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Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filtersWhile 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 time-domain 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 phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait 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 nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.
Document ID
19900059051
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Scargle, Jeffrey D.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
August 14, 2013
Publication Date
August 20, 1990
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 359
ISSN: 0004-637X
Subject Category
Astrophysics
Accession Number
90A46106
Distribution Limits
Public
Copyright
Other

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