HMM and HAC
Conference paper
- 1.4k Downloads
Abstract
Understanding the dynamics of a high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC). The HAC constitute a wide class of models for high dimensional dependencies, and HMM is a statistical technique for describing time varying dynamics. HMM applied to HAC flexibly models high dimensional non-Gaussian time series. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application, and the model’s performance is compared to other dynamic models.
Keywords
Hidden Markov model hierarchical Archimedean copulae multivariate distributionPreview
Unable to display preview. Download preview PDF.
References
- 1.Bickel, P.J., Ritov, Y., Rydén, T.: Asymptotic normality of the maximum-likelihood estimator for general hidden markov models. Annals of Statistics 26(4), 1614–1635 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
- 2.Cappé, O., Moulines, E., Rydén, T.: Inference in Hidden Markov Models. Springer (2005)Google Scholar
- 3.Chen, X., Fan, Y.: Estimation of copula-based semiparametric time series models. Journal of Econometrics 130(2), 307–335 (2005)MathSciNetCrossRefGoogle Scholar
- 4.Chen, X., Fan, Y.: Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspesification. Journal of Econometrics 135, 125–154 (2006)MathSciNetCrossRefGoogle Scholar
- 5.Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the em algorithm (with discussion). J. Roy. Statistical Society B 39, 1–38 (1997)MathSciNetGoogle Scholar
- 6.Engle, R.F., Kroner, K.F.: Multivariate simultaneous generalized arch. Econometric Theory 11, 122–150 (1995)MathSciNetCrossRefGoogle Scholar
- 7.Fuh, C.D.: SPRT and CUSUM in hidden Markov Models. Ann. Statist. 31(3), 942–977 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
- 8.Giacomini, E., Härdle, W.K., Spokoiny, V.: Inhomogeneous dependence modeling with time-varying copulae. Journal of Business and Economic Statistics 27(2), 224–234 (2009)MathSciNetCrossRefGoogle Scholar
- 9.Härdle, W.K., Okhrin, O., Okhrin, Y.: Time varying hierarchical archimedean copulae (2011) (submitted for publication)Google Scholar
- 10.Leroux, B.G.: Maximum-likelihood estimation for hidden markov models. Stochastic Processes and their Applications 40, 127–143 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
- 11.McNeil, A.J., Nešlehová, J.: Multivariate Archimedean copulas, d-monotone functions and l 1 norm symmetric distributions. Annals of Statistics 37(5b), 3059–3097 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
- 12.Nelsen, R.B.: An Introduction to Copulas. Springer, New York (2006)zbMATHGoogle Scholar
- 13.Okhrin, O., Okhrin, Y., Schmid, W.: On the structure and estimation of hierarchical archimedean copulas. Under Revision of Journal of Econometrics (2009)Google Scholar
- 14.Patton, A.J.: On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. Journal of Financial Econometrics 2, 130–168 (2004)CrossRefGoogle Scholar
- 15.Rabiner, L.R.: A tutorial on Hidden Markov Models and selected applications in speech recognition. Proceedings of IEEE 77(2) (1989)Google Scholar
- 16.Rodriguez, J.C.: Measuring financial contagion: a copula approach. Journal of Empirical Finance 14, 401–423 (2007)CrossRefGoogle Scholar
- 17.Sklar, A.: Fonctions dé repartition á n dimension et leurs marges. Publ. Inst. Stat. Univ. Paris 8, 299–231 (1959)Google Scholar
- 18.Whelan, N.: Sampling from Archimedean copulas. Quantitative Finance 4, 339–352 (2004)MathSciNetCrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2013