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Local linear regression estimation for time series with long-range dependence

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  • Masry, Elias
  • Mielniczuk, Jan
Abstract
Consider the nonparametric estimation of a multivariate regression function and its derivatives for a regression model with long-range dependent errors. We adopt local linear fitting approach and establish the joint asymptotic distributions for the estimators of the regression function and its derivatives. The nature of asymptotic distributions depends on the amount of smoothing resulting in possibly non-Gaussian distributions for large bandwidth and Gaussian distributions for small bandwidth. It turns out that the condition determining this dichotomy is different for the estimates of the regression function than for its derivatives; this leads to a double bandwidth dichotomy whereas the asymptotic distribution for the regression function estimate can be non-Gaussian whereas those of the derivatives estimates are Gaussian. Asymptotic distributions of estimates of derivatives in the case of large bandwidth are the scaled version of that for estimates of the regression function, resembling the situation of estimation of cumulative distribution function and densities under long-range dependence. The borderline case between small and large bandwidths is also examined.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:173-193
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    References listed on IDEAS

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    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. 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.
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    5. Cheng, Bing & Robinson, P. M., 1994. "Semiparametric estimation from time series with long-range dependence," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 335-353.
    6. Koul, Hira L., 1992. "M-estimators in linear models with long range dependent errors," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 153-164, May.
    7. 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.
    8. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    9. 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.
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    Cited by:

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    4. Mario Francisco-Fernandez & Juan Vilar-Fernandez, 2004. "Weighted Local Nonparametric Regression with Dependent Errors: Study of Real Private Residential Fixed Investment in the USA," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 69-93, March.

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