ESTIMATION AND VALIDATION OF CONTEMPORANEOUS PARMA MODELS FOR STREAMFLOW SIMULATION

Seasonal streamflow series generally exhibit periodicity in the autoco variance structure. Such periodicity can be represented by PARMA model s, i.e., autoregressive moving average (ARMA) models with parameters t hat vary with the seasons. Statistical properties of low-order models such as the PARMA(2,2) model are examined. The periodic moment equatio ns are derived; they can be used to compute the periodic covariance st ructure of a given model. Simulation of streamflow at several sites ca n be done using the contemporaneous PARMA model. The main problem in u sing such models is to determine the covariance matrices of innovation s. Traditionally, this has been done by the method of maximum likeliho od. However, this method generally leads to significant underestimatio n of the cross correlation of flows. A moment estimator is developed h erein for the contemporaneous PARMA(2,2) model along with three approx imate moment-based estimators for those cases where a feasible moment solution cannot be obtained. The applicability of the proposed methods is illustrated by fitting PARMA models to weekly flow data for two ca tchments in the Ottawa River basin.