Summary: SCALING EXPONENTS ESTIMATION FOR MULTISCALING PROCESSES
B. Lashermes, P. Abry,
CNRS, Physics Laboratory,
Ecole Normale Sup´erieure, Lyon, France.
Universit´e Blaise Pascal, Aubi`ere, France.
We study the statistical performance of multiresolution (wavelet
based) estimators commonly used for the estimation of the scaling
exponents (q) of multifractal processes. So far, such studies were
conducted exclusively using the celebrated Mandelbrot's cascades.
A new class of processes, compound Poisson cascades, with better
statistical properties -- stationary increments and continuous scale
invariance -- has recently been proposed in the literature. Making
use of this new type of processes, we show that the multiresolution
estimators are characterised by a generic and systematic feature:
beyond a critical order q (which is determined analytically), they