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Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets

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  • Haas, Markus
  • Liu, Ji-Chun

Abstract

We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Stationarity conditions are derived, and consistency of the maximum likelihood estimator (MLE) is established under the assumption of Gaussian innovations. A Lagrange Multiplier (LM) test for correct specification of the correlation dynamics is devised, and a simple recursion for computing multi-step-ahead conditional covariance matrices is provided. The theory is illustrated with an application to global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student's t innovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student's t process with correlations which are higher in the turbulent (high-volatility) regime.

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  • Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc15:112855
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    JEL classification:

    • 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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