Articlegreen2001

Conditional Heteroskedasticity Driven by Hidden Markov Chains

Christian Francq · Michel Roussignol · Jean‐Michel Zakoïan

100 citations0/0 files storedJournal of Time Series Analysis

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Time Series Analysis and Forecasting

Abstract

We consider a generalized autoregressive conditionally heteroskedastic (GARCH) equation where the coefficients depend on the state of a nonobserved Markov chain. Necessary and sufficient conditions ensuring the existence of a stationary solution are given. In the case of ARCH regimes, the maximum likelihood estimates are shown to be consistent. The identification problem is also considered. This is illustrated by means of real and simulated data sets.

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