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Determining the Number of Regimes in Markov-Switching VAR and VMA Models


  • Maddalena Cavicchioli

    () (Advanced School of Economics, Department of Economics, University Of Venice C� Foscari)


We give stable finite order VARMA(p*; q*) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p* and q* are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our class of time series include every M-state Markov switching multivariate moving average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997), and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoian (2001) for our classes of dynamic models. Data simulations and an application on foreign exchange rates complete the paper.

Suggested Citation

  • Maddalena Cavicchioli, 2013. "Determining the Number of Regimes in Markov-Switching VAR and VMA Models," Working Papers 2013:03, Department of Economics, University of Venice "Ca' Foscari".
  • Handle: RePEc:ven:wpaper:2013:03

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    References listed on IDEAS

    1. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    2. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    3. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
    4. Zacharias Psaradakis & Nicola Spagnolo, 2003. "On The Determination Of The Number Of Regimes In Markov-Switching Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 237-252, March.
    5. Zacharias Psaradakis & Nicola Spagnolo, 2006. "Joint Determination of the State Dimension and Autoregressive Order for Models with Markov Regime Switching," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 753-766, September.
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    More about this item


    Second-order stationary time series; VMA models; VAR models; State-Space models; Markov chains; changes in regime; regime number.;

    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
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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