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Prediction and nonparametric estimation for time series with heavy tails

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  • Hall, Peter
  • Peng, Liang
  • Yao, Qiwei

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.

Suggested Citation

  • Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Prediction and nonparametric estimation for time series with heavy tails," LSE Research Online Documents on Economics 6086, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:6086
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    File URL: http://eprints.lse.ac.uk/6086/
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    Citations

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    Cited by:

    1. Ghosh, Yashowanto N. & Mukherjee, Bhramar, 2006. "On probabilistic properties of conditional medians and quantiles," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1775-1780, October.
    2. Toshio Honda, 2010. "Nonparametric estimation of conditional medians for linear and related processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 995-1021, December.
    3. Toshio Honda, 2013. "Nonparametric quantile regression with heavy-tailed and strongly dependent errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 23-47, February.
    4. Honda, Toshio, 2013. "Nonparametric LAD cointegrating regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 150-162.
    5. Peng, Liang & Yao, Qiwei, 2017. "Estimating conditional means with heavy tails," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 14-22.
    6. Bonsoo Koo & Oliver Linton, 2013. "Let's get LADE: robust estimation of semiparametric multiplicative volatility models," CeMMAP working papers 11/13, Institute for Fiscal Studies.
    7. Peng, Liang & Yao, Qiwei, 2017. "Estimating conditional means with heavy tails," LSE Research Online Documents on Economics 73082, London School of Economics and Political Science, LSE Library.
    8. Peng, Liang & Yao, Qiwei, 2004. "Nonparametric regression under dependent errors with infinite variance," LSE Research Online Documents on Economics 22874, London School of Economics and Political Science, LSE Library.

    More about this item

    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;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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