Hidden Markov Structures for Dynamic Copulae

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.