Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors

Felix Chan, Michael McAleer and Marcelo C. Medeiros

Working Papers in Economics from University of Canterbury, Department of Economics and Finance

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: Nonlinear time series; regime-switching; smooth transition; STAR; GARCH; log-moment; moment conditions; asymptotic theory (search for similar items in EconPapers)
JEL-codes: E43 Q11 Q13 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2010-12-01
New Economics Papers: this item is included in nep-ecm, nep-mac and nep-ore
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https://repec.canterbury.ac.nz/cbt/econwp/1079.pdf (application/pdf)

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 (2011)
Working Paper: Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:cbt:econwp:10/79

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