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

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Abstract

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.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2001_04.

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Length: 25 pages
Date of creation: 2001
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Handle: RePEc:fir:econom:wp2001_04

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

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References

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  1. Charles Engel, 1992. "Can the Markov Switching Model Forecast Exchange Rates?," NBER Working Papers 4210, National Bureau of Economic Research, Inc.
  2. 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 S61-82, Suppl. De.
  3. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. 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 357-84, March.
  6. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  7. Carter, C.K. & Kohn, R., . "Markov Chain Monte Carlo in Conditionally Gaussian State Space Models," Statistics Working Paper _003, Australian Graduate School of Management.
  8. 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 763-88, August.
  9. 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.
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Cited by:
  1. 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.
  2. Federico Bassetti & Roberto Casarin & Fabrizio Leisen, 2013. "Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference," Working Papers 2013:13, Department of Economics, University of Venice "Ca' Foscari".
  3. Michael Funke & Roberta Colavecchio, 2009. "Volatility dependence across Asia-Pacific onshore and offshore currency forwards markets," Quantitative Macroeconomics Working Papers 20903, Hamburg University, Department of Economics.
  4. 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.
  5. Giampiero Gallo & Edoardo Otranto, 2006. "Volatility Transmission Across Markets: A Multi-Chain Markov Switching Model," Econometrics Working Papers Archive wp2006_04, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  6. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
  7. Silvestro Di Sanzo, 2009. "Testing for linearity in Markov switching models: a bootstrap approach," Statistical Methods and Applications, Springer, vol. 18(2), pages 153-168, July.
  8. Giancarlo Bruno & Edoardo Otranto, 2003. "Dating the Italian Business Cycle: A Comparison of Procedures," Econometrics 0312003, EconWPA.
  9. Bruno, Giancarlo & Otranto, Edoardo, 2008. "Models to date the business cycle: The Italian case," Economic Modelling, Elsevier, vol. 25(5), pages 899-911, September.
  10. Yong Song, 2012. "Modelling Regime Switching and Structural Breaks with an Infinite Hidden Markov Model," Working Paper Series 28_12, The Rimini Centre for Economic Analysis.
  11. 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.
  12. Juan de Dios Tena & Edoardo Otranto, 2006. "Modelling The Discrete And Infrequent Official Interest Rate Change In The Uk," Statistics and Econometrics Working Papers ws062007, Universidad Carlos III, Departamento de Estadística y Econometría.
  13. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods and Applications, Springer, vol. 18(1), pages 87-107, March.
  14. J. De Dios 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.

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