Hall, Peter, Peng, Liang and Yao, Qiwei (2002) Prediction and nonparametric estimation for time series with heavy tails. Journal of time series analysis, 23 (3). pp. 251-375. 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 |
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| Official URL: | http://www.blackwell-synergy.com/toc/jtsa/23/3 |
| Additional Information: | ® 2002 Blackwell Publishing |
| Uncontrolled Keywords: | ARMA model, conditional median, heavy tail, least absolute deviation estimation, local-linear regression, prediction, regular variation, ρ-mixing, stable distribution, strong mixing, time series analysis |
| Library of Congress subject classification: | H Social Sciences > HA Statistics |
| Sets: | Collections > Economists Online Departments > Statistics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/6086/ |
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