, great tutorial, thank you!

    A question: why do you loop through epochs instead of just setting an appropriate number of epochs within fit() function? Would’t it give the same result and be neater?

  44. Avatar
    kotb July 13, 2017 at 6:59 pm #

    Hi, DR jason

    thank you very much for this tutorial.

    I want to have multiple time steps , but i don’t know how to modify function “timeseries_to_supervised()”.
    I found another post of you talking about this , but you use function “create_dataset()”
    i modify this function as follow:

    def create_dataset(dataset, look_back=1):
    dataset = np.insert(dataset,[0]*look_back,0)
    dataX, dataY = [], []
    for i in range(len(dataset)-look_back):
    a = dataset[i:(i+look_back)]
    dataY.append(dataset[i + look_back])
    dataY = np.reshape(dataY,(dataY.shape[0],1))
    dataset = np.concatenate((dataX,dataY),axis=1)
    return dataset

    please, check my modification , is it right OR what?

  45. Avatar
    Eric July 20, 2017 at 2:22 pm #

    Hi Jason,

    Sorry if it seem stupid but there is a part that I don’t understand.

    To predict you use: “yhat = model.predict(X, batch_size=batch_size)”
    But as we see X is :
    train, test = supervised_values[0:-12], supervised_values[-12:]
    scaler, train_scaled, test_scaled = scale(train, test)
    yhat = forecast_lstm(lstm_model, 1, X)

    So X is the 12 value (after being passed in the scale function) that we want to predict. Why are we using them since in normal case we wouldn’t know theirs values.

    Once again really thank you for your tutorial, really helped me in my training on machine learning.

    • Avatar
      Jason Brownlee July 21, 2017 at 9:29 am #

      In the general case, you can pass in whatever you like in order to make a prediction.

      For example, if your model was defined by taking 6 days of values and predicting the next day and you want to predict tomorrow, pass in the values for today and 5 days prior.

      Does that help?

      • Avatar
        Eric July 21, 2017 at 10:48 am #

        I think it does help me. In my case I have values for each minute and I have to predict the next week (so more or less 10K of prediction).
        I have data from the last year so there isn’t any problem with my training, just wondered what I should do at the prediction part (so I can just instead of feeding it test_scaled send him my training set again?)
        Thank you for your help and quick reply!

        • Avatar
          Jason Brownlee July 22, 2017 at 8:29 am #

          Yes, if your model is setup to predict given some fixed set of lags, you must provide those lags to predict beyond the end of the dataset. These may be part of your training dataset.

          • Avatar
            Eric July 24, 2017 at 5:55 pm #

            I don’t think it’s in my training dataset, for this part I’m pretty much doing it like you (the lag appearing when turning a sequence to a supervised learning problem). I’m pretty much feeding my model like you do. The problem for me being to know what to feed it when calling the predict command. Sending it “train_scaled” was a bad idea (got poor result, predicting huge value when it should predict low and predicting low instead of predicting high). I’m working on it but every hint is accepted. Once again thank you and sorry for being a bit slow at learning/understanding.

          • Avatar
            Jason Brownlee July 25, 2017 at 9:36 am #

            The argument to the predict() function is the same as the argument to the fit() function.

            The data must be scaled the same and have the same shape, although the number of samples may vary, e.g. you may have just one sample.

            Obviously, you don’t need to make predictions for the training data, so the data passed to predict will be the input required to make the prediction you require. This really depends on the framing of your problem/model.

            Does that help?

          • Avatar
            Eric July 25, 2017 at 12:09 pm #

            Thank your for your quick reply! I think I’m understanding it better but I have some part I have trouble to understand.

            The input is X right?
            If I follow your tutorial on input/output (https://machinelearningmastery.com/time-series-forecasting-supervised-learning/) and I take my case as an example (the database register the value each 3 minute and we want to predict the next value (so to begin for example it would be 12:24:00)):
            2016-07-08 12:12:00,92
            2016-07-08 12:15:00,80
            2016-07-08 12:18:00,92
            2016-07-08 12:21:00,86

            This is (part of) my training data, when turning it into supervised training data (and shifting) I get:
            X, y
            ?, 92
            92, 80
            80, 92
            92, 86
            86, ?

            The problem is that I don’t know X for predicting, I only know the X I use for my training (train_scaled) and the one used to compare my results (test_scaled).

            What is the input I should feed it? I can’t feed it my test_scaled since in real situation I would have no idea of what it would be.

            Sorry if my question seem stupid and thank you for taking time to explain it.

          • Avatar
            Jason Brownlee July 26, 2017 at 7:45 am #

            It depends how you have framed your model.

            If the input (X) is the observation at t-1 to predict t, then you input the last observation to predict the next time step.

          • Avatar
            Eric July 26, 2017 at 11:49 am #

            It is, each of my input X is the observation at t-1 (pretty similar to the shampoo case used in the tutorial).

            Thank you for your answer, you answered my question, I shouldn’t have any problem now!

            Thanks for the tutorial too, they really helped me!

          • Avatar
            Jason Brownlee July 26, 2017 at 4:01 pm #

            Glad to hear that.

          • Avatar
            Eric July 26, 2017 at 6:49 pm #

            Just to be sure that I didn’t made any mistake in my reasoning, if I take my example from before:
            X, y
            ?, 92 / T-3
            92, 80 / T-2
            80, 92 / T-1
            92, 86 / T
            86, ? / T+1

            to predict the next step (T+1) I have to use “yhat = model.predict(X, , batch_size=batch_size)” where X is 86 (after scaling/reshaping). Right?
            Then I’ll get the value predicted for T+1 (that I have to send to invert_scale and difference to get a readable value).
            If I want to predict farther then I continue (sending the scaled/reshaped value predicted at T+1 to get T+2 and then until I predict as far as wanted).

            Thanks for your time and answers!

          • Avatar
            Jason Brownlee July 27, 2017 at 7:58 am #


          • Avatar
            Eric August 4, 2017 at 12:05 pm #

            Thank you Jason with your help I managed to predict value of each minute of the next week. I had 2 question though:
            First: I removed the code for testing sets (since I wouldn’t have it in reality), the only thing I have are the testing set in the excel file (the last 10000 lines)
            When using this code (to train):
            # transform data to be stationary
            raw_values = data.values
            diff_values = difference(raw_values, 1)

            # transform data to be supervised learning
            supervised = timeseries_to_supervised(diff_values, 1)
            supervised_values = supervised.values

            # split data into train and test-sets
            train = supervised_values[:-10000]

            # transform the scale of the data
            scaler, train_scaled = scale(train)

            and this one (to predict):
            # forecast the entire training dataset to build up state for forecasting
            train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)

            # walk-forward validation on the test data
            predictions = list()
            predictionFeeder = list() #Used to feed the model with the value of T-1
            X, y = train_scaled[0, 0:-1], train_scaled[0, -1]
            predictionFeeder.append(X) #Give the last value of training

            for i in range(0, 10000):
            # make one-step forecast
            yhat = forecast_lstm2(lstm_model, predictionFeeder[i])
            # invert scaling
            yhat2 = invert_scale(scaler, testa[i + 1], yhat)
            yhat3 = inverse_difference(raw_values, yhat2, 10000 + 1 – i)
            and train a model (25 epoch) then predict the results I get result that are way too good (RMSE of 2 or less and prediction that have less than 5% of error).
            Being used of thing going wrong for no reasons I decide to remove the testing data from the excel (even though it shouldn’t change anything since I’m not using them (I’ve even set the variable to None at first)). Then when I do that the prediction is way less good and have some lag (though, if you remove the lag you still have a good results, just way less better than before).
            Why is that?
            My 2nd question is about lag, we can see on the prediction that while the shape of both chart (prediction and reality) look alike the prediction is raising/lowering before the reality, do you have any idea to fix it? Do you think changing the lag or timestep would help?

            Once again thank you for your help, I don’t think I would have achieved this much without your tutorials.

          • Avatar
            Jason Brownlee August 4, 2017 at 3:43 pm #

            Sorry, I cannot debug your code for you.

            Perhaps you are accidentally fitting the model on the training and test data then evaluating it on the test (e.g. on data it has seen before).

            I would encourage you to evaluate different lag values to see what works best for your problem.

          • Avatar
            Eric August 4, 2017 at 4:02 pm #

            Don’t worry, I wouldn’t ask you to debug.

            Maybe, I don’t know, I did remove the variable to be sure to never have affected the testing set and using it but since I’m human I may have made errors.

            So changing lag would help me for theses gap between reality and prediction raise. Thank you I’ll do that.

            Thanks for your answer!

  46. Avatar
    Josep July 21, 2017 at 8:08 pm #

    Can I buy your books physically(not Ebook)?Thanks

    • Avatar
      Josep July 21, 2017 at 8:15 pm #

      Sorry, now I have read that is not possible. Thanks anyway. Your explanations and tutorials are amazing. Congratulations!

  47. Avatar
    Pawel July 26, 2017 at 7:59 pm #

    Thanks for very good tutorial. I have one question/doubt.

    in the following part of the code:

    # invert differencing
    yhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i)

    should not we relay on predicted value instead of already known raw_values? In your example for validation we always refer to the test value(known) while calling inverse difference. But in reality we will have only the predicted values(used as X), and of course known starting point(t=0). Or I missed something?

    my proposal:
    # invert differencing – (starting from 2nd loop cycle (1st woul be the starting point (raw_values[-1]) )

    yhat = inverse_difference(predictions, yhat, 1)

    Thanks in advance

    • Avatar
      Jason Brownlee July 27, 2017 at 8:00 am #

      We could, but in this case the known observations are available and not in the future and it is reasonable to use them for the rescaling (inverting).

      • Avatar
        Pawel July 27, 2017 at 5:03 pm #

        Hi, Thanks for explanation, got it now. Cause I train the model used e.g. MAY data (15 seconds samples) and then used that model to predict whole JUNE data. Afterwards I compared predicted data VS data that I got from JUNE, and I have to say that model does not work, after few prediction there is huge “off sync”,

        In the validation phase as described in your case I got RMSE 0.11 so not bad, but in reality when you use predicted value(t-1) to predict next (t) value there is a problem.

        Do you know how to improve the model? should I use multiple step forecats, or lag features, input time steps?

        Thanks a lot.

  48. Avatar
    Surya July 27, 2017 at 6:49 pm #

    Hey Jason, I am not following one point in your post. You wanted to train a state-full LSTM but reset_states() is executed after every epoch. That means, the states from previous batch are not used in the current batch. How does it make the network state-full?


    • Avatar
      Jason Brownlee July 28, 2017 at 8:30 am #

      State is maintained between the samples within one epoch.

  49. Avatar
    Niklas August 2, 2017 at 12:03 am #

    Hi Jason,

    thanks for the great tutorial. I have one question. Wouldn’t it be better to use a callback for resetting the states? This would enable you to also use for example an EarlyStopping Monitor while training, here is what I changed:
    class resetStates(Callback):
    def on_epoch_end(self, epoch, logs=None):

    model.fit(X, y, epochs=nb_epoch, batch_size=batch_size, verbose=1, shuffle=False, callbacks=[resetStates(),EarlyStopping(monitor=’loss’, patience=5, verbose=1, mode=’min’)])

    • Avatar
      Jason Brownlee August 2, 2017 at 7:54 am #

      Yes, that is a cleaner implementation for those problems that need to reset state at the end of each epoch.

  50. Avatar
    Bharath August 6, 2017 at 2:38 am #

    Hello, can we extend this for anomaly detection techniques ?

    • Avatar
      Jason Brownlee August 6, 2017 at 7:40 am #

      Perhaps, I have not used LSTMs for anomaly detection, I cannot give you good advice.

      Perhaps you would frame it as sequence classification?

  51. Avatar
    Daniel Ruiz August 7, 2017 at 1:36 pm #

    Hi Jason,

    In the persistence model plot there is a one time interval lag. When making single step predictions, is it possible to overcome this issue? What is causing this to happen? It seems like the model places a huge weight on time interval x[t-1].
    Here is an example of the dataset I am analyzing:

    iteration: 969
    Month=970, Predicted=-7.344685, Expected=280.000000
    iteration: 970
    Month=971, Predicted=73.259611, Expected=212.000000
    iteration: 971
    Month=972, Predicted=137.053028, Expected=0.000000

    Expected should be 280 and 212 (high magnitudes), and the model captures this more or less with 73 and 137, but this is one time interval behind.


    • Avatar
      Jason Brownlee August 8, 2017 at 7:41 am #

      LSTMs are not great at autoregression problems and often converge to a persistence type model.

      • Avatar
        Daniel Ruiz August 8, 2017 at 8:57 am #

        Ok thanks. What model would be a good alternative to capture this issue? I ran into the same problem with ARIMA. It could just be a difficult dataset to predict.

        • Avatar
          Jason Brownlee August 8, 2017 at 5:07 pm #

          I recommend starting with a well-tuned MLP + Window and see if anything can do better.

  52. Avatar
    Eric August 9, 2017 at 11:02 am #

    Hi Jason,

    Thanks to you I managed to get a working LSTM network who seem to have a good accuracy (and so a low RMSE)

    But I’ve got a problem, do you know what could be the cause of extreme delay between reality values and predictions (my predictions have the same shape as the reality but increase/decrease way before reality)?

    Best regards and please continue what you are doing, it’s really useful.

    • Avatar
      Jason Brownlee August 10, 2017 at 6:40 am #

      Hi Eric, it might be a bug in the way you are evaluating the model.

      • Avatar
        Eric August 10, 2017 at 10:50 am #

        It might be the case, I had to make some changes to the prediction system to use the last predicted value, I may have missed something at this moment. (Also I have to use Tflearn instead of Tensorflow but it shouldn’t be a problem since Tflearn is a more transparent way to use tensorflow).

        Thank you for your answer!

        • Avatar
          Jason Brownlee August 10, 2017 at 4:40 pm #

          Hang in there Eric!

          • Avatar
            Eric August 10, 2017 at 5:10 pm #

            Thank you!

            Well.. I have a gap of 151 (reference to pokemon?).

            Just to try I removed theses 151 values from my training set, I now have no gap of values (and frankly, the accuracy seem good for a 15 epoch training). I know that this is no way a fix but make me wonder where did I fail..

          • Avatar
            Eric August 10, 2017 at 7:21 pm #

            Could it be that while my training set is on 400K of value my prediction start 151 value before the end (so predicting the value for 399849) of the training set (which is strange since the information from training tell me that I’m training on the 400K of data).
            It would mean that my machine is trying to predict some point of time used for training.
            Or it would mean that the 151 last data weren’t used at all for training (I tried to reduce the number of data but it’s the same problem).

          • Avatar
            Jason Brownlee August 11, 2017 at 6:41 am #

            The algorithm is trained sample by sample, batch by batch, epoch by epoch. The last sample is what is key.

          • Avatar
            Eric August 11, 2017 at 12:24 pm #

            Thanks for the reply.
            When I think about it my prediction is in advance compared to the reality.
            So my model start his prediction not where I finished my training but after (which is strange since my training end where my testing begin and that each input are a value (and each line correspond to a minute like the the line of shampoo data sets correspond to month)).
            I must have made a mistake somewhere.
            Thanks for you answer I think I’m on something!

          • Avatar
            Jason Brownlee August 12, 2017 at 6:45 am #

            Hang in there!

  53. Avatar
    Stone August 9, 2017 at 12:16 pm #

    One thing I don’t understand in these models is, how can I predict future.

    Say, I have trained my model and let’s say we’re living August 8, 2017. Now model.predict() seems to require some test samples to predict anything, in this case values from test_scaled. So what do I give it when I want to get a prediction for August 9, 2017, which we don’t know yet? So I want to know yhat(t+1). Can I ask the model to give me forecasts for the next 5 days?

    • Avatar
      Eric August 9, 2017 at 2:11 pm #

      I may be wrong but in my case I trained my model on the data I had (let’s say one year, until August 8, 2017) and to predict the value T you send the value T-1 (so in this case the value of August 8 2017), you’ll get the value of August 9.
      Then if you want August 10 (T+1) you send the value of August 9 (T). But this code here show a one step forecast implementation. Maybe if you want to predict more you should look for multi step forecasting? I’m think there is some example of it on this website.

      Jason would give you a better answer I think.

      • Avatar
        Jason Brownlee August 10, 2017 at 6:47 am #

        Nice one Eric!

        Yes, I’ll add, if the model was trained to predict one day from the prior day as input, then when finalized, the model will need the observation from the prior day in order to predict the next day.

        It all comes down to how you frame the prediction problem that determines what the inputs you need.

    • Avatar
      Jason Brownlee August 10, 2017 at 6:43 am #

      If you would like to predict one day, the model needs to be trained to predict one day.

      You have to decide what the model will take as input in order to make that prediction, e.g. the last month or year of data. This is how the model is trained.

      Then, when it’s trained, you can use it to predict future values using perhaps the last few values from the training data. You can use a model trained to predict one day to predict may days in a recursive manner where predictions become inputs for subsequent predictions. More about that here:

      You can also make multi-step forecasts directly, here is an example:

      Does that make things clearer?

  54. Avatar
    Stone August 10, 2017 at 11:08 am #

    Thanks Eric and Jason. That’s exactly how I’ve done it, but it seems to me, that the prediction that I get is not one timestep forward (T+1), but it’s a prediction of T, which doesn’t make sense. I’m using close price of a stock as my data. I’ll have to check again, if it’s really is making a prediction for the future, as you insist. and I will check the Jason’s links.

    Anyways, thanks Jason for the excellent tutorials! 🙂

    • Avatar
      Stone August 10, 2017 at 12:22 pm #

      Here’s a sample of the close prices:
      2017-05-30 5.660
      2017-05-31 5.645
      2017-06-01 5.795
      2017-06-02 5.830

      As a matter of fact, it seems to me that the predicted values lags one time step behind from expected ones.

      Day=1, Predicted=5.705567, Expected=5.660000
      Day=1, Predicted=5.671651, Expected=5.645000
      Day=1, Predicted=5.657278, Expected=5.795000
      Day=1, Predicted=5.805318, Expected=5.830000

      Here I’m going forwarding one day at a time and as you see the predicted ones are closer to what was expected one day before than. And anyway,

      Let’s examine the second line:
      Day=1, Predicted=5.671651, Expected=5.645000

      The expected price (which is the actual price on 2017-05-31) is what I give the model on 2017-05-31 after the trading day is closed. What I expect the model to predict is closer to 5.79 than 5.67 (which is closer to the actual price the day before!). See the problem? Have I missed something? I haven’t changed anything in the framework except the data.

    • Avatar
      Jason Brownlee August 10, 2017 at 4:41 pm #

      That is a persistence model and the algorithm will converge to that (e.g. predict the input as the output) if it cannot do better.

      Perhaps explore tuning the algorithm.

      Also, I believe security prices are a random walk and persistence is the best we can do anyway:

  55. Avatar
    Firnas August 12, 2017 at 1:27 pm #

    Please do some tutorials RNN, NN with more categorical values in the dataset? please, I could not find many resources using the categorical values.


    • Avatar
      Jason Brownlee August 13, 2017 at 9:45 am #

      I have a few tutorials on the blog – for example, text data input or output are categorical variables.

      What are you looking for exactly?

  56. Avatar
    nandini August 16, 2017 at 5:23 pm #

    is it possible to write the code RNN Regression ,what is the activation function i need to give for regression RNN,how it is difference from classification to regression?

    • Avatar
      Jason Brownlee August 17, 2017 at 6:36 am #

      Yes. The output would be ‘linear’ for regression.

  57. Avatar
    Maria Jimenez August 17, 2017 at 1:20 am #

    Hi Dr. Brownlee,

    I am trying to understand this code. I am a beginner working with time-series and LSTM.

    My questions about your code:

    1. What does “transform data to be stationary” mean?
    2. Why do you create diff? What does it mean?
    3. If the raw_values are 36 data, why diff has only 35?

    I appreciate your response in advance,


  58. Avatar
    Sourabh August 18, 2017 at 4:41 am #

    Thanks, for the awesome blogs,
    But, I have a doubt, for time series forecasting, classical methods like autoregression and ARIMA, or this machine learning approach using LSTM RNN model, which is the better approach? Both are good on their own, So, what should be our first choice while forecasting any dataset? How should we choose between them?

    • Avatar
      Jason Brownlee August 18, 2017 at 6:27 am #

      It depends on your problem. Try a few methods and see what works best.

      I recommend starting with linear methods like ARIMA, then try some ML methods like trees and such, then an MLP, then perhaps an RNN.

  59. Avatar
    Bilal August 19, 2017 at 10:29 pm #

    When I changed train/test ration to 0.8/0.2 in LSTM code, it took half an hour to predict, and with another data that contains around 4000 records, it’s taking hours(i still couldn’t get result, i don’t know how long it’ll take). Can you please suggest me how I change settings for very long sequences. Thanks

  60. Avatar
    hirohi August 21, 2017 at 12:54 pm #

    Is the evaluation method in this post really “walk-forward”? I’ve read your post about time-series backtest. Walk-forward corresponds to cross validation for not time series data. In both, we make many models to learn, so these methods are not suitable for deep learning, including LSTM, the theme of this post.

  61. Avatar
    hirohi August 22, 2017 at 11:16 am #

    Thank you for your reply. Sorry, that’s not what I mean it. I’ve read the post you pasted above, in which you split data into train/test 2820 times and build 2820 models. But, in this LSTM post, you split data and build a LSTM network only once, so I suggest the test in this article is not walk forward. ordered(not shuffle) hold-out test?

    • Avatar
      hirohi August 22, 2017 at 11:17 am #

      sorry, please delete this comment

    • Avatar
      Jason Brownlee August 23, 2017 at 6:36 am #

      Above, the model is evaluated 30 times.

      Within the evaluation of one model, we use walk forward validation and samples are not shuffled.

      I recommend re-reading the tutorial and code above.

      • Avatar
        hirohi August 23, 2017 at 12:26 pm #

        Thank you for your reply! Oh, repeat=30! Sorry, I misunderstood. But I think in the back-test article, the size of train data changes, while in this LSTM article, the size of train data is fixed, right? Sorry for so many questions.

  62. Avatar
    Gauthier August 23, 2017 at 10:38 pm #

    Thanks for your work, it is seriously awesome.

    I wanted to see the chart comparing training loss vs validation loss per epoch, see the chart here: https://ibb.co/kqcnBk. As you mentioned in your other post:

    “From the plot of loss, we can see that the model has comparable performance on both train and validation datasets (labeled test). If these parallel plots start to depart consistently, it might be a sign to stop training at an earlier epoch.”

    However, in this case, the test loss never really gets lower and both lines are not parallel at all. for this problem, and in general, does that mean that no meaningful test-set pattern is learned from the training, as seems to be corroborated by the RMSE being close on average to the persistent/dummy method?

    Is this the end of the road? Have NN’s failed in their tasks? If not, where to go next?

    The main thing I changed in the code was the end of the fit_lstm function:
    for i in range(nb_epoch):
    e=model.fit(X, y, epochs=10, batch_size=batch_size, verbose=0,validation_split=0.33, shuffle=False)
    return model, e

    • Avatar
      Jason Brownlee August 24, 2017 at 6:42 am #

      Thanks Gauthier.

      It may mean that the model under provisioned for the problem.

      • Avatar
        Gauthier August 24, 2017 at 6:37 pm #

        OK… So in this case would you suggest to include more neurons for example, or try another ML algorithm?

    • Avatar
      malcolm November 10, 2019 at 4:33 pm #

      Hi, @Gauthier, may i know how you editted ur code to get the loss function?

  63. Avatar
    Muni August 28, 2017 at 12:19 pm #


    Thanks for your blogs and tutorials. Being a research scholar, when I was in dilemma how to learn ML, your tutorials gave me an excellent start to carry out my work in Machine Learning and Deep Learning.

    I tried to work with the example in this page, But, I couldnt download the shampoo_sales dataset from datamarket.com. Could you please put the link to the datasets in the blog? If any procedure to download, please let me know.

    • Avatar
      Jason Brownlee August 29, 2017 at 5:01 pm #

      Thanks, I’m glad to hear that.

      Here is the full dataset:

  64. Avatar
    mikiwate September 3, 2017 at 3:35 pm #

    Hi Jason,

    I am getting NAN on the 12 month:::

    Month=1, Predicted=440.400000, Expected=440.400000
    Month=2, Predicted=315.900000, Expected=315.900000
    Month=3, Predicted=439.300000, Expected=439.300000
    Month=4, Predicted=401.300000, Expected=401.300000
    Month=5, Predicted=437.400000, Expected=437.400000
    Month=6, Predicted=575.500000, Expected=575.500000
    Month=7, Predicted=407.600000, Expected=407.600000
    Month=8, Predicted=682.000000, Expected=682.000000
    Month=9, Predicted=475.300000, Expected=475.300000
    Month=10, Predicted=581.300000, Expected=581.300000
    Month=11, Predicted=646.900000, Expected=646.900000
    Month=12, Predicted=646.900000, Expected=nan

    from the code below:

    predictions = list()
    for i in range(len(test_scaled)):
    # make one-step forecast
    X, y = test_scaled[i, 0:-1], test_scaled[i, -1]
    #yhat = forecast_lstm(lstm_model, 1, X)
    # invert scaling
    yhat = invert_scale(scaler, X, yhat)
    # invert differencing
    yhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i)
    # store forecast
    expected = raw_values[len(train) + i + 1]
    print(‘Month=%d, Predicted=%f, Expected=%f’ % (i+1, yhat, expected))

    I do not understand as to why this is happening.

    thanks for the feedback.

  65. Avatar
    Eric September 3, 2017 at 6:30 pm #

    Dear Jason,

    I had a question, what are we supposed to send as first parameter of inverse_difference if we go with the idea that we don’t know the future?

    Regardless what I do, if I give it the testing set then it have perfect accuracy and values. If I send the training set it will look like the last len(test_scaled) training values.

    Best regards

    • Avatar
      Jason Brownlee September 4, 2017 at 4:26 am #

      You would pass a list of past observations so that you can reverse the difference operation.

      • Avatar
        Eric September 4, 2017 at 9:42 am #

        Dear Mr Jason,

        Sorry, I have trouble understanding, what do you mean by “list of past observations”? Would that be what we predict (the predictions list)?
        It would then follow what “Pawel” asked and said previously?
        “my proposal:
        # invert differencing – (starting from 2nd loop cycle (1st would be the starting point (raw_values[-1]) )

        yhat = inverse_difference(predictions, yhat, 1)”

        Best regards,

        • Avatar
          Jason Brownlee September 7, 2017 at 12:32 pm #

          Sorry, I mean it is the true or real values observed in the domain at prior time steps. E.g. not predictions.

          • Avatar
            Eric September 7, 2017 at 5:04 pm #

            Dear Mr Jason,

            Thank you, so let’s imagine a 500 000 entry file.
            My training would be the 490 000 first line. I want to predict the last 10 000 lines.

            For predicting I send the last line of the training set (then for the next prediction I send my first prediction without having unscaled or reversed the difference).
            To get the true value I send as argument of “Invert_difference” my training set, or more specially, my last 10 000 thousands line?

            Best regards,
            Eric Godard.

          • Avatar
            Jason Brownlee September 9, 2017 at 11:40 am #

            I would not recommend prediction 10K time steps. I expect skill would be very poor.

            Nevertheless, observation 490000 would be used to invert observation 490001, then the 490001 transformed prediction would be used to decode 490002 and so on.

            Does that help?

          • Avatar
            Eric September 8, 2017 at 10:09 am #

            Sorry, I may have badly worded myself here.

            My dataset have one entry per minute, one day is 1440 entry, I have years worth of data in my data set. I want to predict the next day, should I send the last day of the training set (trained_scaled[-1440:]) as argument of inverse_difference?

            Best regards,

          • Avatar
            Jason Brownlee September 9, 2017 at 11:49 am #

            Perhaps this post will help you better understand the different transform:

  66. Avatar
    Brian September 16, 2017 at 8:55 pm #

    I keep getting inconsistent result of RMSE every time I rerun the code, so I added

    np.random.seed(1) # for consistent results

    to the very top of my code so now every run produces consistent RMSE.

  67. Avatar
    Irene September 18, 2017 at 8:48 pm #

    When I try to load the data after executing the following code line with Python 3.6 I get the following error:

    series = read_csv(‘shampoo-sales.csv’, header=0, parse_dates=[0], index_col=0,
    squeeze=True, date_parser=parser)

    TypeError: ufunc ‘add’ did not contain a loop with signature matching types dtype(‘<U32') dtype('<U32') dtype('<U32').

    Can you help me, please?

  68. Avatar
    Priyank September 18, 2017 at 10:05 pm #

    Hello Jason,

    Thanks for sharing this post, very helpful as currently I am working on a time series project. I have one query.. How can we save a model with best RSME and use it to further prediction.


  69. Avatar
    Alex September 21, 2017 at 10:27 am #

    Thanks Jason for the great tutorial!

    Can you please clarify this statement for me: “The batch_size must be set to 1. This is because it must be a factor of the size of the training and test datasets”

    I don’t understand how 1 in this case is a factor of the training and test datasets?

    Further, for time series data, can we have a batch size greater than 1? If not, what was the relevance of the above statement?

    Thank you

    • Avatar
      Jason Brownlee September 21, 2017 at 4:21 pm #

      Yes, it is a constraint for the chosen framing of the problem so that we can make one-step forecasts with a stateful LSTM.

      It is not a constraint generally.

  70. Avatar
    Nidhi September 22, 2017 at 9:58 am #

    Great post Jason, very granularly explained LSTM example. Thanks a lot. I am trying to train a model to predict scientific notation data like “9.543301358961403E-9”, could you suggest a good way to rescale this data that fits LSTM the best?

    • Avatar
      Jason Brownlee September 23, 2017 at 5:34 am #

      For input data, rescale values to the range 0-1.

  71. Avatar
    vardhan October 2, 2017 at 4:22 pm #

    Hi, I have gone through many of your posts and still confusing when BPTT is applied?? Does BPTT is applied in this example? or just applied when we take more than one previous inputs to predict the current output??

    And in this example, the parameters are updated at each epoch (batch gradient descent) completely contrast to stochastic gradient descent (online-learning), is this right??

  72. Avatar
    Aljo Jose October 3, 2017 at 11:42 pm #

    Hi Jason,
    Thank you for great tutorial. Please let me know the difference between below two –

    1) model.fit(trainX, trainY, epochs=3000, batch_size=1, verbose=0)

    2) for i in range(3000):
    model.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False)

  73. Avatar
    Nidhi October 16, 2017 at 1:11 am #

    Hi Jason,
    You have reshaped value of X and then predicted the value of yhat, after that invert scaling of yhat is done and then this value is added to the raw value of the previous month. My question is what if I add the reshaped value of yhat and reshaped value of previous month and then call invert scale_function and not call inverse_difference function at all. Will both give the same result?
    Best Regards

    • Avatar
      Jason Brownlee October 16, 2017 at 5:44 am #

      I believe so, we need to group yhat with anything, even 0 values to ensure that we meet the shape requirements when inverting the transform.

  74. Avatar
    Nidhi October 16, 2017 at 1:43 am #

    I ran your code multiple times with different parameters. There is one more question, when we are plotting both “pyplot.plot(raw_values[-12:]) and pyplot.plot(predictions)”, I expected both the lines to coincide at certain points(like in your example graph values for months 1 & 3 are almost close) OR at least show a similar trend, but why in most of the results the orange line for time (t) always seem to be more closely associated with the blue line for time (t-1)?? Initially, I thought it because we must be plotting raw values of month 24-36 and predictions from month 25-37, but that’s not the case, we are plotting both prediction values(predicted from month 23-35) and the raw values(from 24-36). Could be please clarify, why is that the case?. I am definitely missing out something, but not able to figure out! Thanks again.

    • Avatar
      Jason Brownlee October 16, 2017 at 5:45 am #

      This suggests a persistence model (e.g. no skill).

  75. Avatar
    Rubens October 16, 2017 at 4:50 am #

    I’m using lag>1

    Shouldn’t the function “timeseries_to_supervised” revert the range range(1, lag+1) ?

    columns = [df.shift(i) for i in reversed(range(1, lag+1))]

  76. Avatar
    Thong Bui October 16, 2017 at 5:00 am #

    Hi Jason,

    Thanks so much for the in-depth tutorial. I have a question about this block of code in fit_lstm():

    for i in range(nb_epoch):
    model.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False)

    Can it simply be done by this line?
    model.fit(X, y, epochs=nb_epoch, batch_size=batch_size, verbose=0, shuffle=False)

    Thanks for your clarification

  77. Avatar
    Danier October 19, 2017 at 7:14 pm #

    Hi Jason,
    I am a college student. I am particularly interested in machine learning and are working hard on it. But my English is not very good, so my problems may be a little rough.
    1. The rmse in this article is somewhat large, and you have some other articles that describe how to adjust the parameters to reduce the rmse? What are the reasons for regulation?
    2. Would you have a better article about using LSTM to predict time series problems? Ps: in Uni-variate time series. Because I did the experiment myself, if I use the model of this article, my experiment accuracy is 85% to 90%. I want to improve it.
    3. Is there any article to solve the multivariate time series forecasting problem? If so, where is the latest?
    4. I have been running the model several times with my own macbookpro, which is too slow. If I want to be more efficient, can I buy some GPU cloud services? Like amazon? But it seems that these cloud services are especially expensive. Do you have any good solutions?
    Thank you so much! I want to say that you are my machine learning primer teacher.

  78. Avatar
    Danier October 24, 2017 at 3:14 pm #

    Hello, Jason
    Thank you for your last reply. I have improved the accuracy of 4% by various methods. I used bias_regularizer =L1L2 (0.01, 0.01) to reduce the value of rmse. (based on my own dataset). But I would like to ask about Tutorial Extensions.
    I want to know how to complete multi-step Forecast. For example, my training set is 201601 to 201712, 24 sets of data, I would like to predict the six sets of data from 20171-201706. And these six sets of data have no expected value and are empty. I tried 10 or more methods but failed, maybe my python was too bad? Or is my understanding of LSTM not enough?I really can’t figure out a solution.and I was very depressed………..
    I hope you can give me some Suggestions. Thank you. Or do you know of any article that can be used as my reference?

  79. Avatar
    argyn October 25, 2017 at 1:23 am #


    I have an issue with your terminology regarding the dynamic forecasting, which you defined as follows:
    “re-fit the model or update the model each time step of the test data as new observations from the test data are made available (we’ll call this the dynamic approach).”

    That’s not what’s called dynamic forecasting in time series and econometric analysis. The dynamic forecasting involves using the previous forecast value as input into the next forecast. In your case, you are using the lagged value of the dependent variable as a regressor in the estimation of the model: X(t) = Y(t-1). For instance, see this paper https://files.stlouisfed.org/files/htdocs/publications/review/80/06/Forecasting_Jun_Jul1980.pdf

    So, the dynamic multi-step forecast would involve something like this: Yhat(t) = function(Yhat(t-1)). It doesn’t need to re-estimate the model at each step to be dynamic. All it needs is to use the previous forecast value to come up with the next.

    Particularly this step would change to use yhat as X:

    X, y = test_scaled[i, 0:-1], test_scaled[i, -1]
    yhat = forecast_lstm(lstm_model, 1, X)

  80. Avatar
    Sulgi October 25, 2017 at 7:40 pm #

    Hi I like to input time difference between timesteps into LSTM to model a decay. I saw someone manually put this term into the weight, so weight now has the form, W(t). I wonder if we can include the time difference in input, X. Do you have any advice on this?

    • Avatar
      Jason Brownlee October 26, 2017 at 5:26 am #

      Sorry, I have not done this, perhaps talk to the person that raised this idea with you?

  81. Avatar
    Eren October 26, 2017 at 10:55 am #

    My observation is the model tries to predict the previous value so that it is able to pick a moderate precision. (I used another dataset)

  82. Avatar
    tony October 26, 2017 at 5:01 pm #

    Hi, Jason:
    Use the shampoo sales data and my own test data, the results are good.But when the time series with seasonal trends, LSTM result is very bad.So I want to ask is there any way to solve include seasonal time series forecasting problem?
    thank you.

  83. Avatar
    Frank November 7, 2017 at 11:49 am #

    While the visuals and numbers in this tutorial are compelling, there are several things seriously wrong that aren’t apparent until you go over it with a very fine-toothed comb. Among all the arrays, lists, and indices flying all over the place, there are errors that make the results non-reproducible for one.

    At the detail level you’ve got this prediction output:

    Month=1, Predicted=339.700000, Expected=339.700000
    Month=2, Predicted=440.400000, Expected=440.400000
    Month=3, Predicted=315.900000, Expected=315.900000

    However running the code block that is supposed to produce that results in an IndexError because “Expected” is supposed to come from:

    expected = raw_values[len(train) + i + 1]

    Index i starts out at 0 because you are looping through len(train), so raw_values[len(train) + i + 1] will first be raw_values[len(train) + 0 + 1] which is raw_values[25], which is 440.40 (Month 2), not 339.7 (Month 1).

    This kind of thing seems minor, but it’s actually very frustrating to readers who are trying to get some reproducible output, but instead they end up having to track down a bug in the code from the start.

    At a more general level, the purpose of building a machine learning model is not to produce some metrics on test data and leave it at that. Instead, it is to build a model that performs well on out-of-sample data that you haven’t encountered yet. From the beginning, you apply a difference function to the data that is supposed to remove the trend, then you forecast the residuals, and then add the trend back in with an inverse difference function. Right there is a major violation as you are literally imputing known information into what is supposed to be the forecast. The inverse difference function takes raw_values as a parameter, however in a real out-of-sample scenario, you wouldn’t have access to those raw_values, so you couldn’t simply adjust the forecasted residuals to reflect the trend in that manner. How did no one catch this?

    I’m doing a research project on LSTMS for time-series data and trying to extract something useful from this tutorial that I can apply to this problem, but I feel there are too many land-mines hidden throughout.

  84. Avatar
    Luciano November 7, 2017 at 10:37 pm #

    Hi Jason!

    I have a dataset of 200 thousand time-series. Each with 150 timestamps.

    Let’s say they are sales of the same product but for different stores.

    What is the best way to design the problem?

    I can’t figure out what would be the ideal way to structure it. Just feed each sequence of 149 values to predict the 150th; Or should I do a rolling-window? If I give the whole sequence, I’m giving it a lot of context to work on, but I’m afraid the series it to big and training will be hard.

    Any thoughts?
    There is a lack of literature on how to design time-series problems with LSTMs. You are the only one that is talking about it. Thanks!

    • Avatar
      Jason Brownlee November 8, 2017 at 9:23 am #

      I would recommend exploring many different framings of the problem and see what works best.

      200K series is a lot. Perhaps you can group series and use sub-models and combine results in an ensemble of some sort.

  85. Avatar
    Ashima November 9, 2017 at 6:02 am #

    Hi Jason,
    Would like to request your help in updating the above code to a dynamic model which updates itself after every observation and accordingly predicts the future points. Could you suggest how to modify this code to suit that purpose.

  86. Avatar
    Bahar November 14, 2017 at 4:24 pm #

    Hi Jason,

    Thanks for the useful tutorial.
    I have a question about X, y = test_scaled[i, 0:-1], test_scaled[i, -1]
    yhat = forecast_lstm(lstm_model, 1, X)


    I didn’t understand how the prediction will use timestamps to predict on test data set.
    As far as I know, eventually we want to predict based on future time. So we should test based on timestamps (not values) and compare the prediction results with real test values to see the accuracy of the prediction.
    But in the code, it seems that you are predicting based on the values and comparing again with those values!

    Would you please explain it to me? Maybe I misunderstood some part.

    Best Regards,

  87. Avatar
    Pradeep November 19, 2017 at 5:57 pm #

    Jason awesome tutorial which helps in getting folks started out.
    I had 2 quick questions.
    1. Is there a good example of adding other “features” apart form time lags. For example whether a particular hour is rush hour or not, whether a particular day is a weekday or not .
    2. I have hourly data for 3 years and wish to forecast hourly for the next 3 months. So i have approximately 14600 training rows and have to forecast for approximately 2600 test rows. Multi Step seems to be the right approach. However will be able to train a model to forecast so mant steps in advance?

  88. Avatar
    Harini November 20, 2017 at 1:45 am #

    Hi Jason, I have a quarterly sales dataset(below) and tried to use the same code on this post:
    Month, Sales

    I trained the model with data from all preceding quarters to predict the last quarter:
    last quarter: predicted=-1.329951, actual=34.000000

    The sales number can’t be negative but the model has predicted a negative value.
    Is there a way to prevent the model from predicting negative values?

    • Avatar
      Jason Brownlee November 20, 2017 at 10:19 am #

      I would recommend starting with some simple linear models to better understand your data and how time series works:

      • Avatar
        Harini November 25, 2017 at 6:27 am #

        Thanks Jason, I tried linear regression but it din’t seem to give me expected results.

        Then I tuned the LSTM in your code to predict positive values by
        * changing the scaler range from (-1,1) to (0,1)
        * adding the activation function ‘relu’ to the model

  89. Avatar
    SRIRAM P November 21, 2017 at 5:59 pm #

    Hi Jason,

    Need a small clarification,

    Does the for loop started at 100th line ends at 102?

    for r in range(repeats):
    # fit the model
    lstm_model = fit_lstm(train_scaled, 1, 3000, 4)
    # forecast the entire training dataset to build up state for forecasting
    train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
    lstm_model.predict(train_reshaped, batch_size=1)

    here in the above, does the lines
    train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
    lstm_model.predict(train_reshaped, batch_size=1)

    also belongs to for loop?

  90. Avatar
    AB November 28, 2017 at 5:13 am #

    hey Jason,

    How to Predict next one month for above example?

  91. Avatar
    Vijay December 6, 2017 at 11:32 pm #

    Hey Jason,

    Thanks for all your wonderful articles. I’ve trying this model to predict a spending pattern of a customer. I have mean of the weekly expenditure of a customer. Once I finished training, i’m seeing this pattern where the predicted output for current is matching the expected output in the last week. I changed yhat = y to see if all the conversions are taking place correctly. But even yhat = y is showing the same behaviour.

    Week=1, Predicted=975.556027, Expected=989.100588
    Week=2, Predicted=989.100588, Expected=928.604400
    Week=3, Predicted=928.604400, Expected=921.209794
    Week=4, Predicted=921.209794, Expected=919.813532
    Week=5, Predicted=919.813532, Expected=904.214533
    Week=6, Predicted=904.214533, Expected=913.695025
    Week=7, Predicted=913.695025, Expected=971.727005
    Week=8, Predicted=971.727005, Expected=1095.774093
    Week=9, Predicted=1095.774093, Expected=1159.611429
    Week=10, Predicted=1159.611429, Expected=732.743950
    Week=11, Predicted=732.743950, Expected=963.615794
    Week=12, Predicted=963.615794, Expected=896.842055
    Week=13, Predicted=896.842055, Expected=960.630000
    Week=14, Predicted=960.630000, Expected=905.481048
    Week=15, Predicted=905.481048, Expected=994.167244
    Week=16, Predicted=994.167244, Expected=975.601111
    Week=17, Predicted=975.601111, Expected=1210.307037
    Week=18, Predicted=1210.307037, Expected=9293.130000
    Week=19, Predicted=9293.130000, Expected=367.780000

    I’m not differencing the data since my data is stationary, I dont see a increasing/decreasing pattering the spending patterns. Can you help me out ?

    • Avatar
      Jason Brownlee December 7, 2017 at 7:58 am #

      It may suggest that the model is only learning a persistence model (e.g. output what was input).

      I would recommend starting with a simple MLP and see if an LSTM can do better.

  92. Avatar
    Anton December 17, 2017 at 2:04 am #

    First of all, thanks for your great work and all the posts, they are really amazing and helpful!

    Lets look at my changed csv data:


    Its a very simple sequence of “resonant” points, increasing every step over y axis. I didn’t changed any changes in the program code, and here is the result: http://prntscr.com/hob1hf

    Why LSTM can not predict so simple and logical sequence of data? What are we missing here?

    Waiting for your reply, and once again, thanks a lot!

  93. Avatar
    Anton December 17, 2017 at 2:21 am #

    One interesting thing: I made the time serie 2 years longer, but with the same increasing resonant coefficient (0.1):


    Now, we see that LSTM made a predictions more closely, but still don’t see the increment over Y axis (the red lines and arrows are my own paining) http://prntscr.com/hob7eo

    Any ideas?

    • Avatar
      Jason Brownlee December 17, 2017 at 8:53 am #

      Not enough data, model needs tuning, lstms are poor at autoregression.

  94. Avatar
    Anton December 17, 2017 at 3:30 am #

    One more question about the code:

    Why you performs 1 prediction before the predictions cycle:

    train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
    lstm_model.predict(train_reshaped, batch_size=1)

    what is this for?

    And at the line
    # make one-step forecast
    X, y = test_scaled[i, 0:-1], test_scaled[i, -1]

    what is “y” for?

  95. Avatar
    Krasimir December 18, 2017 at 8:28 am #

    Hi Jason,
    Thanks for the great posts, very helpful and informative.

    I am using some of your example for stock market values predictions. The models work well. Could you please provide more detail on why there is a one sample delay (lag) in the response of the model. It can be seen on all your plots and mine too.

  96. Avatar
    Anton December 20, 2017 at 5:53 am #

    Is the model state updated after each

    lstm_model.predict(train_reshaped, batch_size=1)


    So can we be sure that after 100 predictions the model will have actual state for 101 prediction? Or should we use some additional model updates technique after each prediction step? It is not clear for me…

    • Avatar
      Jason Brownlee December 20, 2017 at 5:55 am #

      State does not see to matter that much in this example.

  97. Avatar
    Anton December 20, 2017 at 6:13 am #

    Agree, but in general? Does lstm_model.predict updates the model?

    • Avatar
      Jason Brownlee December 20, 2017 at 3:47 pm #

      It will update internal state variables, but not weights.

      Does that help?

  98. Avatar
    Anton December 21, 2017 at 8:34 am #

    Yes, thank you very much

  99. Avatar
    Novin January 7, 2018 at 1:37 am #

    Thanks Jason for the tutorial.

    What’s your suggestion for adapting this network for different stores shampoo sales? Things that I could think of are:

    1- run this model for different stores separately (maybe we can learn something from sales of all stores together, but with this approach, we can’t benefit that)
    2- giving in the number of sales of each store as features

    • Avatar
      Jason Brownlee January 7, 2018 at 5:10 am #

      Some ideas:

      – model each store separately
      – model each store separately and add data from all stores
      – model each store separately and add data from related stores (regionally? profile? etc.)
      – create a regional store model and ensemble with separate store model.
      – create all store model and ensemble with separate store model
      – so on…

      Think up 100 ideas and try them all to see what works best for your specific data.

  100. Avatar
    mostafa kotb January 8, 2018 at 12:47 am #

    thank you Dr. Jason for this tutorial.
    If i want to perform a walkforward validation on training data to, it is going to be:

    for i in range(len(train_scaled)):
    # make one-step forecast
    X, y = train_scaled[i, 0:-1], train_scaled[i, -1]
    yhat = forecast_lstm(lstm_model, 1, X)
    # invert scaling
    yhat = invert_scale(scaler, X, yhat)
    # invert differencing
    yhat = inverse_difference(raw_values, yhat, len(raw_values)-i)
    # store forecast
    expected = raw_values[ i+1 ]
    print(‘Month=%d, Predicted=%f, Expected=%f’ % (i+1, yhat, expected))

    # report performance
    rmse_train = sqrt(mean_squared_error(raw_values[1:len(train_scaled)+1], predictions_train))

    please, verify if it is right or not

  101. Avatar
    mostafa kotb January 8, 2018 at 6:16 am #

    thanks for your reply…

    let me rephrase my question….i want to know when i compute RMSE for training data, Do i skip the first point in the raw values?

    rmse_train = sqrt(mean_squared_error(raw_values[1:len(train_scaled)+1], predictions_train))

    if you notice in the last equation i started from the second point raw_values[1:len(train_scaled)+1]

    because we don’t predict the first point, actually we start by first point as x and predict the second point as y.

  102. Avatar
    Swapnil January 8, 2018 at 3:53 pm #

    Hi, Thanks for the great article.
    I have some log data from my honeypot. I have encoded the actions taking place with label encoder. Is this data good enough for training the lstm? I finally want to recover the next action. Should i go for word to vector instead?

    • Avatar
      Jason Brownlee January 8, 2018 at 3:55 pm #

      Perhaps try a few representations to see what works best for your data?

  103. Avatar
    Jacques January 9, 2018 at 11:37 am #

    Hey, I’m trying to understand why you implemented the persistence algorithm in a different way compared to your other post (https://machinelearningmastery.com/persistence-time-series-forecasting-with-python/). In your other post, you framed the problem as a supervised learning problem, but you didn’t do the same here? You also talk about t-1 and t+1 on that post, not t-1 and t. Could you clarify why you didn’t convert the problem in this post into supervised until the lstm model?

  104. Avatar
    Swapnil January 9, 2018 at 6:24 pm #

    Hi how do u judge efficacy with rmse? Less is better or more?

  105. Avatar
    Ian January 23, 2018 at 7:02 pm #

    Hi Jason, nice tutorial. I am using XBT data for 2017, but just trying daily. when I follow this suggestion “Update: Consider trying 1500 epochs and 1 neuron, the performance may be better!” the RMSE and the graph look very similar to the persistent model. Was that your finding?

  106. Avatar
    andr January 24, 2018 at 12:44 am #

    is it possible to append to training set some data and update the model recursively? is it correct to do it with the fit function and the updated training set as parmeter?

  107. Avatar
    Antonio Bautista February 1, 2018 at 4:27 am #

    Hello, thanks for this tutorial it is great and gave me a lot of insights. I just have one question.

    Is the historial data still needed after the training of the net ? or just the last observations are needed?

    Thank you!

    • Avatar
      Jason Brownlee February 1, 2018 at 7:26 am #

      You model requires inputs to make predictions. It depends on how you have defined your model as to what you will need to retain.

      Generally, training data is only used to fit the model, then the model is used to make predictions from new obs.

  108. Avatar
    Shotaro February 2, 2018 at 7:36 pm #

    Hi, Jason

    Which type LSTM method do you use in this sample code?

    1:[Hochreiter & Schmidhuber, 95;97] Simple LSTM

    2:[Gers & Schmidhuber, 99] LSTM with Forget Gate

    3:[Gers & Schmidhuber, 00] LSTM with Peephole Connection

    4:[Graves & Schmidhuber, 05] LSTM Full Gradient

    5: Other

    I think that Simpe LSTM. Will you show other model in the future?

  109. Avatar
    Clock ZHONG February 11, 2018 at 4:51 pm #


    Thanks again for you this post. I’ve also followed your instructions in this post, and finished the test.
    But I’ve a question:
    Comparing with other models, training this RNN model is very slow, I checked the code and found that you set the batch_size as 1, I believe one solution to accelerate the training is increasing batch_size to a bigger number, but I fear it will cause some other errors, as you explain as following:
    “The batch_size must be set to 1. This is because it must be a factor of the size of the training and test datasets.”
    Does i mean if we set the batch_size as a common factor of both the size of training and the testing datasets, then it’ll be OK? E.g. if my testset size is 1000, and my training dataset is 100000, then I could set the batch_size as 1000, is my understanding right?
    If my understanding is wrong, what’s other restrictions I need pay attention?

    Thanks in advance.

    Clock ZHONG

  110. Avatar
    Ridhima Kumar February 11, 2018 at 6:44 pm #

    Hi Jason,

    Thanks for the wonderful explanation on LSTM.

    I have tried running the code. However, I am getting an error – Keyword Error 1 when I difference the series.

    The error comes after running the following piece:

    # transform to be stationary
    differenced = difference(series, 1)

    It would be great if you could help me out with this.

    Ridhima Kumar

    • Avatar
      Jason Brownlee February 12, 2018 at 8:28 am #

      Perhaps double check that you have copied all of the code?

  111. Avatar
    Peter February 17, 2018 at 3:50 pm #

    Hi Jason,

    Thanks for the Awesome tutorial. Sorry if I’m stupid asking this here, New to application level ML. Only have amateur knowledge in the area, trying to learn by building a web app.

    I’m using a sample data of three years to forecast the price for next 3 years- made up my dataset exactly like the sample used here, I followed your tutorial and everything worked fine till the last steps (lol I know how to copy-paste)

    But I’m now stuck at writing the code for forecasting the next 3 years price.

  112. Avatar
    Julian February 21, 2018 at 3:54 am #

    Hi Jason,

    thank you for your tutorial. I have a question for you. I copied your source code and changed the parameters for the number of epochs and units (LSTM) to 10 and 1. With this configuration I achieved very good results. If I now comment out the lines that are responsible for training the neural network, I get the same results. How is that possible?

    Is there a bug in your program or do I have problems understanding how your code works?

    • Avatar
      Jason Brownlee February 21, 2018 at 6:41 am #

      Perhaps you did not comment out enough?

      • Avatar
        Julian February 21, 2018 at 8:16 am #

        I have commented out the following lines:

        # for i in range(nb_epoch):
        # model.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False)
        # model.reset_states()


        # train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1)
        # lstm_model.predict(train_reshaped, batch_size=1)

        I mean, that should be enough. Or did I forget to comment out something?

  113. Avatar
    Paula February 22, 2018 at 7:07 am #

    Hi Jason,

    I´m new in LSTM nn. I copied your example, run it and it works but I don´t understand why I get different results each time I run the code. I didn´t find any random number that could make to get all time different results.

    Moreover, I would like to know the reason why you create and fit the model 30 times and not only one. Could I take the best result of those 30?


  114. Avatar
    Ian Zhang March 6, 2018 at 9:47 pm #

    Hi Jason,

    i’m trying to deal with my time prediction problem using LSTM-based architecture.There are

    almost 30 id in my dataset. Each data of id is similar with your sample.(time related

    data.)Here is my question:

    1.Can this model train multiple sets of data at the same time?(e.g. you want to deal with

    sales of different brands of shampoo. And you want to predict each of sale at same

    time.Maybe each set of data is relevant,but you dont care.)If i can, how to decide input

    shape and output shape?Is there any influence in the network of each set data

    2.If my data is stationary ,do i need to process my data by difference?I already try to

    train my data without difference using this architecture.But predictions of test data is linear

    (looks like a horizontal line).I don’t know why it happens.If it’s my fault or this architecture is

    designed for this method(difference)?


    • Avatar
      Jason Brownlee March 7, 2018 at 6:13 am #

      Sure, try it and see how you go. Perhaps start with an MLP instead.

      If the data is stationary, no need to use a difference transform.

  115. Avatar
    Jamie March 10, 2018 at 12:32 am #

    Hi Jason! I have been reading your blog as a reference for a project at my internship and your content is awesome!!

    In my project I need to both do series forecasting and also sequence classification. So I am playing with 2 models as my first approach to the problem: one LSTM network for forecasting and a second model for which I am considering a sliding window MLP to take small patches of my time series and do sequence classification (I have labels for all time steps).

    So the general idea is to classify forecast sequences (classification over my predictions). I hope it makes sense.

    In case it does, I wanted to ask for advice on the sliding window MLP since I really can’t find good references on the web. What would I do in general? Would I stack the inputs from the previous time steps and give it to my network as input? So an example for simplicity: if I have 5 variables, and I want to have a 5-step sliding window, would my input for time t be [[t-4],[t-3],[t-2],[t-1], [t]] -> y[t] and let my network figure out how to learn from it? or would I have to instead take the 5 vectors and aggregate them somehow (e.g. average) and then give my network only 1 resulting vector and its label? I am sorry if my question seems dumb but I really have not been able to find useful information on this topic, if you have anything on this on any of your posts or resources please let me know.


    • Avatar
      Jason Brownlee March 10, 2018 at 6:32 am #

      Yes, in general the lag obs become a window of features as input for the MLP.

      Also, consider LSTM for sequence classification.

      Also, explore a multiple output model to do both predictions from one model to see if it offers a lift in skill (if I understand your data correctly).

      Let me know how you go.

      • Avatar
        Jamie March 12, 2018 at 8:27 pm #

        Thank you Jason, I will definitely explore your suggestions, let me try to explain again and also put it simply to see if the third option is feasable, I am curious to try it as well. I will give an illustration that is not my real problem but I find easier to explain and I think it’s a good illustration.

        Imagine you had weather data and you have to recommend if it is a good day to go out or not, so all that matters to you is simply saying 0 if it’s not a good idea to go out but 1 if it’s a good idea. You have historical data and multiple inputs (humidity, atmospheric pressure, air temperature, etc.), and you want to give recommendations with multiple horizons (1 hour, 2 hours, etc). At every time step, you also have the ground truth labels for each entry.

        So all that matters would be recommending good/bad with multiple horizons, but I thought, how would I be able to do this if not with 2 individual models, one that first forecasts the values for temperature, humidity,etc and a second model that does sequence classification and can classifty the sequences I predicted with my first model?

        Is there a way I could simply do my recommendation forecasts with only 1 model? What type of model would this be (if any)? Thank you Jason!