Structure and asymptotic theory for nonlinear models with GARCH errors - Felix Chan; Michael McAleer; Marcelo C. Medeiros (EconomiA, 2015)
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. – – Modelos n\~ao-lineares com múltiplos regimes e heterpcedasticidade condicional s\~ao muito populares em economia e finanças. Neste artigo derivamos condiç\~oes de estacionaridade para modelos com transiç\~ao suave e erros heterocedásticos. Além disso derivamos condiç\~oes suficientes para consistência e normalidade assintótica do estimador de quase-máxima verossimilhança.
Keywords: C22; 330; Nonlinear time series; Regime-switching; Smooth transition; STAR; GARCH; Asymptotic theory