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Nonparametric Specification Testing for Nonlinear Time Series with Nonstationarity

Author

Listed:
  • Jiti Gao

    () (School of Economics, University of Adelaide)

  • Maxwell King

    (Monash University)

  • Zudi Lu

    (Curtin University of Technology)

  • Dag Tjøstheim

    (The University of Bergen)

Abstract

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for testing whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel test as well as the choice of simulated critical values. An example of implementation is given to show that the proposed test works in practice.

Suggested Citation

  • Jiti Gao & Maxwell King & Zudi Lu & Dag Tjøstheim, 2009. "Nonparametric Specification Testing for Nonlinear Time Series with Nonstationarity," School of Economics Working Papers 2009-03, University of Adelaide, School of Economics.
  • Handle: RePEc:adl:wpaper:2009-03
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    File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2009-03.pdf
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    Citations

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    Cited by:

    1. 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.
    2. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    3. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(05), pages 911-952, October.
    4. repec:eee:econom:v:199:y:2017:i:1:p:12-34 is not listed on IDEAS
    5. Jiti Gao & Maxwell King, 2012. "An Improved Nonparametric Unit-Root Test," Monash Econometrics and Business Statistics Working Papers 16/12, Monash University, Department of Econometrics and Business Statistics.
    6. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    7. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    8. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    9. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.
    10. Gan, Li & Hsiao, Cheng & Xu, Shu, 2014. "Model specification test with correlated but not cointegrated variables," Journal of Econometrics, Elsevier, vol. 178(P1), pages 80-85.
    11. Chaohua Dong & Jiti Gao, 2012. "Specification Testing Driven by Orthogonal Series in Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 20/12, Monash University, Department of Econometrics and Business Statistics.
    12. Jiti Gao, 2012. "Identification, Estimation and Specification in a Class of Semiparametic Time Series Models," Monash Econometrics and Business Statistics Working Papers 6/12, Monash University, Department of Econometrics and Business Statistics.
    13. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, vol. 172(1), pages 1-13.
    14. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    15. Gao, Jiti, 2012. "Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models," MPRA Paper 39256, University Library of Munich, Germany, revised 14 May 2012.
    16. repec:wyi:journl:002195 is not listed on IDEAS
    17. Lin, Zhongjian & Li, Qi & Sun, Yiguo, 2014. "A consistent nonparametric test of parametric regression functional form in fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 178(P1), pages 167-179.
    18. Jiti Gao & Maxwell King, 2011. "A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors," Monash Econometrics and Business Statistics Working Papers 20/11, Monash University, Department of Econometrics and Business Statistics.
    19. Yichen Gao & Zheng Li & Zhongjian Lin, 2014. "Semiparametric Estimation of Partially Linear Varying Coefficient Models with Time Trend and Nonstationary Regressors," Emory Economics 1412, Department of Economics, Emory University (Atlanta).
    20. 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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