Wavelet Based Analysis/Software for Multi-Scale Fractal Processes

Period of Performance: 08/01/2000 - 08/01/2002

$500K

Phase 2 STTR

Recipient Firm

Mathsoft, Inc.
1700 Westlake Avenue N., Suite 500
Seattle, WA 98109
Principal Investigator
Firm POC

Research Institution

University of Washington
Department of Aeronautics&Astronautics, Box 352250
Seattle, WA 98195
Institution POC

Abstract

We propose to conduct research on the analysis of time series that are generated by non-stationary multi-fractal processes (examples of such series include atmospheric turbulence). Because the discrete wavelet transform is a natural tool for use with non-stationary and scale-dependent data, we propose to study estimators based upon this transform. These include wavelet-based approximate maximum likelihood and least squares estimators of fractionally differenced processes adapted to work effectively in the presence of (i) time-varying power laws, (ii) multi-scale fractal characteristics and (iii) large scale trends. We propose to investigate the prediction (extrapolation) of non-stationary multi-fractal processes through a subband decomposition approach in which forecasts on each subband are generated using either stochastic or deterministic predictors and then recombined using the inverse discrete wavelet transform to create a forecast for the original time series. We also propose to apply our methodology to data provided to us by our Air Force sponsors (e.g., weather radar data). We propose to create a commercial-grade set of C routines that will encompass all of the methodology that comes out of our research along with a comprehensive collection of other techniques for dealing with multi-scale fractal processes (e.g., rescaled range analysis, dispersional analysis and scaled windowed variance methods).