Detection and modeling of chaotic dynamics using wavelet techniques
Jeffrey D. Scargle · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
Powerful new data analysis techniques based on wavelets are proving extremely useful in the reduction and interpretation of time series data. The goals of these methods include denoising, characterizing, modeling, and compressing of time series data. The multi-scale nature of wavelet analysis makes it especially useful for detection and characterization of self-similar or 'scaling' behavior, such as is common for chaotic processes. This paper describes how wavelet techniques led to a transient-chaos model for a rapidly fluctuating celestial X-ray source. The methods described here are freely available in a new software package called TeachWave, developed by David Donoho and Iain Johnstone of Stanford University (anonymous ftp to playfair.stanford.edu; the software is in directory /pub/software/wavelets, and a number of related technical papers are in /pub/reports).