IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v170y2012i1p15-31.html
   My bibliography  Save this article

Functional coefficient regression models with time trend

Author

Listed:
  • Liang, Zhongwen
  • Li, Qi

Abstract

We consider the problem of estimating a varying coefficient regression model when regressors include a time trend. We show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result, while a local polynomial estimator yields a consistent estimation result. We establish the asymptotic normality result for the proposed estimator. We also provide asymptotic analysis of the data-driven (least squares cross validation) method of selecting the smoothing parameters. In addition, we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator. Two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models. Simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics.

Suggested Citation

  • Liang, Zhongwen & Li, Qi, 2012. "Functional coefficient regression models with time trend," Journal of Econometrics, Elsevier, vol. 170(1), pages 15-31.
    • Handle: RePEc:eee:econom:v:170:y:2012:i:1:p:15-31
    DOI: 10.1016/j.jeconom.2011.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612000784
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2011.08.009?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

    for a different version of it.

    References listed on IDEAS

    as
    1. T. Stengos & E. Zacharias, 2006. "Intertemporal pricing and price discrimination: a semiparametric hedonic analysis of the personal computer market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 371-386, April.
    2. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    3. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(3), pages 343-360.
    4. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    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. 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.
    7. 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.
    8. 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.
    9. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
    10. Perron, P, 1993. "Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]," Econometrica, Econometric Society, vol. 61(1), pages 248-249, January.
    11. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    12. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    13. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    14. Theofanis P. Mamuneas & Andreas Savvides & Thanasis Stengos, 2006. "Economic development and the return to human capital: a smooth coefficient semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 111-132, January.
    15. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    16. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.
    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. repec:wyi:journl:002112 is not listed on IDEAS
    2. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    3. Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.

    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. 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.
    2. Chuanhua Wei & Lijie Wan, 2015. "Efficient Estimation in Heteroscedastic Varying Coefficient Models," Econometrics, MDPI, vol. 3(3), pages 1-7, July.
    3. Li, Kunpeng & Li, Weiming, 2013. "Estimation of varying coefficient models with time trend and integrated regressors," Economics Letters, Elsevier, vol. 119(1), pages 89-93.
    4. Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    5. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    6. David Neto, 2015. "Testing for and dating structural break in smooth time-varying cointegration parameters, with an application to retail gasoline price and crude oil price long-run relationship," Empirical Economics, Springer, vol. 49(3), pages 909-928, November.
    7. repec:wyi:journl:002096 is not listed on IDEAS
    8. repec:wyi:journl:002112 is not listed on IDEAS
    9. Yuying Sun & Shaoxin Hong & Zongwu Cai, 2023. "Optimal Local Model Averaging for Divergent-Dimensional Functional-Coefficient Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202309, University of Kansas, Department of Economics, revised Sep 2023.
    10. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
    11. Lumsdaine, Robin L. & Ng, Serena, 1999. "Testing for ARCH in the presence of a possibly misspecified conditional mean," Journal of Econometrics, Elsevier, vol. 93(2), pages 257-279, December.
    12. Sun, Yiguo & Hsiao, Cheng & Li, Qi, 2011. "Measuring correlations of integrated but not cointegrated variables: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 164(2), pages 252-267, October.
    13. Gan, Li & Hsiao, Cheng & Xu, Shu, 2014. "Model specification test with correlated but not cointegrated variables," Journal of Econometrics, Elsevier, vol. 178(P1), pages 80-85.
    14. Wang, Ying & Phillips, Peter C.B., 2025. "Limit theory for local polynomial estimation of functional coefficient models with possibly integrated regressors," Journal of Econometrics, Elsevier, vol. 249(PB).
    15. Long, Wei & Ouyang, Min & Shang, Ying, 2013. "Efficient estimation of partially linear varying coefficient models," Economics Letters, Elsevier, vol. 121(1), pages 79-81.
    16. 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.
    17. Peng, Yi-Ting & Chang, Tsangyao & Ranjbar, Omid, 2025. "Analyzing the dynamics of the persistence of energy-related uncertainty of G7 countries: What does the time-varying SUR-ADF model say?," Energy, Elsevier, vol. 320(C).
    18. 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.
    19. Qi Gao & Jingping Gu & Paula Hernandez-Verme, 2012. "A Semiparametric Time Trend Varying Coefficients Model: With An Application to Evaluate Credit Rationing in U.S. Credit Market," Annals of Economics and Finance, Society for AEF, vol. 13(1), pages 189-210, May.
    20. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    21. Nasreen, Samia & Anwar, Sofia & Ozturk, Ilhan, 2017. "Financial stability, energy consumption and environmental quality: Evidence from South Asian economies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 67(C), pages 1105-1122.
    22. Shyh-Wei Chen, 2008. "Non-stationarity and Non-linearity in Stock Prices: Evidence from the OECD Countries," Economics Bulletin, AccessEcon, vol. 3(11), pages 1-11.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • 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

    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:170:y:2012:i:1:p:15-31. 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.