Some machine learning algorithms will achieve better performance if your time series data has a consistent scale or distribution.
Two techniques that you can use to consistently rescale your time series data are normalization and standardization.
In this tutorial, you will discover how you can apply normalization and standardization rescaling to your time series data in Python.
After completing this tutorial, you will know:
- The limitations of normalization and expectations of your data for using standardization.
- What parameters are required and how to manually calculate normalized and standardized values.
- How to normalize and standardize your time series data using scikit-learn in Python.
Let’s get started.
How to Normalize and Standardize Time Series Data in Python
Photo by Sage Ross, some rights reserved.
Minimum Daily Temperatures Dataset
This dataset describes the minimum daily temperatures over 10 years (1981-1990) in the city Melbourne, Australia.
The units are in degrees Celsius and there are 3,650 observations. The source of the data is credited as the Australian Bureau of Meteorology.
Below is a sample of the first 5 rows of data, including the header row.
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"Date","Temperatures" "1981-01-01",20.7 "1981-01-02",17.9 "1981-01-03",18.8 "1981-01-04",14.6 "1981-01-05",15.8 |
Below is a plot of the entire dataset taken from Data Market.
Minimum Daily Temperatures
The dataset shows a strong seasonality component and has a nice, fine-grained detail to work with.
Download and learn more about the dataset here.
This tutorial assumes that the dataset is in your current working directory with the filename “daily-minimum-temperatures-in-me.csv“.
Note: The downloaded file contains some question mark (“?”) characters that must be removed before you can use the dataset. Open the file in a text editor and remove the “?” characters. Also remove any footer information in the file.
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Normalize Time Series Data
Normalization is a rescaling of the data from the original range so that all values are within the range of 0 and 1.
Normalization can be useful, and even required in some machine learning algorithms when your time series data has input values with differing scales.It may be required for algorithms, like k-Nearest neighbors, which uses distance calculations and Linear Regression and Artificial Neural Networks that weight input values.
Normalization requires that you know or are able to accurately estimate the minimum and maximum observable values. You may be able to estimate these values from your available data. If your time series is trending up or down, estimating these expected values may be difficult and normalization may not be the best method to use on your problem.
A value is normalized as follows:
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1 |
y = (x - min) / (max - min) |
Where the minimum and maximum values pertain to the value x being normalized.
For example, for the temperature data, we could guesstimate the min and max observable values as 30 and -10, which are greatly over and under-estimated. We can then normalize any value like 18.8 as follows:
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1 2 3 4 |
y = (x - min) / (max - min) y = (18.8 - -10) / (30 - -10) y = 28.8 / 40 y = 0.72 |
You can see that if an x value is provided that is outside the bounds of the minimum and maximum values, that the resulting value will not be in the range of 0 and 1. You could check for these observations prior to making predictions and either remove them from the dataset or limit them to the pre-defined maximum or minimum values.
You can normalize your dataset using the scikit-learn object MinMaxScaler.
Good practice usage with the MinMaxScaler and other rescaling techniques is as follows:
- Fit the scaler using available training data. For normalization, this means the training data will be used to estimate the minimum and maximum observable values. This is done by calling the fit() function,
- Apply the scale to training data. This means you can use the normalized data to train your model. This is done by calling the transform() function
- Apply the scale to data going forward. This means you can prepare new data in the future on which you want to make predictions.
If needed, the transform can be inverted. This is useful for converting predictions back into their original scale for reporting or plotting. This can be done by calling the inverse_transform() function.
Below is an example of normalizing the Minimum Daily Temperatures dataset.
The scaler requires data to be provided as a matrix of rows and columns. The loaded time series data is loaded as a Pandas Series. It must then be reshaped into a matrix of one column with 3,650 rows.
The reshaped dataset is then used to fit the scaler, the dataset is normalized, then the normalization transform is inverted to show the original values again.
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# Normalize time series data from pandas import Series from sklearn.preprocessing import MinMaxScaler # load the dataset and print the first 5 rows series = Series.from_csv('daily-minimum-temperatures-in-me.csv', header=0) print(series.head()) # prepare data for normalization values = series.values values = values.reshape((len(values), 1)) # train the normalization scaler = MinMaxScaler(feature_range=(0, 1)) scaler = scaler.fit(values) print('Min: %f, Max: %f' % (scaler.data_min_, scaler.data_max_)) # normalize the dataset and print the first 5 rows normalized = scaler.transform(values) for i in range(5): print(normalized[i]) # inverse transform and print the first 5 rows inversed = scaler.inverse_transform(normalized) for i in range(5): print(inversed[i]) |
Running the example prints the first 5 rows from the loaded dataset, shows the same 5 values in their normalized form, then the values back in their original scale using the inverse transform.
We can also see that the minimum and maximum values of the dataset are 0 and 26.3 respectively.
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Date 1981-01-01 20.7 1981-01-02 17.9 1981-01-03 18.8 1981-01-04 14.6 1981-01-05 15.8 Name: Temp, dtype: float64 Min: 0.000000, Max: 26.300000 [ 0.78707224] [ 0.68060837] [ 0.7148289] [ 0.55513308] [ 0.60076046] [ 20.7] [ 17.9] [ 18.8] [ 14.6] [ 15.8] |
There is another type of rescaling that is more robust to new values being outside the range of expected values; this is called Standardization. We will look at that next.
Standardize Time Series Data
Standardizing a dataset involves rescaling the distribution of values so that the mean of observed values is 0 and the standard deviation is 1.
This can be thought of as subtracting the mean value or centering the data.
Like normalization, standardization can be useful, and even required in some machine learning algorithms when your time series data has input values with differing scales.
Standardization assumes that your observations fit a Gaussian distribution (bell curve) with a well behaved mean and standard deviation. You can still standardize your time series data if this expectation is not met, but you may not get reliable results.
This includes algorithms like Support Vector Machines, Linear and Logistic Regression, and other algorithms that assume or have improved performance with Gaussian data.
Standardization requires that you know or are able to accurately estimate the mean and standard deviation of observable values. You may be able to estimate these values from your training data.
A value is standardized as follows:
|
1 |
y = (x - mean) / standard_deviation |
Where the mean is calculated as:
|
1 |
mean = sum(x) / count(x) |
And the standard_deviation is calculated as:
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1 |
standard_deviation = sqrt( sum( (x - mean)^2 ) / count(x)) |
For example, we can plot a histogram of the Minimum Daily Temperatures dataset as follows:
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from pandas import Series from matplotlib import pyplot series = Series.from_csv('daily-minimum-temperatures-in-me.csv', header=0) series.hist() pyplot.show() |
Running the code gives the following plot that shows a Gaussian distribution of the dataset, as assumed by standardization.
Minimum Daily Temperatures Histogram
We can guesstimate a mean temperature of 10 and a standard deviation of about 5. Using these values, we can standardize the first value in the dataset of 20.7 as follows:
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y = (x - mean) / standard_deviation y = (20.7 - 10) / 5 y = (10.7) / 5 y = 2.14 |
The mean and standard deviation estimates of a dataset can be more robust to new data than the minimum and maximum.
You can standardize your dataset using the scikit-learn object StandardScaler.
Below is an example of standardizing the Minimum Daily Temperatures dataset.
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# Standardize time series data from pandas import Series from sklearn.preprocessing import StandardScaler from math import sqrt # load the dataset and print the first 5 rows series = Series.from_csv('daily-minimum-temperatures-in-me.csv', header=0) print(series.head()) # prepare data for standardization values = series.values values = values.reshape((len(values), 1)) # train the standardization scaler = StandardScaler() scaler = scaler.fit(values) print('Mean: %f, StandardDeviation: %f' % (scaler.mean_, sqrt(scaler.var_))) # standardization the dataset and print the first 5 rows normalized = scaler.transform(values) for i in range(5): print(normalized[i]) # inverse transform and print the first 5 rows inversed = scaler.inverse_transform(normalized) for i in range(5): print(inversed[i]) |
Running the example prints the first 5 rows of the dataset, prints the same values standardized, then prints the values back in their original scale.
We can see that the estimated mean and standard deviation were 11.1 and 4.0 respectively.
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Date 1981-01-01 20.7 1981-01-02 17.9 1981-01-03 18.8 1981-01-04 14.6 1981-01-05 15.8 Name: Temp, dtype: float64 Mean: 11.177753, StandardDeviation: 4.071279 [ 2.33888328] [ 1.65113873] [ 1.87219948] [ 0.84058266] [ 1.13533032] [ 20.7] [ 17.9] [ 18.8] [ 14.6] [ 15.8] |
Summary
In this tutorial, you discovered how to normalize and standardize time series data in Python.
Specifically, you learned:
- That some machine learning algorithms perform better or even require rescaled data when modeling.
- How to manually calculate the parameters required for normalization and standardization.
- How to normalize and standardize time series data using scikit-learn in Python.
Do you have any questions about rescaling time series data or about this post?
Ask your questions in the comments and I will do my best to answer.
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I assume that this works like a treat for data sets that you can fit into memory … But what about very large data sets that simply would never fit into a single machine. Would you recommend other techniques?
Great question Marek.
I would suggest estimating the parameters required (min/max for normalization and mean/stdev for standardization) and using those parameters to prepare data just in time prior to use in a model.
Does that help?
IMO
If you have kind of stream data, you need to define a range of data to evaluate.
If you just have distributed data, you need to mapreduce.
Hello Jason,
thank you for your example. I am learning Python und Pandas. Why do you need to reshape the Series.values?
# prepare data for standardization
values = series.values
values = values.reshape((len(values), 1))
Bye
Great question, it’s because the sklearn tools prefer a 2D matrix and the series is 1D.
We just need to be explicit in the numpy array about the number of rows and cols and sklearn will then not throw out a warning.
Does that help?
Yep! Thank you Jason 🙂
In relation to this topic, how do you usually handle variables of mixed types (e.g. a mixture of categorical, continuous, ordinal variables) in a classifier (e.g. logistic regression, SVM, etc.)? I first perform dummy coding on categorical variables, followed by mixing them with the other variables (after normalizing them to [0, 1]); not sure if this is the best practice. On the other hand, the same question for applying clustering algorithms (say, k-means, spectral clusterings). Thank you.
Hi Barnett, yes exactly as you describe.
I try integer encodings if there is an ordinal relationship.
For categorical variables, I use dummy (binary) variables.
I try to make many different views/perspectives of a prediction problem, including transforms, projections and feature selection filters. I then test them all on a suite of methods and see which representations are generally better at exposing the structure of the problem. While that is running, I do the traditional careful analysis, but this automated method is often faster and results in non-intuitive results.
I was not able to run this using the data set as is. In the csv file, there is a footer with 3 columns and some data contains questions marks. However, after removing this and replacing it works )
Thanks for the tip Magnus.
Yes, the tutorial does assume a well-formed CSV file.
A raw download from DataMarket does contain footer info that must be deleted.
What is the mathmatical function to denormalize if the function
y = (x – min) / (max – min) is our normalize function.
solve foe x
Thank you for the nice tutorial.
I wonder how you would normalize the standard deviation for replicate measurements?
Let’s assume that we have three measurements for each day instead of only one and that you would want to plot the temperature normalized to its mean as a time series for a single month. Would the standard deviation for each day have to be normalized as well?
Great question,
Generally, this is a problem specific question and you can choose the period over which to standardize or normalize.
I would prefer to pick min/max or mean/stdev that are suitable for the entire modeling period per variable.
Try other approaches, and see how they fair on your dataset.
Let’s say I have a time series and normalize the data in the range 0,1. I train the model and run my predictions in real time. Later, an “extreme event” occur with values higher than the max value in my training set. The prediction for that event might then saturate, giving me a lower forecast compared to the observation. How to deal with this?
I suppose one possibility is to use e.g. extreme event analysis to estimate a future max value and use this as my max value for normalization. However, then my training data will be in a narrower range, e.g. 0 to 0.9. Of course, I can do this anyway without an analysis. My question is related to e.g. forecasts of extreme weather phenomena or earthquakes etc.
How is it possible to forecast, accurately, an extreme event, when we don’t have this in the training set? After all, extreme events are often very important to be able to forecast.
Great question Magnus.
This is an important consideration when scaling.
Standardization will be more robust. Normalization will require you to estimate the limits of expected values, to detect when new input data exceeds those limits and handle that accordingly (report an error, clip, issue a warning, re-train the model with new limits, etc.).
As for the “best” thing to do, that really depends on the domain and your project requirements.
What about if the data is highly asymmetric with a negative (or positive) skew, and therefore far from being Gaussian?
If I choose a NN, I assume that my data should be normalised. If I standardise the data it will still be skewed, so when using a NN is it better to transform the data to remove the skew? Or is neural networks a bad choice with skewed data?
Consider a power transform like a box-cox to make the data more Gaussian, then standardize.
I don’t think this way of scaling time series works. For instance, the standardization method in python calculates the mean and standard deviation using the whole data set you provide. But in reality, we won’t have that. As a result, scaling this way will have look ahead bias as it uses both past and future data to calculate the mean and std. So we need to figure out a way to calculate the mean and the std based on the data we have at a given point in time.
Yes, you might be better off estimating the coefficients needed for scaling based on domain knowledge.
What if the code shows “NO module named sklearn.preprocessing”. I already downloaded scipy 0.18.1 version.
It sounds like sklearn is not installed.
Hi Jason, thanks for your great work.
I have a question: how to properly normalize train, validation and test dataset for trading forex? Those datasets are splitted in order of time, so training is before validation that is before test. I don’t want to use future data for normalization since i don’t have to use future information for preprocessing my data…
Now my results using Reinforcement Learning are not great but i think that great part of the work is done by normalize well my datasets.
My strategy now is doing standardization for every episode(one week of data) of training/test/validation with mean and standard deviation of 3 weeks before…
I would recommend estimating the min/max or mean/stdev from training data and domain knowledge and scaling the data manually.
Thanks for the reply. It’s exactly what i’m doing now. Probably there is no other standard possibility than domain knowledge. Would be interesting to find something standard but it seems impossible.
Thank you for good information!
And.. Can i standardize & normalize a nominal(categorical) variable?
I’m glad you found it useful.
You can encode a nominal variable as integers and then use a one hot encoding.
What if all my time series have a trend upwards. Or even worse what if half of my time series have a trend upwards and the rest half of them have a trend downwards?
Would detrending the time series be helpful? (“removing” the slope and subtracting the mean)
If yes, what kind of detrending would be useful? Should I detrend each sequence separately from all the others or detrend them all together or detrend them in groups?
But this does not seem like normalization/standardization because you cannot revert the process if you do it separately for each sequence you have lost information.
What are your thoughts on this approach? Thank you
Yes, treat each series separately, make each stationary.
Use differencing:
http://machinelearningmastery.com/difference-time-series-dataset-python/
But if you normalize by this way, you are using information from future, therefore the model will overfit. Let’s say you normalize the columns to train my model with the mean and the std of their content, but a new input data cannot be normalized following the old criteria, and neither the new one (the mean and the std of the last N rows) because of the trend, or the std…
What about using this instead: http://scikit-learn.org/stable/modules/preprocessing.html#custom-transformers
Yes, I would recommend estimating the normalization coefficients (min/max) using training data only.
Ok, that makes sense. But even with your training data you’d have the same problem: working with a timeseries dataset, if you normalize/scale using the min/max of whole training dataset, you are taking into account values of future data as well, and in a real prediction you won’t have this information, right?
Moreover, how would you normalize/scale future data? Using the same saved preprocessing model of your training data, or creating a new MinMaxScaler() using the last N rows? What if the new values are slightly different of the training ones?
That’s why I’ve posted the log1p solution, which is the same as log(1+x) and which will thus work on (-1;∞). Or what about this one:
http://timvieira.github.io/blog/post/2014/02/11/exp-normalize-trick/
I think would be very interesting that you pointing this out in the post because I’m afraid it can affect dramatically to model’s accuracy…
This was my point. If normalizing you need to select min/max values based on available data and domain knowledge (to guestimate the expected max/min that will ever be seen).
Same idea with estimating the mean/stdev for standardization.
If evaluating a model, these estimates should be drawn from the training data only and/or domain expertise.
I hope that is clearer.
I think the best approach would be the following:
scaler = StandardScaler() # or MinMaxScaler()
scaler_train = scaler.fit(X_train)
X_train = scaler_train.transform(X_train)
scaler_full = scaler.fit(X) # X_train + X_test
X_test = scaler_full.transform(X_test)
Further reading:
https://www.researchgate.net/post/If_I_used_data_normalization_x-meanx_stdx_for_training_data_would_I_use_train_Mean_and_Standard_Deviation_to_normalize_test_data
https://stats.stackexchange.com/questions/267012/difference-between-preprocessing-train-and-test-set-before-and-after-splitting/270284
http://sebastianraschka.com/Articles/2014_about_feature_scaling.html
Hi Jason, thank you for your post.
I have question.
I have timestamp and system-up-time where up-time is # of hrs system has been up in its lifetime.
Now I have to predict system failure based on the age of the system or system-up-time hrs.
# of failures might grow based on the age of the system or how many hrs its been running.
I have limited training data and the max up-time hrs in the training data is 1,000 hrs and age is 1,200 hrs. But in real time it could go beyond 100,000 hrs and age could go beyond 150,000 hrs.
How do I standardize timestamp and up-time hrs.
Consider looking into survival analysis:
https://en.wikipedia.org/wiki/Survival_analysis
Hi Jason,
Thank you for your comprehensive explanation. I have a noisy time series with missing data and outliers. Not even sure if the data is normal. Does standardization works in my case? My sample size can be quite big. Looking forward to your feedback.
Hmm, perhaps not. But I generally recommend testing and getting data rather than using opinions/advice. I’m often wrong.
Perhaps try to patch the missing data and trim the outliers as secondary steps and see if that impacts model skill.
Let me know how you go.
Hi! I did not manage to max the MinMaxScaler work for my tensors of rank 5. Someone knows how to scale across all dimensions of a tensor? I guess you could flatten it scale it and then reshape it back. but I prefer not to get lost with all the dimensions. What I did for now is to make my own normalize to scale numpy tensors if someone bumps into the same problem.
class normalize():def fit(self, train, interval=(0,1)):
self.min, self.max = train.min(), train.max()
self.interval = interval
return self
def transform(self, train, val, test):
def trans(x):
y = ((self.interval[1]-self.interval[0])*x + \
(self.interval[0]*self.max-self.interval[1]*self.min)) / \
(self.max-self.min)
return y
train_norm = trans(train)
val_norm = trans(val)
test_norm = trans(test)
return train_norm, val_norm, test_norm
def inverse_transform(self, train_norm, val_norm, test_norm):
def inv_trans(y):
x = ((self.max-self.min)*y + \
(self.interval[1]*self.min-self.interval[0]*self.max)) / \
(self.interval[1]-self.interval[0])
return x
train = inv_trans(train_norm)
val = inv_trans(val_norm)
test = inv_trans(test_norm)
return train, val, test
The sklearn tools will apply across all columns of your data.
Hi,
Would it also be a valid approach to convert the time series to unit vectors before a machine operation such as clustering?
Thanks,
Joel
Perhaps, try it and see how it impacts model skill.
Hi @Jason,
1. What’s difference in Normalize and Standardize time-series data with other data?
2. Should we Normalize and Standardize or both to the time-series data?
3. Can you please update this very good tutorial with “How to save data Normalize and
Standardize and reuse same for test data”?
Thanks,
Khalid
No difference, other than you might need to account for an increasing level (trend).
Depends on the algorithm and the data, try both and evaluate the effects.
You can save a series using NumPy or Pandas.
Hi Jason,
I just would like to ask if the normalization of data only happens during training? During testing where no output data is provide do I need still to normalize data? Thank you.
Great question.
Any transforms performed to data prior to training must also be performed to test or any other data.
What kind of preprocessing required for traffic flow analysis based on time series data? I am referring Highways agency network journey time and traffic flow data of 9 fields namely Link reference, Link description, Date, Time Period, Average journey time, Average speed, Data Quality, Link Length, Flow etc. Which techniques to try for preprocessing such data of 3 months Jan – March 2015? Thanks
Perhaps try a few methods and see what results in models with better skill.
Have you tried using the (from sklearn.preprocessing import Imputer) function?
Is it better than this or are they the same?
I have an example of using the Imputer here:
https://machinelearningmastery.com/handle-missing-data-python/
Choose the method that you prefer.
On what basis we choose data scaling method(Normalization/Standardization)?
Standardization is for gaussian data.
Normalization can be used for gaussian or non-gaussian.
Scaling is appropriate for methods that use distances or weightings.
If in doubt, compare model skill with and without scaling.
using the MinMaxScaler model in sklearn to normalize the features of a model during the training session, one can save the scaler and load it later from a file in forecasting session, for example, is that Possible? is that a good solution
https://stackoverflow.com/questions/41993565/save-minmaxscaler-model-in-sklearn
Is there another more efficient way?
I would recommend saving the coefficients or saving the object via pickle.
Thanks for your advice
Hi Jason, great article.
One question that always bugs me, what is the proper way to standardize data in case when you have multiple instances with multiple parameters each? For example, you are measuring M parameters (time series) for N devices, during T seconds, and you want to perform some analysis/ML on these devices. How would you standardize the data in this case?
Thanks!
It comes down to how you want to model the data, e.g. one model per sensor, group of sensors, all sensors.
Standardize by variable and model.
Does that help?
Hi Jason,
Thank you for your response. So the idea is to have one model which includes values of all parameters (sensors) to be able to integrate the relation between parameters as well.
When you say standardize by variable and model, what would that mean in this case? Find Min/Max or Mean/StdDev for all values of a single parameter (belonging to different instances)? So one statistic for all values of a single parameter for all instances? Standardizing parameter per “per-dataset” and not “per-instance”?
Thanks again!
Yes, each variable and model, if you choose to model the sensors separately.
Hi
Thank you for the post, it was really helpful.
I am using sklearn’s Normalizer for normalization of data before prediction. How do we revert back the predicted data to the original values?
Thank you
Call the invert_transform() function.
Hi Jason,
How would you normalize columns in a dataframe that contains NaN values?
Thanks,
Tom
Ignore/replace/remove/impute the nan values.
Hello Jason,
Are you normalizing/standardizing only the value field? Or the time series as well?
Also, I ran my standarzing/normalizing on my value field and it reported back the exact same histogram when plotted, is this not meant to normalize the data??
Thanks
For univariate data, we prepare the entire series.
The shape will be the same, but the min/max will be different when normalizing and standardizing a Gaussian.
Hi Jason
Thanks for the great tutorial. I keep getting the error “cannot reshape array of size 7300 into shape (3650,1).
I get this error with other sample datasets I tried.
Is there something that I am missing?
Perhaps this tutorial will help you understand numpy arrays:
https://machinelearningmastery.com/index-slice-reshape-numpy-arrays-machine-learning-python/
Hi Jason.
I have a n*n*n matrix contain a sample, time-steps, features for the stock market.
How would you Standardize Time Series Data in n*n dimension and prepare for LSTM?
Thanks,
Not sure what your data dimensions represent. Generally, rescale each series, e.g. series-wise.
Hello Jason,
Great tutorial. I have a question though, there can be multiple outliers which can affect mean and in turn affect both normalization as well as standardization, so why don’t we use median? as it is less prone to outliers and will produce more robust results?
Sounds like a good idea for Gaussian distributed data with outliers.
Should we also normalise the output (y)? Or is it good to have only the inputs (X) normalised?
Yes, the output or target variable should be standardized or normalized.
what about Date will it get normalized automatically?
Date is removed.
Great article.
Jason, one question regarding the difference between the results achied after applying the standartization and stationarity transformation. isn’t it true that data is deemed stationary if it is centerd around the mean and the variation is stable…which , as it appears , is the result of the standartization transformation
Thanks in advance for the clarification and sorry for the silly questions )
It is stationary if it does not have a systematic structure, like trend or seasonality:
https://machinelearningmastery.com/time-series-data-stationary-python/
thanks for another great article.
why not “scaling down” but normalizing?
x………………….y
if we have negative values in an array [5, -7, -3, 6, 7, 9, 10]
after scaling down…………………………..[..-0.7……………….1]
if i normalize…………………………………..[…..0………………..1]
in scaling down I keep the weight of -7 (being -0.7) to pull my Fx to West/negative direction
in normalizing -7 becomes 0 and 10 becomes 1….
-7 will have no weight in
Yes, often very few values are on the boundary. If you have many values on the boundarty, perhaps normalize to a different range.
-7 will have no weight in my equation -0.7x vs 0.x….Meanwhile 10y will be 1.y pulling all the way to East…
Yes, perhaps just standardize or shift the normalized range to [-1, 1] or [0.1, 0.9] and see if it makes a difference to the model skill.
Hi Jason
Its me again. your avid follower.
Does a predicted values (target values) using normalise feature variables is a normalise value? or do we need to transpose the predicted value ?
Thanks again.
What does “transpose the predicted value” mean?
Hi Jason,
Sorry to make you confuse. What I mean when we make prediction on the hold out target value not known to us, and our predictor or features variables are normalise. Does the output of our prediction are normalise value and we need to inverse before submitting to the competition?
Thank you Jason.
Yes.