# How can a combination of Random Forest and Linear Regression improve a time series forecast?

I attended a presentation by some consultants for retail demand forecasting who showed that for one of their clients, they were able to improve their demand forecasting by replacing a traditional time series based demand forecasting system (presumably using ARIMA or ETS) with one that had the following structure:

Time Series forecast $\rightarrow$ Linear Regression $\rightarrow$ Random Forest

Of course they refused to reveal any details, saying that it was proprietary information.

Assuming they are feeding additional explanatory variables to the model besides the time series, why does this approach work better than using a time series model with external regressors? Or are they just using the RF to ensemble a bunch of different forecasts?

Additionally, what purpose would the linear regression in the middle serve? Isn't it kind of redundant given the RF that comes after it?

• Maybe it's a linear regression for time series and/or using also some supplementary explanatory variables which aren't time-dependent. – paf Apr 26 '18 at 19:53