Thresholds, Stability, Nonlinear Forecasting and Irregularly Sampled Data

The central theme in this Chapter is unconventional analysis of time series data, the conventional one being that based on linear models (e.g., autoregressive/moving average models) and second-order moments (e.g., spectral analysis). After the natural emergence of thresholds, attention is focused on the stability of the global system in connection with that of each constituent subsystem delineated by the thresholds. Exotic results are obtained by relying on simple linear algebraic analysis of the system, which may be considered an application of symbolic dynamics. Some unexpected results are described in nonlinear forecasting, which expose a myth generated by linear mentality. Finally, comments are made about nonlinear modeling of irregularly sampled data.