Diffusional approach in time series analysis

Abstract

The identification and prediction of complex series, arising from random or chaotic evolution is one of the main problem in signal processing. The classical way of distinguishing periodic vs. chaotic and chaotic (deterministic) vs. random time series is strongly related to the definition of dynamical invariants such a Ljapunov exponents and metric entropy (a instability parameters) or generalised fractal dimensions (as a measure of the metric complexity). The evaluation of these parameters, using Takens' reconstruction approach implies a long and memory expensive time series processing. This work analyses diffusional identification models, and shows that the diffusional approach in time series processing can lead to practical and meaningful results which improve the analysis of complex and chaotic signals. The principle of the diffusional analysis is related to the temporal behaviour of the correlation function associated to the fluctuation induced by the time series to the motions of a probe particle. >