The segmentation procedure as a tool for discrete modeling of hydrometeorological regimes

Abstract.

 A possible cause of nonstationarity in time series is the existence of some abrupt modification of their statistical parameters, and especially of a sudden change of the mean. Series with such a change exhibit a strong temporal persistence, with high values of the Hurst coefficient, but with poor possibilities to fit any autoregressive model. Some classical tests (Pettitt, 1979; Buishand, 1982) enable to find a possible change point of the mean and then to split the original nonstationary series into two stationary sub-series. The Bayesian procedure defined by Lee and Heghinian (1977) supposes the “a-priori” existence of a change of the mean somewhere in the series and yields at each time step an “a-posteriori” probability of mean change.

But these classical tests and procedures consider only one change point in the original series. To go further and to explore the theoretical multiple singularity models defined by Klemeš (1974) and Potter (1976), a segmentation procedure of time series has been designed. This procedure yields an optimal partition (from a least squares point of view) of the original series into as many subseries as possible, all differences between two contiguous means remaining simultaneously significant. This last requirement is ensured using the Scheffe test of contrasts. The main problem has been to master the combinatory explosion while exploring the tree of all possible segmentations of a series.

Some applications of the procedure to hydrometeorological time series are reviewed and some possible improvements are presented.