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.

A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process / Cavicchioli, M.. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - 29:1(2020), pp. 129-139. [10.1007/s10260-019-00472-y]

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

Cavicchioli M.
2020

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.
2020
25-mag-2019
29
1
129
139
A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process / Cavicchioli, M.. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - 29:1(2020), pp. 129-139. [10.1007/s10260-019-00472-y]
Cavicchioli, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1179638
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