Markov Switching models have had increasing success in time series analysis due to their ability to capture the existence of unobserved discrete states in the dynamics of the variables under study. This result is generally obtained thanks to the inference on states derived from the so--called Hamilton filter. One of the open problems in this framework is the identification of the number of states, generally fixed a priori; it is in fact impossible to apply classical tests due to the problem 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 (in a nonparametric way) independently of the data generation process and that the indicators we use are present in most statistical packages. A final application on real data completes the analysis.

翻译：马尔可夫切换模型在时间序列分析中日益成功，因其能够捕捉研究对象动态中未观测的离散状态存在性。这一结果通常得益于基于汉密尔顿滤波器推导出的状态推断。该框架中的开放性问题之一在于状态数的识别——通常需事先固定，由于仅有备择假设下存在的冗余参数问题，经典检验方法无法适用。本文通过蒙特卡洛模拟证明：模糊聚类能够再现基于汉密尔顿滤波器得到的参数化状态推断，且聚类中用于确定分组数的典型指标可用于识别该框架下的状态数。该过程应用极为简便，因其以非参数方式独立于数据生成过程运行，且所用指标常见于多数统计软件包。最终对真实数据的应用完善了分析。