Structure and asymptotic theory for STAR(1)-GARCH(1,1) models

Marcelo Cunha Medeiros (), Felix Chan and Michael McAller
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Marcelo Cunha Medeiros: Department of Economics PUC-Rio
Michael McAller: University of Western Australia

No 506, Textos para discussão from Department of Economics PUC-Rio (Brazil)

Abstract: Nonlinear time series models, especially those with regime-switching and GARCH errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper we derive necessary and sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order STAR-GARCH model, and sufficient conditions for the existence of moments. This is important, among others, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. Finally, we provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator.

Keywords: Nonlinear time series; regime-switching; STAR; GARCH; log-moment; moment conditions; asymptotic theory. (search for similar items in EconPapers)
Pages: 22p
Date: 2005-11
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:rio:texdis:506

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