Time series forecasting is typically discussed where only a one-step prediction is required.
What about when you need to predict multiple time steps into the future?
Predicting multiple time steps into the future is called multi-step time series forecasting. There are four main strategies that you can use for multi-step forecasting.
In this post, you will discover the four main strategies for multi-step time series forecasting.
After reading this post, you will know:
- The difference between one-step and multiple-step time series forecasts.
- The traditional direct and recursive strategies for multi-step forecasting.
- The newer direct-recursive hybrid and multiple output strategies for multi-step forecasting.
Let’s get started.
Generally, time series forecasting describes predicting the observation at the next time step.
This is called a one-step forecast, as only one time step is to be predicted.
There are some time series problems where multiple time steps must be predicted. Contrasted to the one-step forecast, these are called multiple-step or multi-step time series forecasting problems.
For example, given the observed temperature over the last 7 days:
A single-step forecast would require a forecast at time step 8 only.
A multi-step may require a forecast for the next two days, as follows:
There are at least four commonly used strategies for making multi-step forecasts.
- Direct Multi-step Forecast Strategy.
- Recursive Multi-step Forecast Strategy.
- Direct-Recursive Hybrid Multi-step Forecast Strategies.
- Multiple Output Forecast Strategy.
Let’s take a closer look at each method in turn.
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1. Direct Multi-step Forecast Strategy
The direct method involves developing a separate model for each forecast time step.
In the case of predicting the temperature for the next two days, we would develop a model for predicting the temperature on day 1 and a separate model for predicting the temperature on day 2.
prediction(t+1) = model1(obs(t-1), obs(t-2), ..., obs(t-n))
prediction(t+2) = model1(obs(t-2), obs(t-3), ..., obs(t-n))
Having one model for each time step is an added computational and maintenance burden, especially as the number of time steps to be forecasted increases beyond the trivial.
Because separate models are used, it means that there is no opportunity to model the dependencies between the predictions, such as the prediction on day 2 being dependent on the prediction in day 1, as is often the case in time series.
2. Recursive Multi-step Forecast
The recursive strategy involves using a one-step model multiple times where the prediction for the prior time step is used as an input for making a prediction on the following time step.
In the case of predicting the temperature for the next two days, we would develop a one-step forecasting model. This model would then be used to predict day 1, then this prediction would be used as an observation input in order to predict day 2.
prediction(t+1) = model(obs(t-1), obs(t-2), ..., obs(t-n))
prediction(t+2) = model(prediction(t-1), obs(t-2), ..., obs(t-n))
Because predictions are used in place of observations, the recursive strategy allows prediction errors to accumulate such that performance can quickly degrade as the prediction time horizon increases.
3. Direct-Recursive Hybrid Strategies
The direct and recursive strategies can be combined to offer the benefits of both methods.
For example, a separate model can be constructed for each time step to be predicted, but each model may use the predictions made by models at prior time steps as input values.
We can see how this might work for predicting the temperature for the next two days, where two models are used, but the output from the first model is used as an input for the second model.
prediction(t+1) = model1(obs(t-1), obs(t-2), ..., obs(t-n))
prediction(t+2) = model2(prediction(t-1), obs(t-2), ..., obs(t-n))
Combining the recursive and direct strategies can help to overcome the limitations of each.
4. Multiple Output Strategy
The multiple output strategy involves developing one model that is capable of predicting the entire forecast sequence in a one-shot manner.
In the case of predicting the temperature for the next two days, we would develop one model and use it to predict the next two days as one operation.
prediction(t+1), prediction(t+2) = model(obs(t-1), obs(t-2), ..., obs(t-n))
Multiple output models are more complex as they can learn the dependence structure between inputs and outputs as well as between outputs.
Being more complex may mean that they are slower to train and require more data to avoid overfitting the problem.
See the resources below for further reading on multi-step forecasts.
- Machine Learning Strategies for Time Series Forecasting, 2013
- Recursive and direct multi-step forecasting: the best of both worlds, 2012 [PDF]
In this post, you discovered strategies that you can use to make multiple-step time series forecasts.
Specifically, you learned:
- How to train multiple parallel models in the direct strategy or reuse a one-step model in the recursive strategy.
- How to combine the best parts of the direct and recursive strategies in the hybrid strategy.
- How to predict the entire forecast sequence in a one-shot manner using the multiple output strategy.
Do you have any questions about multi-step time series forecasts, or about this post? Ask your questions in the comments below and I will do my best to answer.
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