Retrospective multivariate Bayesian change-point analysis:: A simultaneous single change in the mean of several hydrological sequences

Although hydrological time series for different sites in a given region are usually correlated and that climate changes should have a regional impact on water resources, very little has appeared in the literature about multivariate change-point analysis. This paper generalizes the univariate Bayesian approach for the detection of a single shift in the mean level to study a change in the mean-vector of a sequence of multivariate normal vectors. Two different problems are considered: the first one is the estimation of the unknown regional change-point under the hypothesis that a shift occurred, while the second one is the overall assessment of change versus no change. This method is illustrated by an application to streamflow data series for six rivers situated in the Northern Quebec Labrador region.