A model for non-stationary time series analysis with clustering methods

Abstract

The object of this paper is to present a model of non-stationary time series generated by switching between a finite number of random processes and to apply clustering algorithms to the task of estimating the model’s parameters. We will also analyze the parameters which govern the algorithm’s behavior to infer a novel cluster validity criterion for fuzzy clustering algorithms of temporal patterns. The model defines a non-stationary composite source generated by randomly switching between elements of a finite number of random processes. The probability distribution which underlies the behavior of the switch is controlled by a temporal parameter vector process which is used to determine a different switching probability in each time instant. This definition allows us to analyze a drift between disjoint states of the composite model.