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Conditional Heteroskedasticity Driven by Hidden Markov Chains

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  • Christian Francq
  • Michel Roussignol
  • Jean‐Michel Zakoian

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.

Suggested Citation

  • Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
  • Handle: RePEc:bla:jtsera:v:22:y:2001:i:2:p:197-220
    DOI: 10.1111/1467-9892.00219
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