Time Series Analysis of Magnetospheric Activity Using Nonlinear Dynamical Methods

Abstract

Several attempts have been made to describe and predict the dynamical behavior of the Earth’s magnetosphere as it is reflected in geomagnetic time series. Early results indicated that the dimension is low so that it might be possible to model the complex interactions giving rise to the irregular time series as a dynamical system with intrinsically unstable dynamics. However, it was recently pointed out that the low dimension may have been due to the long autocorrelation time scale of the system. A subsequent study of different time intervals and algorithmic and physical parameters gave further evidence that, indeed, the convergence of the correlation dimension was due to time correlations rather than global state space structure. Further examination of other diagnostics (exponents, forecasting) in this light shows that, although at first sight they pass several tests and conform to the interpretation of a low-dimensional chaotic system, several of their features are inconsistent with the assumptions of the analysis. The above difficulties inherent to analysis of a variety of real-world time series are pointed out and briefly discussed.