Bayesian change-point analysis in hydrometeorological time series. Part 2. Comparison of change-point models and forecasting

Abstract

This paper provides a methodology to test existence, type, and strength of changes in the distribution of a sequence of hydrometeorological random variables. Unlike most published work on change-point analysis, which consider a single structure of change occurring with certainty, it allows for the consideration in the inference process of the no change hypothesis and various possible situations that may occur. The approach is based on Bayesian model selection and is illustrated using univariate normal models. Four univariate normal models are considered: the no change hypothesis, a single change in the mean level only, a single change in the variance only, and a simultaneous change in both the mean and the variance. First, inference analysis of posterior distributions via Gibbs sampling for a given change-point model is recalled. This scientific reporting framework is then generalized to the problem of selecting among different configurations of a single change and the no change hypothesis. The important operational issue of forecasting a future observation, often neglected in the literature on change-point analysis, is also treated in the previous model selection perspective. To illustrate the approach, a case study involving annual energy inflows for eight large hydropower systems situated in Québec is detailed.