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General framework and model building in the class of Hidden Mixture Transition Distribution models

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  • Bolano, Danilo
  • Berchtold, André

Abstract

Modeling time series that present non-Gaussian features plays as central role in many fields, including finance, seismology, psychological, and life course studies. The Hidden Mixture Transition Distribution model is an answer to the complexity of such series. The observed heterogeneity can be induced by one or several latent factors, and each level of these factors is related to a different component of the observed process. The time series is then treated as a mixture and the relation between the components is governed by a Markovian latent transition process. This framework generalizes several specifications that appear separately in related literature. Both the expectation and the standard deviation of each component are allowed to be functions of the past of the process. The latent process can be of any order, and can be modeled using a discrete Mixture Transition Distribution. The effects of covariates at the visible and hidden levels are also investigated. One of the main difficulties lies in correctly specifying the structure of the model. Therefore, we propose a hierarchical model selection procedure that exploits the multilevel structure of our approach. Finally, we illustrate the model and the model selection procedure through a real application in social science.

Suggested Citation

  • Bolano, Danilo & Berchtold, André, 2016. "General framework and model building in the class of Hidden Mixture Transition Distribution models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 131-145.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:131-145
    DOI: 10.1016/j.csda.2014.09.011
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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Oded Netzer & James M. Lattin & V. Srinivasan, 2008. "A Hidden Markov Model of Customer Relationship Dynamics," Marketing Science, INFORMS, vol. 27(2), pages 185-204, 03-04.
    3. Takaki Hayashi, 2004. "A duscrete-time model of high-frequency stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 140-150.
    4. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    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 357-384, March.
    6. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    7. Kim, Dongcheol & Kon, Stanley J, 1994. "Alternative Models for the Conditional Heteroscedasticity of Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(4), pages 563-598, October.
    8. G. Kapetanios, 2008. "A bootstrap procedure for panel data sets with many cross-sectional units," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 377-395, July.
    9. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    10. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    11. Frydman, Halina & Schuermann, Til, 2008. "Credit rating dynamics and Markov mixture models," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1062-1075, June.
    12. Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, March.
    13. Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 309-321, June.
    14. Hassan, Mohamed Yusuf & Lii, Keh-Shin, 2006. "Modeling Marked Point Processes via Bivariate Mixture Transition Distribution Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1241-1252, September.
    15. Paolo Giudici & Tobias Ryden & Pierre Vandekerkhove, 2000. "Likelihood-Ratio Tests for Hidden Markov Models," Biometrics, The International Biometric Society, vol. 56(3), pages 742-747, September.
    16. Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
    17. Gabadinho, Alexis & Ritschard, Gilbert & Müller, Nicolas S & Studer, Matthias, 2011. "Analyzing and Visualizing State Sequences in R with TraMineR," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i04).
    18. Berchtold, Andre, 2003. "Mixture transition distribution (MTD) modeling of heteroscedastic time series," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 399-411, January.
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