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Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space

Author

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  • Francq, Christian
  • Horvath, Lajos
  • Zakoian, Jean-Michel

Abstract

We consider linearity testing in a general class of nonlinear time series model of order 1, involving a nonnegative nuisance parameter which (i) is not identified under the null hypothesis and (ii) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the Likelihood Ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite sample properties of the sup-tests are studied by simulations.

Suggested Citation

  • Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2008. "Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space," MPRA Paper 16669, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:16669
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    File URL: https://mpra.ub.uni-muenchen.de/16669/1/MPRA_paper_16669.pdf
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    References listed on IDEAS

    as
    1. Terasvirta, Timo & van Dijk, Dick & Medeiros, Marcelo C., 2005. "Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination," International Journal of Forecasting, Elsevier, vol. 21(4), pages 755-774.
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    3. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
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    5. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
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    7. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
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    More about this item

    Keywords

    Diagnostic checking; Exponential autoregressive (EXPAR) model; Lagrange Multiplier (LM) tests; Least Squares Estimator; Likelihood Ratio (LR); Non Linear models; Supremum Tests; Smooth Transition Autoregressive (STAR); Threshold AR (TAR); Wald test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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