Optimal choice of type and order of river flow time series models

The performance of various types of models for river flows are compared by using a decision rule derived from the Bayes criterion. The decision rule has the property that it minimizes the probability of error. The best model among the autoregressive, autoregressive moving average, and moving average models of various orders for the annual flows of about 10 rivers is found by using this decision rule. For the monthly flows, not only the best seasonal autoregressive integrated moving average model but also the best type of transformation is determined. The models for the log transformed monthly data are superior to the models fitted to the observed data without transformation. The variability in the decisions caused by the different prior probability density functions is also discussed.