Testing Clustered Equal Predictive Ability with Unknown Clusters

Abstract

We develop tests of clustered equal predictive ability (C-EPA) in panels where the clusters are unknown and estimated by the Panel Kmeans algorithm. To address the challenge of testing hypotheses that depend on data-driven clusters, we adopt a selective conditional inference framework. Specifically, we first derive a Wald-type test for pairwise equality and show that the limiting distribution of its square root conditional on the estimated clusters is that of a truncated $\ddot{I}‡$ variable. We characterize the associated truncation set by quadratic inequalities in the data space. Then, for the C-EPA hypothesis, we propose a $p$-value combination method by aggregating the evidence against the pairwise equality and overall EPA null hypotheses. The Monte Carlo results show accurate size control and good finite-sample power of the proposed tests. An empirical application to exchange-rate forecasting, using both traditional time-series models and machine-learning methods, illustrates the practical relevance of our procedure.