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Inference on nonparametrically trending time series with fractional errors

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  • Robinson, Peter

Abstract

The central limit theorem for nonparametric kernel estimates of a smooth trend, with linearly-generated errors, indicates asymptotic independence and homoscedasticity across fixed points, irrespective of whether disturbances have short memory, long memory, or antipersistence. However, the asymptotic variance depends on the kernel function in a way that varies across these three circumstances, and in the latter two involves a double integral that cannot necessarily be evaluated in closed form. For a particular class of kernels, we obtain analytic formulae. We discuss extensions to more general settings, including ones involving possible cross-sectional or spatial dependence.

Suggested Citation

  • Robinson, Peter, 2008. "Inference on nonparametrically trending time series with fractional errors," LSE Research Online Documents on Economics 25471, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:25471
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    References listed on IDEAS

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    1. Peter M Robinson, 1997. "Large-Sample Inference for Nonparametric Regression with Dependent Errors - (Now published in 'Annals of Statistics', 28 (1997), pp.2054-2083.)," STICERD - Econometrics Paper Series 336, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    3. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    4. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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