In this paper we derive matrix formulae in closed form for higher order moments and give sufficient conditions for higher order stationarity of Markov switching VARMA models. We provide asymptotic theory for sample higher order moments which can be used for testing multivariate normality. As an application, we propose new definitions of multivariate skewness and kurtosis measures for such models, and relate them with the existing concepts in the literature. Our work completes the statistical analysis developed in the fundamental paper of Francq and Zakoian (2001) and relates with the concepts of multivariate skewness and kurtosis proposed by Mardia (1970), Mori et al. (1993), and Kollo (2008). Under suitable assumptions, our results imply that the sample estimators of the skewness and kurtosis measures proposed by these authors are consistent and asymptotically normally distributed. Finally, we check our theory statements numerically via Monte Carlo simulations.

Higher order moments of Markov switching VARMA models / Cavicchioli, Maddalena. - In: ECONOMETRIC THEORY. - ISSN 0266-4666. - STAMPA. - 33:6(2017), pp. 1502-1515. [10.1017/S0266466616000438]

Higher order moments of Markov switching VARMA models

CAVICCHIOLI, MADDALENA
2017

Abstract

In this paper we derive matrix formulae in closed form for higher order moments and give sufficient conditions for higher order stationarity of Markov switching VARMA models. We provide asymptotic theory for sample higher order moments which can be used for testing multivariate normality. As an application, we propose new definitions of multivariate skewness and kurtosis measures for such models, and relate them with the existing concepts in the literature. Our work completes the statistical analysis developed in the fundamental paper of Francq and Zakoian (2001) and relates with the concepts of multivariate skewness and kurtosis proposed by Mardia (1970), Mori et al. (1993), and Kollo (2008). Under suitable assumptions, our results imply that the sample estimators of the skewness and kurtosis measures proposed by these authors are consistent and asymptotically normally distributed. Finally, we check our theory statements numerically via Monte Carlo simulations.
2017
33
6
1502
1515
Higher order moments of Markov switching VARMA models / Cavicchioli, Maddalena. - In: ECONOMETRIC THEORY. - ISSN 0266-4666. - STAMPA. - 33:6(2017), pp. 1502-1515. [10.1017/S0266466616000438]
Cavicchioli, Maddalena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1111921
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