Prediction and nonparametric estimation for time series with heavy tails

Peter Hall*, Liang Peng, Qiwei Yao

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    19 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)313-331
    Number of pages19
    JournalJournal of Time Series Analysis
    Volume23
    Issue number3
    DOIs
    Publication statusPublished - May 2002

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