By Cees Diks
ISBN-10: 9810235054
ISBN-13: 9789810235055
Tools of nonlinear time sequence research are mentioned from a dynamical platforms standpoint at the one hand, and from a statistical standpoint at the different. After giving an off-the-cuff review of the speculation of dynamical structures suitable to the research of deterministic time sequence, time sequence generated through nonlinear stochastic platforms and spatio-temporal dynamical platforms are thought of. a number of statistical equipment for the research of nonlinear time sequence are provided and illustrated with functions to actual and physiological time sequence.
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Extra info for Nonlinear Time Series Analysis: Methods And Applications
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E. the disturbance is of the same order of magnitude as it would be for observational noise), whereas the invariant measure is disturbed to a much larger extend for other parameter values. 2. Stochastic Time Series Models A brief summary of stochastic time series modeling is given here. For a review of stochastic models, including nonlinear analogs of ARMA models, we refer to the book by Tong (1990) and references therein. Traditionally, noise sources have been considered to be the essential el ements for models of erratic time series, and a large amount of theory on stochastic models is available at present.
1. Observational Noise Observational noise, or measurement noise, can be thought of as noise im posed upon a time series by the measurement apparatus. d. d. noise. 29 30 3. 1: Phase portraits for (a) a clean Rossler time series and (b) the same time series with 5% Gaussian observational noise. 1 which shows phase portraits of an i-component time series generated by Rossler's model and of the same time series with Gaussian observational noise with a standard deviation of 5% of the standard deviation of the clean time series.
Strictly speaking, however, this noise source is deterministic and one might wonder what effect this has on the properties of estimators of linear model parameters. Motivated by this idea Stockis and Tong (1998) have ex amined the properties of estimators of model parameters of chaos driven linear AR models. 12) where {e n } is a chaotic process. 5 with en = yn - 1/2, where yn evolves according to the logistic map yn+l = 4j/„(l - yn). d. Gaussian sequence of random variables. It turns out that under relatively weak mixing conditions on the chaotic driving process one still obtains asymptotic normality for these estimators.