Nonlinear Time Series — Bifurcation, Chaos, and Stationarity

Wolfgang Kliemann
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Wolfgang Kliemann: Iowa State University, Department of Mathematics

A chapter in Modelling and Prediction Honoring Seymour Geisser, 1996, pp 389-401 from Springer

Abstract: Abstract The qualitative behavior of time series (like stationarity and ergodicity) is often assumed to be known for time series analysis (like estimation and prediction). For nonlinear time series, the qualitative behavior is often difficult to study. Using associated control systems, we describe a method to determine the system behavior that is successful for series with bounded random term. In the process, we also analyze the relation between deterministic dynamical systems and their random counterparts. This includes bifurcation behavior depending on the parameters of the system, and random perturbations of chaotic attractors.

Keywords: Bifurcation Diagram; Chaotic Attractor; Deterministic System; Invariant Distribution; Nonlinear Time Series (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2414-3_25

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DOI: 10.1007/978-1-4612-2414-3_25

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