Prediction and nonparametric estimation for time series with heavy tails

Hall, Peter, Peng, Liang and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2002) Prediction and nonparametric estimation for time series with heavy tails. Journal of Time Series Analysis, 23 (3). pp. 313-331. ISSN 0143-9782

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Abstract

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance.

Item Type:	Article
Official URL:	http://www.blackwell-synergy.com/toc/jtsa/23/3
Additional Information:	® 2002 Blackwell Publishing
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	26 Jun 2008 10:13
Last Modified:	20 Oct 2021 00:41
URI:	http://eprints.lse.ac.uk/id/eprint/6086

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