Testing Clustered Equal Predictive Ability with Unknown Clusters

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 $\chi$ 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.