Structure and asymptotic theory for nonlinear models with GARCH errors

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 theo...

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Main Authors: Chan, Felix, McAleer, M., Medeiros, M.
Format: Journal Article
Published: Elsevier Ltd 2015
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/76323
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author Chan, Felix
McAleer, M.
Medeiros, M.
author_facet Chan, Felix
McAleer, M.
Medeiros, M.
author_sort Chan, Felix
building Curtin Institutional Repository
collection Online Access
description 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
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publishDate 2015
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spelling curtin-20.500.11937-763232019-09-19T06:28:47Z Structure and asymptotic theory for nonlinear models with GARCH errors Chan, Felix McAleer, M. Medeiros, M. Nonlinear time series Regime-switching Smooth transition STAR GARCH Asymptotic theory 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 2015 Journal Article http://hdl.handle.net/20.500.11937/76323 10.1016/j.econ.2015.01.001 http://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier Ltd fulltext
spellingShingle Nonlinear time series
Regime-switching
Smooth transition
STAR
GARCH
Asymptotic theory
Chan, Felix
McAleer, M.
Medeiros, M.
Structure and asymptotic theory for nonlinear models with GARCH errors
title Structure and asymptotic theory for nonlinear models with GARCH errors
title_full Structure and asymptotic theory for nonlinear models with GARCH errors
title_fullStr Structure and asymptotic theory for nonlinear models with GARCH errors
title_full_unstemmed Structure and asymptotic theory for nonlinear models with GARCH errors
title_short Structure and asymptotic theory for nonlinear models with GARCH errors
title_sort structure and asymptotic theory for nonlinear models with garch errors
topic Nonlinear time series
Regime-switching
Smooth transition
STAR
GARCH
Asymptotic theory
url http://hdl.handle.net/20.500.11937/76323