A hidden Markov model segmentation procedure for hydrological and environmental time series

Abstract

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Hubert’s segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Hubert’s least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.