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Asymptotic Fisher information matrix of Markov switching VARMA models

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  • Cavicchioli, Maddalena

Abstract

We study the Fisher information (FI) matrix of Markov switching vector autoregressive moving average (MS VARMA) models and derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model. Our result is more general than the available one in the literature for linear VARMA models, which has been recently studied in Bao and Hua (2014), in two respects. First, we treat the variance of the error term in a more general setting rather than considering it as a nuisance parameter. Then, we consider non-trivial intercept in the MS VARMA model. Under general conditions, the asymptotic FI matrix can be used to derive the asymptotic covariance matrix of the Gaussian maximum likelihood estimator of the model parameters. Some examples and numerical applications illustrate the results.

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  • Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:124-135
    DOI: 10.1016/j.jmva.2017.03.004
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    1. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Maddalena Cavicchioli, 2020. "A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 129-139, March.
    3. BenSaïda, Ahmed & Litimi, Houda & Abdallah, Oussama, 2018. "Volatility spillover shifts in global financial markets," Economic Modelling, Elsevier, vol. 73(C), pages 343-353.
    4. Maddalena Cavicchioli, 2020. "Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 61-86, January.
    5. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.

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