Inference on Nonparametrically Trending Time Series with Fractional Errors

19 Pages Posted: 13 May 2009

See all articles by Peter M. Robinson

Peter M. Robinson

London School of Economics & Political Science (LSE) - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: January 2009

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.

JEL Classification: D74;H77;F13;019

Suggested Citation

Robinson, Peter M., Inference on Nonparametrically Trending Time Series with Fractional Errors (January 2009). LSE STICERD Research Paper No. EM532, Available at SSRN: https://ssrn.com/abstract=1401781

Peter M. Robinson (Contact Author)

London School of Economics & Political Science (LSE) - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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