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Conditional Heteroskedasticity Driven by Hidden Markov Chains
Author(s) -
Francq Christian,
Roussignol Michel,
Zakoian JeanMichel
Publication year - 2001
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00219
Subject(s) - heteroscedasticity , mathematics , markov chain , autoregressive conditional heteroskedasticity , autoregressive model , econometrics , identification (biology) , statistics , volatility (finance) , botany , biology
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.