We give stable finite-order vector autoregressive moving average (p*; q*) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p* and q* are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving-average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our classes of time series include every M-state Markov switching multi-variate moving-average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997) and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoïan (2001) for our classes of dynamic models. A Monte Carlo experiment and an application on foreign exchange rates complete the article.

Determining the Number of Regimes in Markov-Switching VAR and VMA Models / Cavicchioli, Maddalena. - In: JOURNAL OF TIME SERIES ANALYSIS. - ISSN 0143-9782. - STAMPA. - 35:2(2014), pp. 173-186. [10.1002/jtsa.12057]

Determining the Number of Regimes in Markov-Switching VAR and VMA Models

CAVICCHIOLI, MADDALENA
2014

Abstract

We give stable finite-order vector autoregressive moving average (p*; q*) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p* and q* are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving-average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our classes of time series include every M-state Markov switching multi-variate moving-average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997) and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoïan (2001) for our classes of dynamic models. A Monte Carlo experiment and an application on foreign exchange rates complete the article.
2014
35
2
173
186
Determining the Number of Regimes in Markov-Switching VAR and VMA Models / Cavicchioli, Maddalena. - In: JOURNAL OF TIME SERIES ANALYSIS. - ISSN 0143-9782. - STAMPA. - 35:2(2014), pp. 173-186. [10.1002/jtsa.12057]
Cavicchioli, Maddalena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1040116
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