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Inference On Nonparametrically Trending Time Series With Fractional Errors


  • Robinson, P.M.


The central limit theorem for nonparametric kernel estimates of a smooth trend, with linearly generated errors, indicates asymptotic independence and homoskedasticity 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 it involves a double integral that cannot necessarily be evaluated in closed form. For a particular class of kernels, we obtain analytic formulas. We discuss extensions to more general settings, including ones involving possible cross-sectional or spatial dependence.

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  • Robinson, P.M., 2009. "Inference On Nonparametrically Trending Time Series With Fractional Errors," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1716-1733, December.
  • Handle: RePEc:cup:etheor:v:25:y:2009:i:06:p:1716-1733_99

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    References listed on IDEAS

    1. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    2. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    3. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, March.
    4. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
    5. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    6. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(04), pages 865-887, August.
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