Markov Switching models have had increasing success in time series analysisdue to their ability to capture the existence of unobserved discrete states inthe dynamics of the variables under study. This result is generally obtainedthanks 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 numberof states, generally fixed a priori; it is in fact impossible to applyclassical tests due to the problem of the nuisance parameters present onlyunder the alternative hypothesis. In this work we show, by Monte Carlosimulations, that fuzzy clustering is able to reproduce the parametric stateinference derived from the Hamilton filter and that the typical indices used inclustering to determine the number of groups can be used to identify the numberof states in this framework. The procedure is very simple to apply, consideringthat it is performed (in a nonparametric way) independently of the datageneration process and that the indicators we use are present in moststatistical packages. A final application on real data completes the analysis.
On the Relationship between Markov Switching Models and Fuzzy Clustering: a Nonparametric Method to Detect the Number of States
Edoardo Otranto;Luca Scaffidi Domianello
2023-01-01
Abstract
Markov Switching models have had increasing success in time series analysisdue to their ability to capture the existence of unobserved discrete states inthe dynamics of the variables under study. This result is generally obtainedthanks 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 numberof states, generally fixed a priori; it is in fact impossible to applyclassical tests due to the problem of the nuisance parameters present onlyunder the alternative hypothesis. In this work we show, by Monte Carlosimulations, that fuzzy clustering is able to reproduce the parametric stateinference derived from the Hamilton filter and that the typical indices used inclustering to determine the number of groups can be used to identify the numberof states in this framework. The procedure is very simple to apply, consideringthat it is performed (in a nonparametric way) independently of the datageneration process and that the indicators we use are present in moststatistical packages. A final application on real data completes the analysis.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
