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HIDDEN MARKOV STRUCTURES FOR DYNAMIC COPULAE

Published online by Cambridge University Press:  22 December 2014

Wolfgang Karl Härdle ,
Ostap Okhrin  and
Weining Wang
Wolfgang Karl Härdle
Affiliation:
Humboldt-Universität zu Berlin
Ostap Okhrin
Affiliation:
Humboldt-Universität zu Berlin
Weining Wang*
Affiliation:
Humboldt-Universität zu Berlin
*
*Address correspondence to Weining Wang, Hermann-Otto-Hirschfeld Junior Professor in Nonparametric Statistics and Dynamic Risk Management at the Ladislaus von Bortkiewicz Chair of Statistics of Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178 Berlin, Germany; e-mail: wangwein@cms.hu-berlin.de.
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Abstract

Understanding the time series dynamics of a multi-dimensional dependency structure is a challenging task. Multivariate covariance driven Gaussian or mixed normal time varying models have only a limited ability to capture important features of the data such as heavy tails, asymmetry, and nonlinear dependencies. The present paper tackles this problem by proposing and analyzing a hidden Markov model (HMM) for hierarchical Archimedean copulae (HAC). The HAC constitute a wide class of models for multi-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 its forecasting performance with that of 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.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 5 , October 2015 , pp. 981 - 1015
Copyright
Copyright © Cambridge University Press 2014 

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