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Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy

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  • Maddalena Cavicchioli

Abstract

In this work we consider multivariate autoregressions subject to Markovian changes in regime. Estimation methods and filtering techniques for such processes are well established in the literature as well as the asymptotic distribution of the maximum likelihood estimators. Assuming the conditions under which the standard asymptotic distribution theory holds, the likelihood ratio (LR) has the null distribution. We give explicit formulae for LR tests of various hypotheses of interest in the context of Markov switching VAR models. The proposed LR statistic has a rather simple form as it reduces to the use of the estimated unrestricted and restricted variance-covariance matrices. Moreover, we derive simple expressions for some information criteria to address the question of linearity versus nonlinearity. An application to Italian macroeconomic data gives new insights on the number of regimes and the dynamics characterizing the economy. Copyright Società Italiana degli Economisti (Italian Economic Association) 2015

Suggested Citation

  • Maddalena Cavicchioli, 2015. "Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(3), pages 315-332, November.
    • Handle: RePEc:spr:italej:v:1:y:2015:i:3:p:315-332
    DOI: 10.1007/s40797-015-0015-6
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    Cited by:

    1. Cavicchioli, Maddalena, 2024. "A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    2. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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    More about this item

    Keywords

    Markov-switching VAR models; Filtering; Smoothing ; MLE; LR tests; Information criteria; Italian economy; C01; C32; C51;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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