9.1 Why, when and how to combine forecasts
9.1.1 Why do we combine forecasts?
If you have different approaches and you know that they are both contribution with some valuable information, making discrete selection, hence one forecast method, will permanently exclude the information from the other model.
Hence, by combining methods, we are able to collect more information in the model, that would not be captured with only using a single model.
9.1.2 When to combine forecasts?
Combining models is usually applied with methods, that are not from the same group, e.g., ARIMA and ARIMA, but instead e.g., ARIMA and exponential smoothing, as it approaches data in two different ways.
Also, you often want to include different models that contain different information, to capture different perspectives, e.g., in terms of data analysis or in terms of different variables.
9.1.3 How to combine forecasts?
See an example in section 9.2.1
How to combine forecasts?
- You assign weights to the forecasts, hence:
\[\begin{equation} F_{combined}=w_1F_1+w_2F_2 \tag{9.1} \end{equation}\]
How to find the weights? The following are different methods;
- Nelson combination method! Here there are restrictions on the weights (How much? I think to one.)
- Granger-Ramanathan - it has shown to be better than Nelson combination method.
- This has no restrictions, the weights must not sum to 1.
- Time-varying weights: for each period of time, we are calculate the weight is each period of time.
Diebold-Mariano test
Are MSE’s of different forecasts equal?
- Says that, we are going to compare two forecasts and see if there is a difference in performance or not.
- Hence: H0: MSE1=MSE1
- This use Diebold-Mariano test statistic
- If we are not able to reject H0, then there
- This use Diebold-Mariano test statistic
- Hence: H0: MSE1=MSE1
- Rule of thumb, if you have two different methods yielding the same result, then you can make a DM test to see if the MSEs are actually different, if not, then you should consider combining
- But notice, if the models are the same approach, then you should probably just pick one