Hidden Markov Structures for Dynamic Copulae

45 Pages Posted: 2 Mar 2016

See all articles by Wolfgang K. Härdle

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Ostap Okhrin

Humboldt University of Berlin - School of Business and Economics

Weining Wang

Humboldt University of Berlin

Date Written: February 2, 2014

Abstract

Understanding the time series dynamics of a multivariate dimensional dependency structure is a challenging task. A multivariate covariance driven Gaussian or mixed normal time varying models are limited in capturing important data features such as heavy tails, asymmetry, and nonlinear dependencies. This research aims at tackling this problem by proposing and analysing a hidden Markov model (HMM) for hierarchical Archimedean copulae (HAC). The HAC constitute a wide class of models for multivariate dimensional dependencies, and HMM is a statistical technique for describing regime switching dynamics. HMM applied to HAC flexibly models multivariate dimensional non-Gaussian time series.

We apply the expectation maximization (EM) algorithm for parameter estimation. 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. This example is motivated by a local adaptive analysis that yields a time varying HAC model. We compare the forecasting performance with other classical dynamic models. In another, second, application we model a rainfall process. This task is of particular theoretical and practical interest because of the specific structure and required untypical treatment of precipitation data.

Keywords: Hidden Markov Model, Hierarchical Archimedean Copulae, Multivariate Distribution

JEL Classification: C13, C14, G50

Suggested Citation

Härdle, Wolfgang K. and Okhrin, Ostap and Wang, Weining, Hidden Markov Structures for Dynamic Copulae (February 2, 2014). Available at SSRN: https://ssrn.com/abstract=2740339 or http://dx.doi.org/10.2139/ssrn.2740339

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Ostap Okhrin

Humboldt University of Berlin - School of Business and Economics ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Weining Wang (Contact Author)

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

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