• Media type: E-Book
  • Title: Prediction and Nonparametric Estimation for Time Series with Heavy Tails
  • Contributor: Hall, Peter [Author]; Peng, Liang [Author]; Yao, Qiwei [Author]
  • Published: [S.l.]: SSRN, 2004
  • Extent: 1 Online-Ressource (19 p)
  • Language: English
  • Origination:
  • Footnote:
  • Description: 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
  • Access State: Open Access