Learning from Forecast Errors: A New Approach to Forecast Combinations

TL;DR

This paper introduces the Factor Graphical Model (FGM), a novel method for forecast combination that separates common and idiosyncratic errors, improving forecast accuracy in macroeconomic series.

Contribution

The paper develops FGM, a new approach leveraging factor structure and sparsity in forecast errors, with proven consistency and superior empirical performance.

Findings

FGM outperforms equal-weighted and non-factor graphical models in macroeconomic forecasting.

The method is supported by theoretical proof of consistency.

Extensive simulations validate the effectiveness of FGM.

Abstract

Forecasters often use common information and hence make common mistakes. We propose a new approach, Factor Graphical Model (FGM), to forecast combinations that separates idiosyncratic forecast errors from the common errors. FGM exploits the factor structure of forecast errors and the sparsity of the precision matrix of the idiosyncratic errors. We prove the consistency of forecast combination weights and mean squared forecast error estimated using FGM, supporting the results with extensive simulations. Empirical applications to forecasting macroeconomic series shows that forecast combination using FGM outperforms combined forecasts using equal weights and graphical models without incorporating factor structure of forecast errors.