Hedging Forecast Combinations With an Application to the Random Forest

ArXiv ID: 2308.15384 “View on arXiv”

Authors: Unknown

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.

Keywords: forecast combination, mean-variance portfolio, portfolio construction, weighted random forests, out-of-sample performance, General / Methodological

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like mean-variance optimization and convex optimization with L1 constraints, demonstrating high mathematical density. It also validates the method on 14 benchmark datasets with out-of-sample performance metrics, showing solid empirical rigor though not as extensive as full-scale trading backtests.

  flowchart TD
    A["Research Goal:<br>Optimal Forecast Combination"] --> B["Identify Problem:<br>Mean-Variance Portfolio Analogy"]
    B --> C["Methodology:<br>Estimate Population Mean & Covariance"]
    C --> D["Computational Process:<br>Compute Optimal Hedge Weights"]
    D --> E["Data Input:<br>14 Datasets for Weighted Random Forests"]
    E --> F["Application:<br>Combine Tree Forecasts"]
    F --> G["Outcome:<br>Improved Out-of-Sample Performance"]
    G --> H["Key Finding:<br>Hedging Weights Outperform Standard Methods"]