Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors
AbstractNonlinear 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.
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Bibliographic InfoPaper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/79.
Length: 28 pages
Date of creation: 01 Dec 2010
Date of revision:
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Nonlinear time series; regime-switching; smooth transition; STAR; GARCH; log-moment; moment conditions; asymptotic theory;
Other versions of this item:
- Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2010. "Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors," KIER Working Papers 754, Kyoto University, Institute of Economic Research.
- Chan, F. & McAleer, M.J. & Medeiros, M.C., 2011. "Structure and Asymptotic theory for Nonlinear Models with GARCH Errors," Econometric Institute Research Papers EI 2010-79, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- Q11 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Aggregate Supply and Demand Analysis; Prices
- Q13 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agricultural Markets and Marketing; Cooperatives; Agribusiness
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-03 (All new papers)
- NEP-ECM-2011-01-03 (Econometrics)
- NEP-MAC-2011-01-03 (Macroeconomics)
- NEP-ORE-2011-01-03 (Operations Research)
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