Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models

Abstract

The paper compares forecasts of mean monthly water levels up to six months ahead at Ladário, on the Upper Paraguay River, Brazil, estimated from two long-range dependence models. In one of them, the marked seasonal cycle was removed and a fractionally differenced model was fitted to the transformed series. In the other, a seasonal fractionally differenced model was fitted to water levels without transformation. Forecasts from both models for periods up to six months ahead were compared with forecasts given by simpler "short-range dependence" Box-Jenkins models, one fitted to the transformed series, the other a seasonal autoregressive moving average (ARMA) model. Estimates of parameters in the four models (two "long-range dependence", two "short-range dependence") were updated at six-monthly intervals over a 20 year period, and forecasts were compared using root mean square errors (rmse) between water-level forecasts and observed levels. As judged by rmse, performances of the two long-range dependence models, and of the ARMA (1,1) short-range dependence model, were very similar; all three out-performed the seasonal short-range dependence ARMA model. There was evidence that all models performed better during recession periods, than on the hydrograph rising limb.