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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 modelling. Lu and Linton (2007) 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 modelling.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 28 (2012)
Issue (Month): 05 (October)
Pages: 935-958

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Handle: RePEc:cup:etheor:v:28:y:2012:i:05:p:935-958_00

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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.
  2. Linton, Oliver & Sancetta, Alessio, 2009. "Consistent estimation of a general nonparametric regression function in time series," Journal of Econometrics, Elsevier, vol. 152(1), pages 70-78, September.
  3. Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. 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.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(01), pages 37-70, February.
  7. Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(3), pages 447-468, September.
  8. 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.
  9. Oliver Linton & Enno Mammen, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
  10. 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.
  11. Qiying Wang & Peter C.B. Phillips, 2008. "Structural Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1657, Cowles Foundation for Research in Economics, Yale University.
  12. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
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  14. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  15. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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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. 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.

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