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Structure and asymptotic theory for nonlinear models with GARCH erros

Author

Listed:
  • Felix Chan

    (School of Economics and Finance, Curtin University of Technology, Australia)

  • Michael McAleer

    (Econometric Institute, Erasmus University Rotterdam, The Netherlands)

  • Marcelo C. Medeiros

    (Department of Economics, Pontifical Catholic University of Rio de Janeiro, Brazil)

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..

Suggested Citation

  • Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    • Handle: RePEc:anp:econom:v:16:y:2015:1:1_21
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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.

    More about this item

    Keywords

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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