IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v157y2010i1p151-164.html
   My bibliography  Save this article

Nonparametric transfer function models

Author

Listed:
  • Liu, Jun M.
  • Chen, Rong
  • Yao, Qiwei

Abstract

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example.

Suggested Citation

  • Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:1:p:151-164
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00282-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Su, Liangjun & Ullah, Aman, 2006. "More Efficient Estimation In Nonparametric Regression With Nonparametric Autocorrelated Errors," Econometric Theory, Cambridge University Press, vol. 22(1), pages 98-126, February.
    2. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    3. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    4. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    5. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    6. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. Michael Smith & Chi‐Ming Wong & Robert Kohn, 1998. "Additive nonparametric regression with autocorrelated errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 311-331.
    9. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    10. 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.
    11. Tsay, Ruey S, 1985. "Model Identification in Dynamic Regression (Distributed Lag) Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 228-237, June.
    12. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    13. Xiao Z. & Linton O.B. & Carroll R.J. & Mammen E., 2003. "More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 980-992, January.
    14. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
    15. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    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. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
    2. Peng, Liang & Einmahl, John, 2021. "Improved regression inference using a second overlapping regression model," Other publications TiSEM c529c2b9-0eee-440e-b015-8, Tilburg University, School of Economics and Management.
    3. Markku Lanne & Jani Luoto & Henri Nyberg, 2014. "Is the Quantity Theory of Money Useful in Forecasting U.S. Inflation?," CREATES Research Papers 2014-26, Department of Economics and Business Economics, Aarhus University.
    4. Alan T. K. Wan & Jinhong You & Riquan Zhang, 2016. "A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 894-928, May.
    5. Wei, Honglei & Zhang, Hongfan & Jiang, Hui & Huang, Lei, 2022. "On the semi-varying coefficient dynamic panel data model with autocorrelated errors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    6. Bingduo Yang & Xiaohui Liu & Liang Peng & Zongwu Cai, 2018. "Unified Tests for a Dynamic Predictive Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201808, University of Kansas, Department of Economics, revised Sep 2018.
    7. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    8. Peng, Liang & Einmahl, John, 2021. "Improved regression inference using a second overlapping regression model," Discussion Paper 2021-029, Tilburg University, Center for Economic Research.
    9. Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.

    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. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    2. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    3. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," LSE Research Online Documents on Economics 28868, London School of Economics and Political Science, LSE Library.
    4. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    5. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    6. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    7. Aneiros-Perez, G. & Vilar-Fernandez, J.M., 2008. "Local polynomial estimation in partial linear regression models under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2757-2777, January.
    8. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    9. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    10. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    11. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    12. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    13. Xialu Liu & Zongwu Cai & Rong Chen, 2015. "Functional coefficient seasonal time series models with an application of Hawaii tourism data," Computational Statistics, Springer, vol. 30(3), pages 719-744, September.
    14. Deniz Ozabaci & Daniel Henderson, 2015. "Additive kernel estimates of returns to schooling," Empirical Economics, Springer, vol. 48(1), pages 227-251, February.
    15. Jin-Hong Park, 2012. "Nonparametric approach to intervention time series modeling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1397-1408, December.
    16. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    17. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    18. Dette, Holger & Weißbach, Rafael, 2009. "A bootstrap test for the comparison of nonlinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1339-1349, February.
    19. Park, Jin-Hong & Bandyopadhyay, Dipankar & Letourneau, Elizabeth, 2014. "Examining deterrence of adult sex crimes: A semi-parametric intervention time-series approach," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 198-207.
    20. Čížek, Pavel & Lei, Jinghua, 2018. "Identification and estimation of nonseparable single-index models in panel data with correlated random effects," Journal of Econometrics, Elsevier, vol. 203(1), pages 113-128.

    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:157:y:2010:i:1:p:151-164. 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.