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Inference On Nonparametrically Trending Time Series With Fractional Errors

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  • Peter M Robinson
Abstract
The central limit theorem for nonparametric kernel estimates of a smooth trend,with linearly-generated errors, indicates asymptotic independence andhomoscedasticity across fixed points, irrespective of whether disturbances haveshort memory, long memory, or antipersistence. However, the asymptotic variancedepends on the kernel function in a way that varies across these threecircumstances, and in the latter two involves a double integral that cannotnecessarily be evaluated in closed form. For a particular class of kernels, weobtain analytic formulae. We discuss extensions to more general settings,including ones involving possible cross-sectional or spatial dependence.

Suggested Citation

  • Peter M Robinson, 2009. "Inference On Nonparametrically Trending Time Series With Fractional Errors," STICERD - Econometrics Paper Series 532, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:532
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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. 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.
    3. 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.
    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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    Cited by:

    1. Mahmoud, Hamdy F.F. & Kim, Inyoung, 2019. "Semiparametric spatial mixed effects single index models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 108-122.

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