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.
Original language | English |
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Pages (from-to) | 313-331 |
Number of pages | 19 |
Journal | Journal of Time Series Analysis |
Volume | 23 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 2002 |