Structure and Asymptotic theory for Nonlinear Models with GARCH Errors

Felix Chan, Michael McAleer and Marcelo Medeiros ()

No EI 2010-79, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: Nonlinear time series models, especially those with regime-switching and conditionally heteroskedastic 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 first derive necessary conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is important, among other reasons, to establish the conditions under which the traditional LMlinearity tests based on Taylor expansions are valid. Second, we provide sufficient conditions for consistency and asymptotic normality of the Quasi- Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.

Keywords: GARCH; STAR; asymptotic theory; log-moment; moment conditions; nonlinear time series; regime-switching; smooth transition (search for similar items in EconPapers)
Date: 2011-01-24
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Related works:
Journal Article: Structure and asymptotic theory for nonlinear models with GARCH erros (2015)
Working Paper: Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors (2010)
Working Paper: Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:22216

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