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INFERENCE ON NONPARAMETRICALLY TRENDING TIME SERIES WITH FRACTIONAL ERRORS

Published online by Cambridge University Press:  01 December 2009

P.M. Robinson
P.M. Robinson*
Affiliation:
London School of Economics
*
*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.
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Abstract

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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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Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1716 - 1733
Copyright
Copyright © Cambridge University Press 2009

References

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