Prediction and nonparametric estimation for time series analysis with heavy tails
Date
2002
Authors
Hall, Peter
Peng, L
Yao, Qiwei
Journal Title
Journal ISSN
Volume Title
Publisher
Blackwell Publishing Ltd
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.
Description
Keywords
Keywords: ?-mixing; ARMA model; Conditional median; Heavy tail; Least absolute deviation estimation; Local-linear regression; Prediction; Regular variation; Stable distribution; Strong mixing; Time series analysis
Citation
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Source
Journal of Time Series Analysis
Type
Journal article