IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2109.html
   My bibliography  Save this paper

Kernel-Based Inference In Time-Varying Coefficient Cointegrating Regression

Author

Listed:

Abstract

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fully-modified kernel estimator whose limit distribution theory corresponds to the prototypical pure (i.e., exogenous covariate) cointegration case, thereby facilitating inference using a generalized Wald-type test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of co-moving regressors. Finally an empirical illustration to aggregate US data on consumption, income, and interest rates is provided.

Suggested Citation

  • Degui Li & Peter C.B. Phillips & Jiti Gao, 2017. "Kernel-Based Inference In Time-Varying Coefficient Cointegrating Regression," Cowles Foundation Discussion Papers 2109, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2109
    Note: Includes Supplimental Material
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d21/d2109-a.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    2. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    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. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    5. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    6. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    7. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    8. Bin Chen & Yongmiao Hong, 2012. "Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression," Econometrica, Econometric Society, vol. 80(3), pages 1157-1183, May.
    9. 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.
    10. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    11. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    12. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    13. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, vol. 15(5), pages 664-703, October.
    14. 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.
    15. Xu Cheng & P eter C. B. Phillips, 2009. "Semiparametric cointegrating rank selection," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 83-104, January.
    16. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    17. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    18. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    19. 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.
    20. Kunpeng Li & Degui Li & Zhongwen Liang & Cheng Hsiao, 2017. "Estimation of semi-varying coefficient models with nonstationary regressors," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 354-369, March.
    21. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    22. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    24. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    25. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(4), pages 557-614, August.
    26. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    27. 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.
    28. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ying Wang & Peter C. B. Phillips, 2024. "Limit Theory of Local Polynomial Estimation in Functional Coefficient Regression," Cowles Foundation Discussion Papers 2398, Cowles Foundation for Research in Economics, Yale University.
    2. Haiqi Li Author-Name-First: Haiqi & Jing Zhang & Chaowen Zheng, 2023. "Estimating and Testing for Functional Coefficient Quantile Cointegrating Regression," Economics Discussion Papers em-dp2023-07, Department of Economics, University of Reading.
    3. Polbin, Andrey & Skrobotov, Anton, 2022. "On decrease in oil price elasticity of GDP and investment in Russia," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 66, pages 5-24.
    4. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    5. Yicong Lin & Mingxuan Song, 2023. "Robust bootstrap inference for linear time-varying coefficient models: Some Monte Carlo evidence," Tinbergen Institute Discussion Papers 23-049/III, Tinbergen Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    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. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    5. Gu, Jingping & Liang, Zhongwen, 2014. "Testing cointegration relationship in a semiparametric varying coefficient model," Journal of Econometrics, Elsevier, vol. 178(P1), pages 57-70.
    6. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    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. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    9. 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.
    10. Haiqi Li Author-Name-First: Haiqi & Jing Zhang & Chaowen Zheng, 2023. "Estimating and Testing for Functional Coefficient Quantile Cointegrating Regression," Economics Discussion Papers em-dp2023-07, Department of Economics, University of Reading.
    11. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.
    12. Javier Fernandez-Macho, 2013. "A Test for the Null of Multiple Cointegrating Vectors," Economics Series Working Papers 657, University of Oxford, Department of Economics.
    13. Polbin, Andrey & Skrobotov, Anton, 2022. "On decrease in oil price elasticity of GDP and investment in Russia," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 66, pages 5-24.
    14. Xiao, Zhijie & Phillips, Peter C. B., 2002. "A CUSUM test for cointegration using regression residuals," Journal of Econometrics, Elsevier, vol. 108(1), pages 43-61, May.
    15. Lütkepohl, Helmut, 1999. "Vector autoregressions," SFB 373 Discussion Papers 1999,4, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    17. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    18. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    19. Kunpeng Li & Degui Li & Zhongwen Liang & Cheng Hsiao, 2017. "Estimation of semi-varying coefficient models with nonstationary regressors," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 354-369, March.
    20. Phillips, Peter C.B. & Leirvik, Thomas & Storelvmo, Trude, 2020. "Econometric estimates of Earth’s transient climate sensitivity," Journal of Econometrics, Elsevier, vol. 214(1), pages 6-32.

    More about this item

    Keywords

    Cointegration; FM-kernel estimation; Generalized Wald test; Global rotation; Kernel degeneracy; Local rotation; Super-consistency; Time-varying coefficients;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:2109. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.