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Partially Linear Models With Unit Roots

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  • Juhl, Ted
  • Xiao, Zhijie

Abstract

This paper studies the asymptotic properties of a nonstationary partially linear regression model. In particular, we allow for covariates to enter the unit root (or near unit root) model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988). It is proven that the autoregressive parameter can be estimated at rate N even though part of the model is estimated nonparametrically. Unit root tests based on the semiparametric estimate of the autoregressive parameter have a limiting distribution which is a mixture of a standard normal and the Dickey-Fuller distribution. A Monte Carlo experiment is conducted to evaluate the performance of the tests for various linear and nonlinear specifications.
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Suggested Citation

  • Juhl, Ted & Xiao, Zhijie, 2005. "Partially Linear Models With Unit Roots," Econometric Theory, Cambridge University Press, vol. 21(05), pages 877-906, October.
  • Handle: RePEc:cup:etheor:v:21:y:2005:i:05:p:877-906_05
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    Cited by:

    1. Peter C.B. Phillips & Binbin Guo & Zhijie Xiao, 2002. "Efficient Regression in Time Series Partial Linear Models," Cowles Foundation Discussion Papers 1363, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. 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.
    4. 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.
    5. George Athanasopoulos & Minfeng Deng & Gang Li & Haiyan Song, 2013. "Domestic and outbound tourism demand in Australia: a System-of-Equations Approach," Monash Econometrics and Business Statistics Working Papers 6/13, Monash University, Department of Econometrics and Business Statistics.
    6. 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.
    7. Luya Wang & Zhongwen Liang & Juan Lin & Qi Li, 2015. "Local Constant Kernel Estimation of a Partially Linear Varying Coefficient Cointegration Model," Annals of Economics and Finance, Society for AEF, vol. 16(2), pages 353-369, November.
    8. 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).

    More about this item

    JEL classification:

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