Combining local and global models to capture fast and slow dynamics in time series data

Many time series exhibit dynamics over vastly different time scales. The standard way to capture this behavior is to assume that the slow dynamics are a "trend", to de-trend the data, and then to model the fast dynamics. However, for nonlinear dynamical systems this is generally insufficient. In this paper we describe a new method, utilizing two distinct nonlinear modeling architectures to capture both fast and slow dynamics. Slow dynamics are modeled with the method of analogues, and fast dynamics with a deterministic radial basis function network. When combined the resulting model out-performs either individual system.