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Semiparametric Profile Likelihood Estimation of Varying Coefficient Models with Nonstationary Regressors

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  • Kunpeng Li
  • Degui Li
  • Zhongwen Lian
  • Cheng Hsiao

Abstract

We study a partially linear varying coefficient model where the regressors are generated by the multivariate unit root I(1) processes. The influence of the explanatory vectors on the response variable satisfies the semiparametric partially linear structure with the nonlinear component being functional coefficients. The profile likelihood estimation methodology with the first-stage local polynomial smoothing is applied to estimate both the constant coefficients in the linear component and the functional coefficients in the nonlinear component. The asymptotic distribution theory for the proposed semiparametric estimators is established under some mild conditions, from which both the parametric and nonparametric estimators are shown to enjoy the well-known super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the developed methodology and results.

Suggested Citation

  • Kunpeng Li & Degui Li & Zhongwen Lian & Cheng Hsiao, 2013. "Semiparametric Profile Likelihood Estimation of Varying Coefficient Models with Nonstationary Regressors," Monash Econometrics and Business Statistics Working Papers 2/13, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2013-2
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp02-13.pdf
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    References listed on IDEAS

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    1. 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.
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    3. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    4. Yiguo Sun & Qi Li, 2011. "Data-Driven Bandwidth Selection for Nonstationary Semiparametric Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 541-551, October.
    5. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    6. Juhl, Ted & Xiao, Zhijie, 2005. "Partially Linear Models With Unit Roots," Econometric Theory, Cambridge University Press, vol. 21(5), pages 877-906, October.
    7. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
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    Cited by:

    1. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.

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    More about this item

    Keywords

    Functional coefficients; local polynomial fitting; profile likelihood; semiparametric estimation; unit root process.;
    All these keywords.

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