Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

Abstract

view Abstract Citations (23) References (52) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Studies in Astronomical Time Series Analysis. IV. Modeling Chaotic and Random Processes with Linear Filters Scargle, Jeffrey D. 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 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. 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 full text sources ADS | Related Materials (5) Part 1: 1981ApJS...45....1S Part 2: 1982ApJ...263..835S Part 3: 1989ApJ...343..874S Part 5: 1998ApJ...504..405S Part 6: 2013ApJ...764..167S