Testing Clustered Equal Predictive Ability with Unknown Clusters

Abstract

This paper proposes a selective inference procedure for testing equal predictive ability in panel data settings with unknown heterogeneity. The framework allows predictive performance to vary across unobserved clusters and accounts for the data-driven selection of these clusters using the Panel Kmeans Algorithm. A post-selection Wald-type statistic is constructed, and valid $p$-values are derived under general forms of autocorrelation and cross-sectional dependence in forecast loss differentials. The method accommodates conditioning on covariates or common factors and permits both strong and weak dependence across units. Simulations demonstrate the finite-sample validity of the procedure and show that it has very high power. An empirical application to exchange rate forecasting using machine learning methods illustrates the practical relevance of accounting for unknown clusters in forecast evaluation.