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Structure and Asymptotic theory for Nonlinear Models with GARCH Errors

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  • Chan, F.
  • McAleer, M.J.
  • Medeiros, M.C.

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.

Suggested Citation

  • 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.
  • Handle: RePEc:ems:eureir:22216
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    References listed on IDEAS

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    Cited by:

    1. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.

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    More about this item

    Keywords

    GARCH; STAR; asymptotic theory; log-moment; moment conditions; nonlinear time series; regime-switching; smooth transition;
    All these keywords.

    JEL classification:

    • 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

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