You are here:
FALSE DETERMINATIONS OF CHAOS IN SHORT NOISY TIME SERIES. (R828745)
Citation:
Hunt, W., J. Antle, AND K. Paustian. FALSE DETERMINATIONS OF CHAOS IN SHORT NOISY TIME SERIES. (R828745). ENVIRONMENTAL MANAGEMENT. American Chemical Society, Washington, DC.
Description:
A method (NEMG) proposed in 1992 for diagnosing chaos in noisy time series with 50 or fewer observations entails fitting the time series with an empirical function which predicts an observation in the series from previous observations, and then estimating the rate of divergence or convergence of two nearby trajectories of the function (sensitive dependence on initial conditions). Workers applying NEMG have concluded that chaos exists in some natural biological populations. However, there are insufficient published tests of the reliability of NEMG using time series from biologically realistic models with numerous (>4) state variables. Also, there are unresolved technical issues for NEMG: whether or not the data should be detrended (removal of linear or quadratic trends) before analysis, and how long a sampling interval should be used to define the time series. We addressed these issues by applying NEMG to time series of 50 observations generated by four different chaotic models, ranging from simple models of physical systems to a complex ecosystem model. We also analyzed output from non-chaotic versions of each model. Previously recommended guidelines for specifying parameters affecting NEMG diagnoses of chaos were often ineffective. For the models we examined, NEMG produced high incidences of false determinations of chaos in non-chaotic time series, and of the absence of chaos in chaotic time series. Thus the method appears to be unreliable for the circumstances we examined.
Author Keywords: Autocorrelation; Ecological models; Feedforward neural networks; Polynomial functions; Simplex optimization