Estimation of the self-similarity parameter in linear fractional stable motion

  • Authors:

  • Stilian Stoev;Vladas Pipiras;Murad S. Taqqu

  • Affiliations:

  • Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA;Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA;Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA

  • Venue:
  • Signal Processing - Signal processing with heavy-tailed models
  • Year:
  • 2002

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Abstract

We estimate the self-similarity parameter of linear fractional stable motion (lfsm, in short) using two types of estimators referred to as the "power" and the "log" estimators. These estimators involve either approximations to the usual wavelet transform coefficients or are defined by using a discrete linear filter transformation. They can be used in practice, because they involve only discrete time observations. When the index of stability α is in the range (1,2), we show that these estimators are consistent and asymptotically normal for a range of parameter values of lfsm. We use simulated discrete-time lfsm to test and compare them, and we include an extensive discussion on how to compute these estimators in practice. The simulation results indicate that both the "power" and "log" estimators work well when α 1, and the estimator based on the discrete linear filter works well also when α ≤ 1.