River stream flows in the northern Québec Labrador region: A multivariate change point analysis via maximum likelihood

Abstract

Spring stream flows of six rivers that flow in the northern Québec Labrador region are modeled in a multivariate Gaussian framework and have been analyzed for possible change points in their average flows. The multivariate formulation takes into account correlations among the flows of the six rivers that flow in the same region. Significant change was detected in the multivariate mean vector, and the unknown change point is estimated by the method of maximum likelihood estimation. We then establish the asymptotic distribution of the change point maximum likelihood estimate, wherein we show that the multivariate case can be transformed into an equivalent univariate problem. A simulation study is carried out to investigate the robustness of the asymptotic distribution to departures from normality and independence as well as its closeness to finite samples. The asymptotic distribution allowed us to compute confidence interval estimates of the change point in the river flows. A decrease in the mean river flows in 1984 identified by the methodology may have been a consequence of a sharp decline in the region's snow cover that occurred about a year or two ahead.