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, gener-ally fixed a priori; it is impossible to apply classical tests due to the issue of the nuisanceparameters present only under the alternative hypothesis. In this work, we show, by MonteCarlo simulations, that fuzzy clustering is able to reproduce the parametric state inferencederived from the Hamilton filter and that the typical indices used in clustering to determinethe number of groups can be used to identify the number of states in this framework. Theprocedure is very simple to apply, considering that it is performed independently of the datagenerating 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 thedata generating processes. A final application of real data completes the analysis.