IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v187y2015i1p189-200.html
   My bibliography  Save this article

Semiparametric model building for regression models with time-varying parameters

Author

Listed:
  • Zhang, Ting

Abstract

This paper considers the problem of semiparametric model building for linear regression models with potentially time-varying coefficients. By allowing the response variable and explanatory variables be jointly a nonstationary process, the proposed methods are widely applicable to nonstationary and dependent observations. We propose a local linear shrinkage method that can simultaneously achieve parameter estimation and variable selection. Its selection consistency and the favorable oracle property are established. Due to the fear of losing efficiency, an information criterion is further proposed for distinguishing between time-varying and time-constant components. Numerical examples are presented to illustrate the proposed methods.

Suggested Citation

  • Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:189-200
    DOI: 10.1016/j.jeconom.2015.02.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615000469
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.02.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746, November.
    4. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
    5. Jiti Gao & Kim Hawthorne, 2006. "Semiparametric estimation and testing of the trend of temperature series," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 332-355, July.
    6. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    7. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    8. 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.
    9. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    10. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    11. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    12. 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.
    13. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    14. 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.
    15. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    16. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    17. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    18. Dahlhaus, R. & Neumann, M. & Von Sachs, R., 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    19. Cheng, Ming-Yen & Zhang, Wenyang & Chen, Lu-Hung, 2009. "Statistical Estimation in Generalized Multiparameter Likelihood Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1179-1191.
    20. Kevin Q. Wang, 2003. "Asset Pricing with Conditioning Information: A New Test," Journal of Finance, American Finance Association, vol. 58(1), pages 161-196, February.
    21. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    22. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    23. Melissa Dell & Benjamin F. Jones & Benjamin A. Olken, 2012. "Temperature Shocks and Economic Growth: Evidence from the Last Half Century," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(3), pages 66-95, July.
    24. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    25. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
    26. Ting Zhang & Wei Biao Wu, 2011. "Testing parametric assumptions of trends of a nonstationary time series," Biometrika, Biometrika Trust, vol. 98(3), pages 599-614.
    27. Degui Li & Jia Chen & Zhengyan Lin, 2009. "Variable selection in partially time-varying coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 553-566.
    28. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    29. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    30. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    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. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    2. Likai Chen & Ekaterina Smetanina & Wei Biao Wu, 2022. "Estimation of nonstationary nonparametric regression model with multiplicative structure [Income and wealth distribution in macroeconomics: A continuous-time approach]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 176-214.

    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. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    2. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    3. Weihua Zhao & Riquan Zhang & Jicai Liu & Yazhao Lv, 2014. "Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 165-191, February.
    4. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    5. Chen, Bin & Maung, Kenwin, 2023. "Time-varying forecast combination for high-dimensional data," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Zhao, Weihua & Zhang, Riquan & Liu, Jicai & Hu, Hongchang, 2015. "Robust adaptive estimation for semivarying coefficient models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 132-141.
    7. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    8. Tian, Ruiqin & Xue, Liugen & Liu, Chunling, 2014. "Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 94-110.
    9. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
    10. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    11. Lian, Heng, 2015. "Quantile regression for dynamic partially linear varying coefficient time series models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 49-66.
    12. Zhao, Weihua & Lian, Heng, 2017. "Quantile index coefficient model with variable selection," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 40-58.
    13. Huazhen Lin & Hyokyoung G. Hong & Baoying Yang & Wei Liu & Yong Zhang & Gang-Zhi Fan & Yi Li, 2019. "Nonparametric Time-Varying Coefficient Models for Panel Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 548-566, December.
    14. Bin Chen & Kenwin Maung, 2020. "Time-varying Forecast Combination for High-Dimensional Data," Papers 2010.10435, arXiv.org.
    15. Zhaoping Hong & Yuao Hu & Heng Lian, 2013. "Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 887-908, October.
    16. Xia, Xiaochao & Yang, Hu & Li, Jialiang, 2016. "Feature screening for generalized varying coefficient models with application to dichotomous responses," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 85-97.
    17. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    18. Heng Lian & Peng Lai & Hua Liang, 2013. "Partially Linear Structure Selection in Cox Models with Varying Coefficients," Biometrics, The International Biometric Society, vol. 69(2), pages 348-357, June.
    19. Weihua Zhao & Riquan Zhang & Jicai Liu, 2013. "Robust variable selection for the varying coefficient model based on composite L 1 -- L 2 regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2024-2040, September.
    20. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.

    More about this item

    Keywords

    Information criterion; Nonstationary processes; Penalization methods; Semiparametric variable selection; Time-varying coefficient models;
    All these keywords.

    JEL classification:

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

    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:eee:econom:v:187:y:2015:i:1:p:189-200. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.