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A Nonparametric Bayesian Approach to Detect the Number of Regimes in Markov Switching Models



The literature on Markov switching models is increasing and producing interesting results both at theoretical and applied levels. Most often the number of regimes, i.e., of data generating processes, is considered known; this strong hypothesis is adopted to somewhat bypass the nuisance parameter problem which affects hypothesis testing for the number of regimes. In this paper we take the view that some results derived from a nonparametric Bayesian approach provide a convenient way to deal with the issue of detecting the number of components in the mixture density, based on the assumption that the parameter distributions are generated by a Dirichlet process. The advantage is that we need no testing (in a classical sense) for the number of regimes, and the approach is not affected by a change point at the beginning or at the end of the sample. A Monte Carlo experiment provides some insights into the performance of the procedure. The potentiality of the approach is illustrated in reference with some well known results on exchange rate modelling.

Suggested Citation

  • Edoardo Otranto & Giampiero M. Gallo, 2001. "A Nonparametric Bayesian Approach to Detect the Number of Regimes in Markov Switching Models," Econometrics Working Papers Archive wp2001_04, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:wp2001_04

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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. Engel, Charles, 1994. "Can the Markov switching model forecast exchange rates?," Journal of International Economics, Elsevier, vol. 36(1-2), pages 151-165, February.
    3. Carter, C.K. & Kohn, R., "undated". "Markov Chain Monte Carlo in Conditionally Gaussian State Space Models," Statistics Working Paper _003, Australian Graduate School of Management.
    4. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. 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.
    7. 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.
    8. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    9. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    10. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-788, August.
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    Cited by:

    1. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    2. Giampiero M. Gallo & Edoardo Otranto, 2007. "Volatility transmission across markets: a Multichain Markov Switching model," Applied Financial Economics, Taylor & Francis Journals, vol. 17(8), pages 659-670.
    3. I.Fatnassi & S.Chawechi & Z.Ftiti & A.Ben Maatoug, 2014. "Effects of Monetary Policy on the REIT Returns," Working Papers 2014-63, Department of Research, Ipag Business School.
    4. Colavecchio, Roberta & Funke, Michael, 2009. "Volatility dependence across Asia-Pacific onshore and offshore currency forwards markets," Journal of Asian Economics, Elsevier, vol. 20(2), pages 174-196, March.
    5. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    6. Bäuerle Nicole & Gilitschenski Igor & Hanebeck Uwe, 2015. "Exact and approximate hidden Markov chain filters based on discrete observations," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 159-176, December.
    7. Bruno, Giancarlo & Otranto, Edoardo, 2008. "Models to date the business cycle: The Italian case," Economic Modelling, Elsevier, vol. 25(5), pages 899-911, September.
    8. Giampiero M. Gallo & Edoardo Otranto, 2014. "Forecasting Realized Volatility with Changes of Regimes," Econometrics Working Papers Archive 2014_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
    9. JdD Tena & E. Otranto, 2008. "A Realistic Model for Official Interest Rates," Working Paper CRENoS 200802, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    10. Fatnassi, Ibrahim & Slim, Chaouachi & Ftiti, Zied & Ben Maatoug, Abderrazek, 2014. "Effects of monetary policy on the REIT returns: Evidence from the United Kingdom," Research in International Business and Finance, Elsevier, vol. 32(C), pages 15-26.
    11. Giancarlo Bruno & Edoardo Otranto, 2003. "Dating the Italian Business Cycle: A Comparison of Procedures," Econometrics 0312003, EconWPA.
    12. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 87-107, March.
    13. Gallo, Giampiero M. & Otranto, Edoardo, 2015. "Forecasting realized volatility with changing average levels," International Journal of Forecasting, Elsevier, vol. 31(3), pages 620-634.
    14. E. Otranto, 2011. "Classification of Volatility in Presence of Changes in Model Parameters," Working Paper CRENoS 201113, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    15. Tena Horrillo, Juan de Dios & Otranto, Edoardo, 2006. "Modelling the discrete and infrequent official interest rate change in the UK," DES - Working Papers. Statistics and Econometrics. WS ws062007, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Yong Song, 2014. "Modelling Regime Switching And Structural Breaks With An Infinite Hidden Markov Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 825-842, August.
    17. repec:ipg:wpaper:2014-063 is not listed on IDEAS
    18. Silvestro Di Sanzo, 2009. "Testing for linearity in Markov switching models: a bootstrap approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(2), pages 153-168, July.
    19. Giampiero M. Gallo & Edoardo Otranto, 2017. "Combining Sharp and Smooth Transitions in Volatility Dynamics: a Fuzzy Regime Approach," Econometrics Working Papers Archive 2017_05, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    20. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849,, revised Dec 2014.
    21. Edoardo Otranto, 2005. "The multi-chain Markov switching model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(7), pages 523-537.

    More about this item


    Markov switching models; nuisance parameters; specification testing; exchange rate determination.;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • F3 - International Economics - - International Finance


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