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Nonlinear regressions with nonstationary time series

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  • Chan, Nigel
  • Wang, Qiying

Abstract

This paper develops asymptotic theory for a nonlinear parametric cointegrating regression model. We establish a general framework for weak consistency that is easy to apply for various nonstationary time series, including partial sums of linear processes and Harris recurrent Markov chains. We provide limit distributions for nonlinear least square estimators, extending the previous works. We also introduce endogeneity to the model by allowing the error to be serially dependent on and cross correlated with the regressors.

Suggested Citation

  • Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
  • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:182-195
    DOI: 10.1016/j.jeconom.2014.04.025
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    References listed on IDEAS

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    1. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    2. Wagner, Martin, 2008. "The carbon Kuznets curve: A cloudy picture emitted by bad econometrics?," Resource and Energy Economics, Elsevier, vol. 30(3), pages 388-408, August.
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    5. Berkes, István & Horváth, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(2), pages 304-322, April.
    6. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    7. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
    8. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    9. 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.
    10. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    11. Piaggio, Matías & Padilla, Emilio, 2012. "CO2 emissions and economic activity: Heterogeneity across countries and non-stationary series," Energy Policy, Elsevier, vol. 46(C), pages 370-381.
    12. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 143-164, February.
    13. Wang, Qiying, 2014. "Martingale Limit Theorem Revisited And Nonlinear Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 509-535, June.
    14. Muller-Furstenberger, Georg & Wagner, Martin, 2007. "Exploring the environmental Kuznets hypothesis: Theoretical and econometric problems," Ecological Economics, Elsevier, vol. 62(3-4), pages 648-660, May.
    15. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    16. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    17. List, John A. & Gallet, Craig A., 1999. "The environmental Kuznets curve: does one size fit all?," Ecological Economics, Elsevier, vol. 31(3), pages 409-423, December.
    18. Youngsoo Bae & Robert M. de Jong, 2007. "Money demand function estimation by nonlinear cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 767-793.
    19. Elbert Dijkgraaf & Herman Vollebergh, 2005. "A Test for Parameter Homogeneity in CO 2 Panel EKC Estimations," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 32(2), pages 229-239, October.
    20. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, March.
    21. Shi, Xiaoxia & Phillips, Peter C.B., 2012. "Nonlinear Cointegrating Regression Under Weak Identification," Econometric Theory, Cambridge University Press, vol. 28(3), pages 509-547, June.
    22. Choi, In & Saikkonen, Pentti, 2010. "Tests For Nonlinear Cointegration," Econometric Theory, Cambridge University Press, vol. 26(3), pages 682-709, June.
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    Cited by:

    1. Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
    2. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: A New Angle on the Environmental Kuznets Curve," Papers 2009.02262, arXiv.org.
    3. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2020. "Macroeconomic Data Transformations Matter," CIRANO Working Papers 2020s-42, CIRANO.
    4. Berenguer-Rico, Vanessa & Nielsen, Bent, 2020. "Cumulated Sum Of Squares Statistics For Nonlinear And Nonstationary Regressions," Econometric Theory, Cambridge University Press, vol. 36(1), pages 1-47, February.
    5. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    6. Zhishui Hu & Peter C.B. Phillips & Qiying Wang, 2019. "Nonlinear Cointegrating Power Function Regression with Endogeneity," Cowles Foundation Discussion Papers 2211, Cowles Foundation for Research in Economics, Yale University.
    7. Rickard Sandberg, 2017. "Sample Moments and Weak Convergence to Multivariate Stochastic Power Integrals," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1000-1009, November.
    8. Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    9. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.

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    More about this item

    Keywords

    Cointegration; Nonlinear regressions; Consistency; Limit distribution; Nonstationarity; Nonlinearity; Endogeneity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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