Conditional heteroskedasticity driven by hidden Markov chains

Christian Francq; Michel Roussignol; Jean Michel Zakoian

doi:10.1111/1467-9892.00219

Conditional heteroskedasticity driven by hidden Markov chains

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	197-220
Number of pages	24
Journal	Journal of Time Series Analysis
Volume	22
Issue number	2
DOIs	https://doi.org/10.1111/1467-9892.00219
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

ARCH models
Consistency
Hidden Markov chain
Maximum likelihood
Nonlinear time series models
Stationary solution
Switching models

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10.1111/1467-9892.00219

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title = "Conditional heteroskedasticity driven by hidden Markov chains",

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.",

keywords = "ARCH models, Consistency, Hidden Markov chain, Maximum likelihood, Nonlinear time series models, Stationary solution, Switching models",

author = "Christian Francq and Michel Roussignol and Zakoian, \{Jean Michel\}",

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AU - Roussignol, Michel

AU - Zakoian, Jean Michel

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N2 - 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.

AB - 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.

KW - ARCH models

KW - Consistency

KW - Hidden Markov chain

KW - Maximum likelihood

KW - Nonlinear time series models

KW - Stationary solution

KW - Switching models

U2 - 10.1111/1467-9892.00219

DO - 10.1111/1467-9892.00219

M3 - Article

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VL - 22

SP - 197

EP - 220

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

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ER -

Conditional heteroskedasticity driven by hidden Markov chains

Abstract

Keywords

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