Testing for clustering under switching

I refine the test for clustering of Patton and Weller (2022) to allow for cluster switching. In a multivariate panel setting, clustering on timeaverages produces consistent estimators of means and group assignments. Once switching is introduced, we lose the consistency. In fact, under switching the time-averaged k-means clustering converges to equal, indistinguishable means. This causes the test for a single cluster to lose power under the alternative of multiple clusters. Power can be regained by clustering the N times T observations independently and carefully subsampling the time dimension. When applied to the empirical setting of Bonhomme and Manresa (2015) of an autoregression of democracy in a panel of countries, we are able to detect clusters in the data under noisier conditions than the original test.