Least absolute deviations estimation for ARCH and GARCH models

Liang Peng and Qiwei Yao

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

Abstract: Hall & Yao (2003) showed that, for ARCH/GARCH, i.e. autoregressive conditional heteroscedastic/generalised autoregressive conditional heteroscedastic, models with heavy‐tailed errors, the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow convergence rates. In this paper three types of absolute deviations estimator have been examined, and the one based on logarithmic transformation turns out to be particularly appealing. We have shown that this estimator is asymptotically normal and unbiased. Furthermore it enjoys the standard convergence rate of n1/2 regardless of whether the errors are heavy‐tailed or not. Simulation lends further support to our theoretical results.

Keywords: ARCH; asymptotic normality; GARCH; gaussian likelihood; heavy tail; least absolute deviations estimator; maximum quasilikelihood estimator; Time series. (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2003-05
References: Add references at CitEc
Citations: View citations in EconPapers (57)

Published in Biometrika, May, 2003, 90(4), pp. 967-975. ISSN: 0006-3444

Downloads: (external link)
http://eprints.lse.ac.uk/5828/ 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:5828

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 ().