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Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors

Author

Listed:
  • Felix Chan

    (School of Economics and Finance, Curtin University of Technologyy)

  • Michael McAleer

    (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University)

  • Marcelo C. Medeiros

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

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

  • Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2010. "Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors," KIER Working Papers 754, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:754
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP754.pdf
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    References listed on IDEAS

    as
    1. Mayte Suarez -Farinas & Carlos E. Pedreira & Marcelo C. Medeiros, 2004. "Local Global Neural Networks: A New Approach for Nonlinear Time Series Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1092-1107, December.
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    6. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    7. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
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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

    Nonlinear time series; regime-switching; smooth transition; STAR; GARCH; log-moment; moment conditions; asymptotic theory.;
    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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