Robust Wavelet-Domain Estimation of the Fractional Difference Parameter in Heavy-Tailed Time Series: An Empirical Study Articles uri icon

authors

  • JACH, AGNIESZKA EWELINA
  • KOKOSZKA, PIOTR

publication date

  • March 2010

start page

  • 177

end page

  • 197

issue

  • 1

volume

  • 12

international standard serial number (ISSN)

  • 1387-5841

electronic international standard serial number (EISSN)

  • 1573-7713

abstract

  • We investigate the performance of several wavelet-based estimators of the fractional difference parameter. We consider situations where, in addition to long-range dependence, the time series
    exhibit heavy tails and are perturbed by polynomial and change-point
    trends. We make detailed study of a wavelet-domain pseudo
    Maximum Likelihood Estimator (MLE), for which we provide an asymptotic
    and finite-sample justification. Using numerical experiments,
    we show that unlike the traditional time-domain estimators,
    estimators based on the wavelet transform are robust to
    additive trends and change points in mean, and produce accurate
    estimates
    even under significant departures from normality. The
    Wavelet-domain MLE appears to dominate a regression-based wavelet
    estimator
    in terms of smaller root mean squared error. These findings are
    derived from a simulation study and application to computer
    traffic traces.