New approach to the segmentation problem for time series of arbitrary nature

Abstract

We consider the problem of splitting time series of arbitrary nature (stochastic, deterministic, or mixed) into segments generated by the same mechanism. We introduce a new concept of ∈-complexity of continuous functions and give a characterization of this quantity for Hölder continuous functions. On the basis of the ∈-complexity parameters, we propose a new technique for the segmentation of time series that does not require any a priori knowledge of how these series were generated.