Matstat seminarium fredagen 14 december 2001 kl 13:15 i MH:227

Constant versus Changing Self-Similarity Index  

Marc Raimondo

School of Mathematics and Statistics
The University of Sydney
NSW 2006, AUSTRALIA.}

Abstract
 
Many experimental data can be modelled using self-similar processes. 
In such applications, one needs to estimate the  self-similar 'index'
(or scaling exponent) from the data.
Most of existing methods for the estimation 
of the scaling exponent (index) assumed that the index is constant.
Medical,  Hydrological, 
Geophysical and Financial data  exhibit self-similarity behaviour but it
is it is often the case, with real data, 
that the  self-similarity behaviour changes as the phenomenon evolves. 
In such setting, the assumption of a constant  scaling exponent may 
be unrealistic. It is therefore of interest to develop statistical
 methods to assess the nature of the self-similar process involved in a given
phenomenon.  In this talk, we will present a procedure 
to test and estimate  time-varying scaling exponent.
We first use a wavelet-based method to estimate the scaling exponent  
at different time points. In a second step, we use polynomial
regression to model the  self-similarity index over time. 
Particular feature of our method includes testing 
Constant versus Changing Self-Similarity Index.
\end{abstract}

Keywords: Fractals, long-memory, polynomial
regression, self-similarity, time series, translation invariant wavelets.