Developing diagnostics for input-output systems: the effects of certain linear and nonlinear filters on the correlation integral

Abstract

Input-output systems are characterized by applying time series analysis techniques developed for autonomous systems to the input and the output time series separately and using the results as nonlinear statistics of the time series distributions. Two examples are presented using the correlation integral as a nonlinear statistic: the first one examines the change in the statistic when several sample input time series are passed through a nonlinear filter. The rectifier is chosen as the filter because it models, at first approximation, the effect of dayside magnetospheric reconnection to the interplanetary magnetic field and solar wind input. The changes in the correlation integral are used to characterize the filter response. A second example compares a linear filter of the rectified solar wind input to the observed auroral geomagnetic activity in terms of their correlation integrals. Implications for models of the solar wind-magneto- sphere coupling are discussed.