Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis

River flow data are usually subject to several sources of discontinuity and inhomogeneity. An example is seasonality, because climatic oscillations occurring on inter-annual timescale have an obvious impact on the river flow. Further sources of alteration can be caused by changes in reservoir management, instrumentation or even unexpected shifts in climatic conditions. When such changes are ignored the results of a statistical analysis can be strongly misleading, so flexible procedures are needed for building the appropriate models, which may be very complex. This paper develops an automatic procedure to estimate the number and locations of changepoints in Periodic AutoRegressive (PAR) models, which have been extensively used to account for seasonality in hydrology. We aim at filling the literature gap on multiple changepoint detection by allowing several time segments to be detected, inside of which a different PAR structure is specified, with the resulting model being employed to successfully capture the discontinuities of river flow data. The model estimation is performed by optimization of an objective function based on an information criterion using genetic algorithms. The proposed methodology is evaluated by means of simulation studies and it is then employed in the analysis of two river flows: the South Saskatchewan, measured at Saskatoon, Canada, and the Colorado, measured at Lees Ferry, Arizona. For these river flows we build changepoint models, discussing the possible events that caused discontinuity, and evaluate their forecasting accuracy. Comparisons with the literature on river flow analysis and on existing methods for changepoint detection confirm the efficiency of our proposal.