Econometric Theory

ARTICLES

INFERENCE ON NONPARAMETRICALLY TRENDING TIME SERIES WITH FRACTIONAL ERRORS

P.M. Robinsona1 c1

a1 London School of Economics

Abstract

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.

Correspondence

c1 Address correspondence to Peter M Robinson, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: p.m.robinson@lse.ac.uk.

Footnotes

This research was supported by ESRC Grant RES-062-23-0036. I am grateful for the comments of three referees and Rob Taylor.

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