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Duration Dependent Markov-Switching Vector Autoregression: Properties, Bayesian Inference, Software and Application


  • Matteo Pelagatti


Duration dependent Markov-switching VAR (DDMS-VAR) models are time series models with data generating process consisting in a mixture of two VAR processes. The switching between the two VAR processes is governed by a two state Markov chain with transition probabilities that depend on how long the chain has been in a state. In the present paper we analyze the second order properties of such models and propose a Markov chain Monte Carlo algorithm to carry out Bayesian inference on the model’s unknowns. Furthermore, a freeware software written by the author for the analysis of time series by means of DDMS-VAR models is illustrated. The methodology and the software are applied to the analysis of the U.S. business cycle.

Suggested Citation

  • Matteo Pelagatti, 2003. "Duration Dependent Markov-Switching Vector Autoregression: Properties, Bayesian Inference, Software and Application," Working Papers 20051101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica, revised Nov 2005.
  • Handle: RePEc:mis:wpaper:20051101

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    References listed on IDEAS

    1. Sichel, Daniel E, 1991. "Business Cycle Duration Dependence: A Parametric Approach," The Review of Economics and Statistics, MIT Press, vol. 73(2), pages 254-260, May.
    2. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    3. Durland, J Michael & McCurdy, Thomas H, 1994. "Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 279-288, July.
    4. Francis X. Diebold & Glenn Rudebusch & Daniel Sichel, 1993. "Further Evidence on Business-Cycle Duration Dependence," NBER Chapters,in: Business Cycles, Indicators and Forecasting, pages 255-284 National Bureau of Economic Research, Inc.
    5. Diebold, Francis X & Rudebusch, Glenn D, 1990. "A Nonparametric Investigation of Duration Dependence in the American Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 596-616, June.
    6. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
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    Cited by:

    1. Marjan Petreski, 2010. "An Overhaul of a Doctrine: Has Inflation Targeting Opened a New Era in Developing-country Peggers?," FIW Working Paper series 057, FIW.
    2. Matteo Pelagatti & Valeria Negri, 2008. "Milan’s Cycle as an Accurate Leading Indicator for the Italian Business Cycle," Working Papers 20080601, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
    3. Marjan Petreski, 2011. "A Markov Switch to Inflation Targeting in Emerging Market Peggers with a Focus on the Czech Republic, Poland and Hungary," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 3, pages 57-75.

    More about this item


    Markov-switching; business cycle; Gibbs sampler; duration dependence; vector autoregression;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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