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On the relationship between Markov Switching inference and Fuzzy Clustering: A Monte Carlo evidence

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  • L. Scaffidi Domianello
  • E. Otranto

Abstract

Markov Switching models have had increasing success in time series analysis due to their ability to capture the existence of unobserved discrete states in the dynamics of the variables under study. This result is generally obtained thanks to the inference on states derived from the so–called Hamilton filter. One of the open problems in this framework is the identification of the number of states, generally fixed a priori; it is in fact impossible to apply classical tests due to the problem of the nuisance parameters present only under the alternative hypothesis. In this work we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to determine the number of states in this framework. The procedure is very simple to apply, considering that it is performed (in a nonparametric way) independently of the data generation process and that the indicators we use are present in most statistical packages.

Suggested Citation

  • L. Scaffidi Domianello & E. Otranto, 2023. "On the relationship between Markov Switching inference and Fuzzy Clustering: A Monte Carlo evidence," Working Paper CRENoS 202304, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    • Handle: RePEc:cns:cnscwp:202304
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    References listed on IDEAS

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    1. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    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. Smith, Aaron & Naik, Prasad A. & Tsai, Chih-Ling, 2006. "Markov-switching model selection using Kullback-Leibler divergence," Journal of Econometrics, Elsevier, vol. 134(2), pages 553-577, October.
    4. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Degras, David & Ting, Chee-Ming & Ombao, Hernando, 2022. "Markov-switching state-space models with applications to neuroimaging," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Edoardo Otranto & Giampiero Gallo, 2002. "A Nonparametric Bayesian Approach To Detect The Number Of Regimes In Markov Switching Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 477-496.
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    Keywords

    Simulations; Number of states; Nuisance parameters; Markov chains; Groups identification;
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