Bulla, Jan (2009): Hidden Markov models with t components. Increased persistence and other aspects.

PDF
MPRA_paper_21830.pdf Download (790kB)  Preview 
Abstract
Hidden Markov models have been applied in many different fields during the last decades, including econometrics and finance. However, the lion’s share of the investigated models is Markovian mixtures of Gaussian distributions. We present an extension to conditional tdistributions, including models with unequal distribution types in different states. It is shown that the extended models, on the one hand, reproduce various stylized facts of daily returns better than the common Gaussian model. On the other hand, robustness to outliers and persistence of the visited states increases significantly.
Item Type:  MPRA Paper 

Original Title:  Hidden Markov models with t components. Increased persistence and other aspects 
Language:  English 
Keywords:  Hidden Markov model, Markovswitching model, state persistence, tdistribution, daily returns 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E44  Financial Markets and the Macroeconomy 
Item ID:  21830 
Depositing User:  Jan Bulla 
Date Deposited:  07. Apr 2010 05:45 
Last Modified:  20. May 2015 17:35 
References:  Baum, L. E. & Petrie, T. (1966), ‘Statistical inference for probabilistic functions of finite state Markov chains’, Ann. Math. Statist. 37, 1554–1563. Baum, L. E., Petrie, T., Soules, G. & Weiss, N. (1970), ‘A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains’, Ann. Math. Statist. 41, 164–171. Bialkowski, J. (2003), ‘Modelling returns on stock indices for western and central european stock exchanges  Markov switching approach’, Southeast. Eur. J. Econ. 2(2), 81–100. Breunig, R., Najarian, S. & Pagan, A. (2003), ‘Specification testing of markov switching models’, Oxford Bull. Econ. Statist. 65(Supplement), 703–725. Bulla, J. & Berzel, A. (2008), ‘Computational issues in parameter estimation for stationary hidden Markov models’, Computation. Stat. 23(1), 1–18. Bulla, J. & Bulla, I. (2006), ‘Stylized facts of financial time series and hidden semiMarkov models’, Comput. Statist. Data Anal. 51(4), 2192–2209. Campbell, J. Y., Lettau, M., Malkiel, B. G. & Xu, Y. (2001), ‘Have individual stocks become more volatile? an empirical exploration of idiosyncratic risk’, J. Financ. 56(1), 1–43. Cappé, O., Moulines, E. & Ryden, T. (2007), Inference in Hidden Markov Models, Springer Series in Statistics, SpringerVerlag, New York  Heidelberg  Berlin. Cecchetti, S. G., Lam, P.S. & Mark, N. C. (1990), ‘Mean reversion in equilibrium asset prices’, Am. Econ. Rev. 80(3), 398–418. Chan, W.s. (1995), ‘Time series outliers and spurious autocorrelations’, J. Appl. Stat. Sci. 2(2), 153–162. Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977), ‘Maximum likelihood from incomplete data via the EM algorithm’, J. Roy. Statist. Soc. Ser. B 39(1), 1–38. With discussion. Durbin, R., Eddy, S. R., Krogh, A. & Mitchison, G. (1998), Biological sequence analysis. Probabilistic models of proteins and nucleic acids, Cambridge University Press, Cambridge, UK. Ephraim, Y. & Merhav, N. (2002), ‘Hidden Markov processes’, IEEE Trans. Inform. Theory 48(6), 1518–1569. Special issue on Shannon theory: perspective, trends, and applications. Gettinby, G. D., Sinclair, C. D., Power, D. M. & Brown, R. A. (2004), ‘An analysis of the distribution of extreme share returns in the uk from 1975 to 2000’, J. Bus. Fin. Account. 31(5), 607–646. Granger, C. W. J. & Ding, Z. (1995a), ‘Some properties of absolute return: An alternative measure of risk’, Ann. Economie Stat. 40, 67–91. Granger, C. W. J. & Ding, Z. (1995b), Stylized facts on the temporal and distributional properties of daily data from speculative markets. Department of Economics, University of California, San Diego, unpublished paper. Granger, C. W. J., Spear, S. & Ding, Z. (2000), ‘Stylized facts on the temporal and distributional properties of absolute returns: An update’, Proc. HK Int. Workshop Stat. Fin.: An Interface pp. 97–120. Imperial College Press. Guidolin, M. & Timmermann, A. (2005), ‘Economic implications of bull and bear regimes in UK stock and bond returns’, Econ. J. 115(500), 111–143. Hamilton, J. D. (1989), ‘A new approach to the economic analysis of nonstationary time series and the business cycle’, Econometrica 57(2), 357–384. Hamilton, J. D. (1990), ‘Analysis of time series subject to changes in regime’, J. Econometrics 45(12), 39–70. Harris, R. D. & Kücüközmen, C. C. (2001), ‘The empirical distribution of uk and us stock returns’, J. Bus. Fin. Account. 28(5–6), 715–740. Kent, J. T., Tyler, D. E. & Vardi, Y. (1994), ‘A curious likelihood identity for the multivariate tdistribution’, Comm. Statist. Simulation Comput. 23(2), 441–453. Koski, T. (2001), Hidden Markov models for bioinformatics, Vol. 2 of Computational Biology, Springer Netherlands. Kluwer Academic Publishers, Dordrecht. Linne, T. (2002), A Markov switching model of stock returns: an application to the emerging markets in central and eastern europe, in ‘in: East European Transition and EU Enlargement’, PhysicaVerlag, pp. 371–384. MacDonald, I. L. & Zucchini, W. (1997), Hidden Markov and other models for discretevalued time series, Vol. 70 of Monographs on Statistics and Applied Probability, Chapman & Hall, London. MacDonald, I. L. & Zucchini, W. (2009), Hidden Markov for Time Series: An Introduction Using R, CRC Monographs on Statistics and Applied Probability, Chapman & Hall, London. Maheu, J. M. & McCurdy, T. H. (2001), ‘Identifying bull and bear markets in stock returns’, J. Bus. Econ. Statist. 18(1), 100–112. Peel, D. & McLachlan, G. J. (2000), ‘Robust mixture modelling using the tdistribution’, Statistics and Computing 10, 339–348. Peria, M. S. M. (2002), ‘A regimeswitching approach to the study of speculative attacks: A focus on ems crises’, Empirical Econ. 27(2), 299–334. Rabiner, L. (1989), ‘A tutorial on hidden Markov models and selected applications in speech recognition’, IEEE Trans. Inf. Theory 77(2), 257–284. Redner, R. A. & Walker, H. F. (1984), ‘Mixture densities, maximum likelihood and the EM algorithm’, SIAM Rev. 26(2), 195–239. Robert, C. P. & Titterington, D. M. (1998), ‘Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation’, Stat. Comput. 8, 145–158. Rydén, T., Terasvirta, T. & Asbrink, S. (1998), ‘Stylized facts of daily return series and the hidden Markov model’, J. Appl. Econom. 13(3), 217–244. Schwert, G. W. (1989), ‘Why does stock market volatility change over time’, J. Financ. 44(5), 1115–1153. Taylor, S. J. (1986), Modelling Financial Time Series, John Wiley & Sons, Chichester, UK. Titterington, D. M., Smith, A. F. M. & Makov, U. E. (1985), Statistical Analysis of Finite Mixture Distributions, Wiley. Turner, C. M., Startz, R. & Nelson, C. R. (1989), ‘A Markov model of heteroskedasticity, risk, and learning in the stock market’, J. Finan. Econ. 25(1), 3–22. Visser, I., Raijmakers, M. E. J. & Molenaar, P. C. M. (2000), ‘Confidence intervals for hidden Markov model parameters’, Brit. J. Math. Stat. Psy. 53(2), 317–327. Visser, I., Raijmakers, M. E. J. & Molenaar, P. C. M. (2002), ‘Fitting hidden markov models to psychological data’, Sci. Program. 10, 185199 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/21830 