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HIGHER ORDER MOMENTS OF MARKOV SWITCHING VARMA MODELS

Published online by Cambridge University Press:  28 October 2016

Maddalena Cavicchioli
Maddalena Cavicchioli*
Affiliation:
University of Modena and Reggio Emilia
*
*Address correspondence to Maddalena Cavicchioli, Department of Economics “Marco Biagi,” University of Modena and Reggio Emilia, Viale Berengario 51, 41121 Modena, Italy; e-mail: maddalena.cavicchioli@unimore.it.
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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 Zakoïan (2001, Econometric Theory 18, 815–818) and relates with the concepts of multivariate skewness and kurtosis proposed by Mardia (1970, Biometrika 57, 519–530), Móri, Rohatgi, and Székely (1993, Theory of Probability and its Applications 38, 547–551), and Kollo (2008, Journal of Multivariate Analysis 99, 2328–2338). 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.

Type
MISCELLANEA
Information
Econometric Theory , Volume 33 , Issue 6 , December 2017 , pp. 1502 - 1515
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

I am very grateful to Professor Zakoïan (CREST, France) who suggested the interesting problem of computation of higher order moments for MS VARMA models during my PhD defence, held in March 2014 at the University of Venice, Italy. I would like to thank the Editor of the journal, Professor Peter C.B. Phillips, the Co-Editor, Professor Giuseppe Cavaliere, and the three anonymous referees for their constructive comments and useful suggestions which were most valuable for improvement of the final version of the paper.

References

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