Wavelet-Based Analysis/Software for Multi-Scale Fractal

RES810 – Airforce “Fractal II”

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. Insightful intends 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. And also, to apply our methodology to data provided to use 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).