Iterated function system models in data analysis: detection and separation

We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete-time dynamical system in which each time step corresponds to the application of one of the finite collection of maps. The maps, which represent distinct dynamical regimes, may be selected deterministically or stochastically. Given a time series from an IFS, our algorithm detects the sequence of regime switches under the assumption that each map is continuous. This method is tested on a simple example and an experimental computer performance data set. This methodology has a wide range of potential uses: from change-point detection in time-series data to the field of digital communications.