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Structure and estimation of a class of nonstationary yet nonexplosive GARCH models

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  • Nazim Regnard
  • Jean‐Michel Zakoïan

Abstract

This article considers GARCH(1,1) models in which the time‐varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi‐maximum likelihood estimator are derived under mild assumptions.

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  • Nazim Regnard & Jean‐Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:5:p:348-364
    DOI: 10.1111/j.1467-9892.2010.00669.x
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    3. Regnard, Nazim & Zakoïan, Jean-Michel, 2011. "A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices," Energy Economics, Elsevier, vol. 33(6), pages 1240-1251.

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