Combining Trading Forecasts

Getting a stronger, more robust forecast from multiple forecasts

Imagine you have a few different models that you use to forecast asset returns.
One model tells you that BTC is going up by 0.1% in the next hour, another model tells you it’s going up by 0.2% and yet another model tells you it’s going down by 0.05%.

One way you could combine those forecasts is by just taking the average, in this case 0.0833%.
This is a very naive approach though for multiple reasons.

1. Forecasts can be correlated.
   When you have 5 models all telling you that BTC is going up this doesn’t necessarily mean that the chance of BTC going up is now really high. The 5 models could all be very similar in which case you’d expect them to give a similar forecast most of the time.

2. Not all forecasts are equally good.
   If you have a good model and a bad model you would want to give more weight to the good model.

In this article we will go over different methods that we can use to combine multiple forecasts.

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Table of Conent

1. Multiple Regression

2. Nonlinear Regression and Splines

3. Transforming Predictions

4. Stepwise Regression

5. Best Subsets Regression

6. L0 Penalization

7. Ridge Regression and Lasso Regression

8. Voting and Stacking

9. Bayesian Model Averaging

10. Final Remarks