Nonparametric regression under dependent errors with infinite variance

Liang Peng and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic limit of the estimator is established under the assumption that the process has either short or long memory autocorrelation. For a short memory process, the estimator admits the same convergence rate as if the process has the finite variance. The optimal rate of convergence n−2/5 is obtainable by using appropriate bandwidths. This is distinctly different from local least squares estimation, of which the convergence is slowed down due to the existence of heavy tails. On the other hand, the rate of convergence of the LLAD estimator for a long memory process is always slower than n−2/5 and the limit is no longer normal.

JEL-codes: C1 (search for similar items in EconPapers)
Date: 2004-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Published in Annals of the Institute of Statistical Mathematics, March, 2004, 56(1), pp. 73-86. ISSN: 0020-3157

Downloads: (external link)
http://eprints.lse.ac.uk/22874/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:22874

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().