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LAD ASYMPTOTICS UNDER CONDITIONALHETEROSKEDASTICITY WITH POSSIBLY INFINITE ERRORDENSITIES

Published online by Cambridge University Press:  05 March 2010

Abstract

Least absolute deviations (LAD) estimation of lineartime series models is considered under conditionalheteroskedasticity and serial correlation. The limittheory of the LAD estimator is obtained withoutassuming the finite density condition for the errorsthat is required in standard LAD asymptotics. Theresults are particularly useful in application ofLAD estimation to financial time series data.

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Type
Brief Report
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

We thank Paolo Paruolo and three referees forhelpful comments on the original version. Thepaper is motivated by technical considerationsthat arose in revising Han, Cho, and Phillips(2009, manuscript) for the Journal ofBusiness & Economics Statistics, andwe are grateful to the JBESreview for raising them. Han acknowledges researchsupport from a Korea University Special FacultyResearch Fund. Phillips acknowledges support froma Kelly Fellowship and the NSF under grant SES06-47086.

References

REFERENCES

Bose, A. & Chatterjee, S. (2001) Generalised bootstrap in non-regular M-estimation problems. Statistics and Probability Letters 55, 319328.CrossRefGoogle Scholar
Geyer, C.J. (1996) On the Asymptotics of Convex Stochastic Optimization. Manuscript, University of Minnesota, School of Statistics.Google Scholar
Han, C., Cho, J.S., & Phillips, P.C.B. (2009) Infinite Density at the Median and the Typical Shape of Stock Return Distributions. Cowles Foundation Discussion Paper No. 1701, Yale University.Google Scholar
Knight, K. (1998) Limiting distributions for L 1 regression estimators under general conditions. Annals of Statistics 26, 755770.CrossRefGoogle Scholar
Knight, K. (1999) Asymptotics for L 1-estimators of regression parameters under heteroscedasticity. Canadian Journal of Statistics 27, 497507.CrossRefGoogle Scholar
Koenker, R. & Zhao, Q. (1996) Conditional quantile estimation and inference for ARCH models. Econometric Theory 12, 793813.CrossRefGoogle Scholar
McLeish, D.L. (1974) Dependent central limit theorems and invariance principles. Annals of Probability 2, 620628.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) A shortcut to LAD estimator asymptotics. Econometric Theory 7, 450463.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 9711001.CrossRefGoogle Scholar
Rogers, A.J. (2001) Least absolute deviations regression under nonstandard conditions. Econometric Theory 17, 820852.CrossRefGoogle Scholar