IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v65y1996i1p81-101.html
   My bibliography  Save this article

Multivariate regression estimation local polynomial fitting for time series

Author

Listed:
  • Masry, Elias

Abstract

We consider the estimation of the multivariate regression function m(x1, ..., xd) = E[[psi](Yd)X1 = x1, ..., Xd = xd], and its partial derivatives, for stationary random processes Yi, Xi using local higher-order polynomial fitting. Particular cases of [psi] yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and [varrho]-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:81-101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(96)00095-6
    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. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    2. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    3. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    4. 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.
    5. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    Full references (including those not matched with items on IDEAS)

    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. Masry, Elias & Mielniczuk, Jan, 1999. "Local linear regression estimation for time series with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 173-193, August.
    2. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April.
    3. Seok Young Hong & Oliver Linton, 2016. "Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of in finite order," CeMMAP working papers 53/16, Institute for Fiscal Studies.
    4. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    5. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    6. Hong, Seok Young & Linton, Oliver, 2020. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Journal of Econometrics, Elsevier, vol. 219(2), pages 389-424.
    7. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    8. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    9. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. 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.
    11. Karlsen, Hans Arnfinn & Tjostheim, Dag, 1998. "Nonparametric estimation in null recurrent times series," SFB 373 Discussion Papers 1998,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    13. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 97-120.
    14. 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.
    15. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(5), pages 911-952, October.
    16. Franke, Jürgen & Kreiss, Jens-Peter & Mammen, Enno, 1997. "Bootstrap of kernel smoothing in nonlinear time series," SFB 373 Discussion Papers 1997,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    17. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    18. Kim, Woocheol & Linton, Oliver, 2003. "A local instrumental variable estimation method for generalized additive volatility models," LSE Research Online Documents on Economics 2028, London School of Economics and Political Science, LSE Library.
    19. Jürgen Franke & Peter Mwita & Weining Wang, 2015. "Nonparametric estimates for conditional quantiles of time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 107-130, January.
    20. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.

    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:spapps:v:65:y:1996:i:1:p:81-101. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.