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

Maddalena Cavicchioli ()
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Maddalena Cavicchioli: University of Modena and Reggio Emilia

Statistical Methods & Applications, 2020, vol. 29, issue 1, No 6, 129-139

Abstract: Abstract 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.

Keywords: Fisher information matrix; Matrix differential calculus; Markov switching VARMA process; 62B10; 62F12; 62M10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-019-00472-y

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