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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

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.

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

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References

REFERENCES

Csorgo, S. & Mielniczuk, J. (1995) Nonparametric regression under long-range dependent normal errors. Annals of Statistics 23, 1000–1014.CrossRefGoogle Scholar
Fox, R. & Taqqu, M.S. (1985) Non-central limit theorems for quadratic forms in random variables having long-range dependence. Annals of Probability 13, 428–446.CrossRefGoogle Scholar
Gradshteyn, I.R. & Ryzhik, I.M. (1994) Table of Integrals, Series and Products. Academic Press.Google Scholar
Hall, P.. & Hart, J.D. (1990) Nonparametric regression with long-range dependence. Stochastic Processes and Their Applications 36, 339–351.CrossRefGoogle Scholar
Knuth, D.E. (1968) The Art of Computer Programming, vol. 1. Fundamental Algorithms. Addison-Wesley.Google Scholar
Robinson, P.M. (1997) Large-sample inference for nonparametric regression with dependent errors. Annals of Statistics 28, 2054–2083.Google Scholar
Robinson, P.M. (2007) Nonparametric regression with spatial data. Working paper, London School of Economics.Google Scholar
Roussas, G., Tran, L.T., & Ioannides, O.A. (1992) Fixed design regression for time series: Asymptotic normality. Journal of Multivariate Analysis 40, 262–291.CrossRefGoogle Scholar
Yong, C.H. (1974) Asymptotic Behaviour of Trigonometric Series. Chinese University of Hong Kong.Google Scholar