GENERALIZED AUTOREGRESSION AND THE ANALYSIS OF DYNAMICAL PROCESSES

The dynamics of nonlinear systems can be characterized in terms of res ponse functions. Mathematical representations of data that contain mix ed stochastic-deterministic components are likely to have coefficients that are not well behaved. In these circumstances, statistical averag ing can be used to obtain a moment hierarchy that has well behaved coe fficients and that can be inverted for the response function values. T he moment hierarchy is generated by operating on a convolution series expansion that is truncated so that a tractable set of equations with well behaved coefficients can be solved. The moment hierarchy is used in two contexts. First the analysis of noiseless deterministic mapping s is considered as the precursor to the analysis of experimental data. A chaotic numerical example is used to demonstrate the accuracy of th e moment hierarchy method to identify the order and from of the mappin g and to predict the future behavior of the chaotic sequence. Second, Wolf's annual sunspot number, which is theoretically predicted to be a delayed logistic map, is analyzed and discussed. Finally experimental data from a driven electronic anharmonic oscillator that exhibits per iod doubling and chaotic behavior is analyzed and discussed.