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Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model

Author

Listed:
  • Dakyung Seong

    (University of California)

  • Jin Seo Cho

    (Yonsei University)

  • Timo Teräsvirta

    (Aarhus University and CREATES)

Abstract

This paper examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic that tests linearity condition using the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a Gaussian stochastic process under the null of linearity by resolving the issue of twofold identification meaning that Davies’s (1977, 1987) identification problem arises in two different ways under the null. We illustrate our theory using the exponential STAR and logistic STAR models and also conduct Monte Carlo simulations. Finally, we test for neglected nonlinearity in the German money demand, growth rates of US unemployment, and German industrial production. These empirical examples also demonstrate that the QLR test statistic complements the linearity test of the Lagrange multiplier test statistic in Teräsvirta (1994).

Suggested Citation

  • Dakyung Seong & Jin Seo Cho & Timo Teräsvirta, 2019. "Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model," CREATES Research Papers 2019-17, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2019-17
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    References listed on IDEAS

    as
    1. Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
    2. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    4. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    5. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    6. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    7. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    8. Cho, Jin Seo & White, Halbert, 2018. "Directionally Differentiable Econometric Models," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1101-1131, October.
    9. Jin Seo Cho & Peter C. B. Phillips, 2018. "Sequentially testing polynomial model hypotheses using power transforms of regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 141-159, January.
    10. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    11. Skalin, Joakim & Terasvirta, Timo, 1999. "Another Look at Swedish Business Cycles, 1861-1988," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(4), pages 359-378, July-Aug..
    12. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    13. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    14. Cho, Jin Seo & Ishida, Isao, 2012. "Testing for the effects of omitted power transformations," Economics Letters, Elsevier, vol. 117(1), pages 287-290.
    15. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
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    Cited by:

    1. Jin Seo Cho & Matthew Greenwood‐Nimmo & Yongcheol Shin, 2023. "Recent developments of the autoregressive distributed lag modelling framework," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 7-32, February.

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    More about this item

    Keywords

    QLR test statistic; STAR model; linearity test; Gaussian process; null limit distribution; nonstandard testing problem;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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