摘要：Abstract Nonlinear time series models, especially those with regime-switching and/or 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 derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional \{LM\} linearity tests based on Taylor expansions are valid. We also 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.
关键词：Nonlinear time series ;Regime-switching ;Smooth transition ;\{STAR\} ;\{GARCH\} ;Asymptotic theory ;modelos não-lineares ;modelos com transição suave ;\{GARCH\} ;teoria assintótica
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