Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T04:09:29.133Z Has data issue: false hasContentIssue false
  • English
  • Français

LAD ASYMPTOTICS UNDER CONDITIONAL HETEROSKEDASTICITY WITH POSSIBLY INFINITE ERROR DENSITIES

Published online by Cambridge University Press:  05 March 2010

Jin Seo Cho ,
Chirok Han  and
Peter C.B. Phillips
Get access Rights & Permissions [Opens in a new window]

Abstract

Least absolute deviations (LAD) estimation of linear time series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data.

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 953 - 962
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank Paolo Paruolo and three referees for helpful comments on the original version. The paper is motivated by technical considerations that arose in revising Han, Cho, and Phillips (2009, manuscript) for the Journal of Business & Economics Statistics, and we are grateful to the JBES review for raising them. Han acknowledges research support from a Korea University Special Faculty Research Fund. Phillips acknowledges support from a Kelly Fellowship and the NSF under grant SES 06-47086.

References

REFERENCES

Bose, A. & Chatterjee, S. (2001) Generalised bootstrap in non-regular M-estimation problems. Statistics and Probability Letters 55, 319–328.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, 755–770.CrossRefGoogle Scholar
Knight, K. (1999) Asymptotics for L 1-estimators of regression parameters under heteroscedasticity. Canadian Journal of Statistics 27, 497–507.CrossRefGoogle Scholar
Koenker, R. & Zhao, Q. (1996) Conditional quantile estimation and inference for ARCH models. Econometric Theory 12, 793–813.CrossRefGoogle Scholar
McLeish, D.L. (1974) Dependent central limit theorems and invariance principles. Annals of Probability 2, 620–628.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) A shortcut to LAD estimator asymptotics. Econometric Theory 7, 450–463.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Rogers, A.J. (2001) Least absolute deviations regression under nonstandard conditions. Econometric Theory 17, 820–852.CrossRefGoogle Scholar