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Specification Testing in Nonstationary Time Series Models

Author

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  • Jia Chen
  • Jiti Gao
  • Degui Li
  • Zhengyan Lin

Abstract

In this paper, we consider a specification testing problem in nonlinear time series models with nonstationary regressors and propose using a nonparametric kernel-based test statistic. The nullasymptotics for the proposed nonparametric test statistic have been well developed in the existing literature such as Gao et al (2009b) and Wang and Phillips (2012). In this paper, we study the local asymptotics of the test statistic, i.e., the asymptotic properties of the test statistic under a sequence of general nonparametric local alternatives, and show that the asymptotic distribution depends on the asymptotic behaviour of the distance function which is the local deviation from the parametrically specified model in the null hypothesis. In order to implement the proposed test in practice, we introduce a bootstrap procedure to approximate the critical values of the test statistic and establish a novel result of Edgeworth expansion which is used to justify the use of such an approximation. Based on the approximate critical values, we develop a bandwidth selection method, which chooses the optimal bandwidth that maximises the local power of the test while its size is controlled at a given significance level. The local power is defined as the power of the proposed test for a given sequence of local alternatives. Such a bandwidth selection is made feasible by an approximate expression for the local power of the test as a function of the bandwidth. A Monte-Carlo simulation study is provided to illustrate the finite sample performance of the proposed test.

Suggested Citation

  • Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2014. "Specification Testing in Nonstationary Time Series Models," Discussion Papers 14/19, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:14/19
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    References listed on IDEAS

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    1. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1869-1892, December.
    2. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
    3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    4. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
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    8. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
    9. Gao, Jiti & Wang, Qiying & Yin, Jiying, 2011. "Specification Testing In Nonlinear Time Series With Long-Range Dependence," Econometric Theory, Cambridge University Press, vol. 27(2), pages 260-284, April.
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    13. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
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    18. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
    19. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
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    Cited by:

    1. Russell Davidson & Victoria Zinde-Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1595-1631, December.
    2. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.

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    More about this item

    Keywords

    Asymptotic distribution; Edgeworth expansion; local power function; nonlinear time series; quadratic form; size function; specification testing; unit root.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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