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Linearity and misspecification tests for vector smooth transition regression models

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  • Terasvirta, Timo

    (Aarhus University)

  • Yang, Yukai

    (Université catholique de Louvain, CORE, Belgium)

Abstract

In this paper, we derive Lagrange multiplier and Lagrange multiplier type specification and misspecification tests for vector smooth transition models. We report results from simulation studies in which the size and power properties of the proposed tests in small samples are considered. The results show that these asymptotic tests generally suffer from size distortion. We find that Wilks’s and Rao’s F statistic both have satisfactory size properties and can be recommended for empirical use. Bootstrapping the standard asymptotic LM statistic offers another solution to the problem.

Suggested Citation

  • Terasvirta, Timo & Yang, Yukai, 2014. "Linearity and misspecification tests for vector smooth transition regression models," LIDAM Discussion Papers CORE 2014061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2014061
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    References listed on IDEAS

    as
    1. Laitinen, Kenneth, 1978. "Why is demand homogeneity so often rejected?," Economics Letters, Elsevier, vol. 1(3), pages 187-191.
    2. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    3. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    4. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    5. Meisner, James F., 1979. "The sad fate of the asymptotic Slutsky symmetry test for large systems," Economics Letters, Elsevier, vol. 2(3), pages 231-233.
    6. Terasvirta, Timo & Yang, Yukai, 2014. "Specification, estimation and evaluation of vector smooth transition autoregressive models with applications," LIDAM Discussion Papers CORE 2014062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Saikkonen, Pentti, 2008. "Stability Of Regime Switching Error Correction Models Under Linear Cointegration," Econometric Theory, Cambridge University Press, vol. 24(1), pages 294-318, February.
    8. Changli He & Timo Terasvirta & Andres Gonzalez, 2009. "Testing Parameter Constancy in Stationary Vector Autoregressive Models Against Continuous Change," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 225-245.
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    More about this item

    Keywords

    Vector STAR models; linearity test; misspecification test; vector nonlinear time series; serial correlation; parameter constancy; residual nonlinearity test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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