On using fuzzy clustering for detecting the number of states in Markov switching models

An open problem of Markov switching models is identifying the number of states, generally fixed a priori; it is impossible to apply classical tests due to the issue of the nuisance parameters present only under the alternative hypothesis. In this work, we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to identify the number of states in this framework. The procedure is very simple to apply, considering that it is performed independently of the data generating process and that the indicators we use are available in most statistical packages. Furthermore, the proposed approach appears to be sufficiently robust to perturbations in the data generating processes. A final application of real data completes the analysis.