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Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates

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  • Li, Degui
  • Lu, Zudi
  • Linton, Oliver

Abstract

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton ( 2007 , Econometric Theory 23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

Suggested Citation

  • Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(05), pages 935-958, October.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:05:p:935-958_00
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    References listed on IDEAS

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    1. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1433-1445, October.
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    3. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
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    5. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    6. Lu, Zudi, 1996. "A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 305-311, November.
    7. 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(02), pages 258-289, February.
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    10. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    11. Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 447-468, September.
    12. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    13. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(06), pages 995-1045, December.
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    Citations

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    Cited by:

    1. 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.
    2. Jia Chen & Degui Li & Oliver Linton & Zudi Lu, 2015. "Semiparametric model averaging of ultra-high dimensional time series," CeMMAP working papers CWP62/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Chen, Jia & Li, Degui & Linton, Oliver & Lu, Zudi, 2016. "Semiparametric dynamic portfolio choice with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 194(2), pages 309-318.
    4. Yang, Lixiong & Lee, Chingnun & Shie, Fu Shuen, 2014. "How close a relationship does a capital market have with other markets? A reexamination based on the equal variance test," Pacific-Basin Finance Journal, Elsevier, vol. 26(C), pages 198-226.
    5. Lee, Jiyon, 2015. "A semiparametric single index model with heterogeneous impacts on an unobserved variable," Journal of Econometrics, Elsevier, vol. 184(1), pages 13-36.
    6. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    7. James A. Duffy, 2015. "Uniform Convergence Rates over Maximal Domains in Structural Nonparametric Cointegrating Regression," Economics Papers 2015-W03, Economics Group, Nuffield College, University of Oxford.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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

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