Hedging Forecast Combinations With an Application to the Random Forest

TL;DR

This paper introduces a novel forecast combination methodology based on a portfolio analogy, optimizing mean-squared error by estimating error statistics, and demonstrates improved performance in ensemble tree models across multiple datasets.

Contribution

It presents a high-level, portfolio-inspired approach for forecast combination that allows negative weights and improves out-of-sample accuracy in ensemble methods.

Findings

Enhanced forecast accuracy over standard methods

Effective in combining tree forecasts in diverse datasets

Supports negative weights for risk hedging

Abstract

This papers proposes a generic, high-level methodology for generating forecast combinations that would deliver the optimal linearly combined forecast in terms of the mean-squared forecast error if one had access to two population quantities: the mean vector and the covariance matrix of the vector of individual forecast errors. We point out that this problem is identical to a mean-variance portfolio construction problem, in which portfolio weights correspond to forecast combination weights. We allow negative forecast weights and interpret such weights as hedging over and under estimation risks across estimators. This interpretation follows directly as an implication of the portfolio analogy. We demonstrate our method's improved out-of-sample performance relative to standard methods in combining tree forecasts to form weighted random forests in 14 data sets.