A PERSONAL OVERVIEW OF NONLINEAR TIME-SERIES ANALYSIS FROM A CHAOS PERSPECTIVE

A personal overview of non-linear time series from a chaos perspective is given in an informal but, it is hoped, informative style. Recent d evelopments which, in a radically new way, formulate the notion of ini tial-value sensitivity with special reference to stochastic dynamical systems are surveyed. Its practical importance in prediction is highli ghted and its statistical estimation included by appealing to the mode rn technique of locally linear non-parametric regression. The related notions of an embedding dimension and correlation dimension are also s urveyed from the statistical stand-point. It is shown that determinist ic dynamical systems theory, including chaos, has much to offer to the subject. In return, some current results in the subject are summarize d, which suggest that some of the standard practice in the former may have to be revised when dealing with real noisy data. Several open pro blems are identified.