时间序列多步预测的一般方法

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There are at least four commonly used strategies for making multi-step forecasts.
They are:
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) = model2(obs(t-2), obs(t-3), ..., obs(t-n))

2.Recursive Multi-step Forecast Strategy.
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-1), ..., 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 Multi-step Forecast 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-1), ..., obs(t-n))

Combining the recursive and direct strategies can help to overcome the limitations of each.

4.Multiple Output Forecast 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.