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. 1 Fast and slow dynamics Scalar time series often exhibit deterministic dynamics on very different time scales (see Fig. 1). For example, sound waves exhibit fast intra-cycle variation and slow inter-cycle fluctuations. It is difficult for a single model to describe both behaviors simultaneously. A standard method for treating such data is to first apply some s...

• Type: Conference
• Year: 2004
• Where: IDEAL
• Authors: Michael Small
• Keywords: Fast Dynamics, IDEAL 2004, Model, Slow Dynamics