New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings

TL;DR

This paper develops a theoretical foundation for tests comparing forecast accuracy in factor-augmented regressions, especially accounting for weak factor loadings, which enhances their practical applicability.

Contribution

It provides the first theoretical justification for forecast accuracy tests in factor-augmented models with weak loadings, extending existing methods.

Findings

Theoretical validation of forecast accuracy tests in weak-loading scenarios

Incorporation of weak factor loadings into forecast comparison theory

Enhanced understanding of forecast test performance with weak factors

Abstract

We provide the theoretical foundation for the recent tests of equal forecast accuracy and encompassing by Pitarakis (2023) and Pitarakis (2025), when the competing forecast specification is that of a factor-augmented regression model. This should be of interest for practitioners, as there is no theory justifying the use of these simple and powerful tests in such context. In pursuit of this, we employ a novel theory to incorporate the empirically well-documented fact of homogeneously/heterogeneously weak factor loadings, and track their effect on the forecast comparison problem.