Studies in Astronomical Time Series Analysis. IV. Modeling Chaotic and Random Processes with Linear Filters
Abstract
While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This timedomain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phasevolume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phaseportrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimumdelay pulse shapes in nonGaussian processes, both random and chaotic.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1990
 DOI:
 10.1086/169079
 Bibcode:
 1990ApJ...359..469S
 Keywords:

 Astronomical Models;
 Chaos;
 Computational Astrophysics;
 Linear Filters;
 Random Processes;
 Time Series Analysis;
 Algorithms;
 Autoregressive Processes;
 Luminosity;
 Astrophysics;
 NUMERICAL METHODS