InterJournal Complex Systems, 387
Status: Accepted
Manuscript Number: [387]
Submission Date: 508
Multifractal Wavelet Estimation
Author(s): Carlos Morales ,Eric Kolaczyk

Subject(s): CX.08, CX.01

Category: Brief Article

Abstract:

Fractal processes have become a successful and widely used modeling tool, from turbulence and finance to network traffic and geophysics. The multi-fractal spectrum (MFS) quantifies the presence of possibly multiple local scaling behavior from sample paths of these processes. Fractional Brownian motion (fBm) is a very important subclass of uni-scaling fractal processes which is both mathematically tractable and appealing for modeling data. In this paper, we present a novel, wavelet-based procedure for MFS estimation,and explore its properties in the context of fBm processes. Sample Moments of the Discrete Wavelet Transform (DWT) of fBm are used to estimate the so-calledscaling (partition) function. The latter is intimately linked to the MFS via a Lengendre Transform. While typical practice calculates the Lengendre of a linear regression smoothing of the scaling function, via numerical differencing, we find that an alternative approach, based on a linear smoothing of the derivative of the scaling function yields improved results. We present statistical properties of the novel procedure, comparing its performance to alternative procedures via a simulation study.

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