A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process

  • Maddalena CavicchioliEmail author
Original Paper


We study the asymptotic and exact Fisher information (FI) matrices of Markov switching vector autoregressive moving average (MS VARMA) models. In a related paper (2017), we propose a method to derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model, and use such a matrix to derive the asymptotic covariance matrix of the Gaussian maximum likelihood (ML) estimator of the parameters in the MS VARMA model. In this paper, the exact FI matrix of a Gaussian MS VARMA process is considered for a time series of length T in relation to the exact ML estimation method. Furthermore, we prove that the Gaussian exact FI matrix converges in probability to the asymptotic FI matrix when the sample size T goes to infinity.


Fisher information matrix Matrix differential calculus Markov switching VARMA process 

Mathematics Subject Classification

62B10 62F12 62M10 



Work financially supported by FAR (2017) research Grant of the University of Modena and Reggio Emilia, Italy. We are grateful to the Editor-in-Chief Prof. Tommaso Proietti, and two anonymous referees for their very useful suggestions and remarks which improved the final version of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Economics “Marco Biagi”University of Modena and Reggio EmiliaModenaItaly

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