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Estimating smooth structural change in cointegration models

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  • Phillips, Peter C.B.
  • Li, Degui
  • Gao, Jiti

Abstract

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to re-orient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:196:y:2017:i:1:p:180-195
    DOI: 10.1016/j.jeconom.2016.09.013
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    2. Lopes Moreira Da Veiga, María Helena & Mao, Xiuping & Casas Villalba, Maria Isabel, 2020. "Adaptative predictability of stock market returns," DES - Working Papers. Statistics and Econometrics. WS 31648, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Li, Degui & Phillips, Peter C. B. & Gao, Jiti, 2016. "Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 32(3), pages 655-685, June.
    4. Kapetanios, George & Millard, Stephen & Price, Simon & Petrova, Katerina, 2018. "Time varying cointegration and the UK Great Ratios," Essex Finance Centre Working Papers 23320, University of Essex, Essex Business School.
    5. Isabel Casas & Eva Ferreira & Susan Orbe, 2017. "Time-varying coefficient estimation in SURE models. Application to portfolio management," CREATES Research Papers 2017-33, Department of Economics and Business Economics, Aarhus University.
    6. Li, Degui & Phillips, Peter C.B. & Gao, Jiti, 2020. "Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression," Journal of Econometrics, Elsevier, vol. 215(2), pages 607-632.
    7. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    8. Harris, A.R. & Rogers, Michelle Marinich & Miller, Carol J. & McElmurry, Shawn P. & Wang, Caisheng, 2015. "Residential emissions reductions through variable timing of electricity consumption," Applied Energy, Elsevier, vol. 158(C), pages 484-489.
    9. Isabel Casas & Xiuping Mao & Helena Veiga, 2018. "Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium," CREATES Research Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    10. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    11. Kapetanios, George & Millard, Stephen & Petrova, Katerina & Price, Simon, 2020. "Time-varying cointegration with an application to the UK Great Ratios," Economics Letters, Elsevier, vol. 193(C).
    12. Kashif Yousuf & Serena Ng, 2019. "Boosting High Dimensional Predictive Regressions with Time Varying Parameters," Papers 1910.03109, arXiv.org.

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    More about this item

    Keywords

    Cointegration; Endogeneity; Kernel degeneracy; Nonparametric regression; Super-consistency; Time varying coefficients;
    All these keywords.

    JEL classification:

    • 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
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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