Modeling of aggregated hydrologic time series

The concept of aggregation of the most commonly used models of seasonal hydrologic time series is the main subject discussed herein. The PAR(1) and PARMA(1, 1) models are assumed for representing the seasonal series and their equivalent stationarity and invertibility conditions are given. Likewise explicit expressions are given for determining the periodic covariance structure of such models and the concept of aggregation is illustrated by deriving the model of the corresponding annual series. Since the models of the seasonal series dictate the type of model of the annual series, then a unique structural linkage in the usual linear disaggregation model may be obtained in closed form. Seasonal and annual flows of the Niger River are used to illustrate some of the estimation procedures based on the foregoing aggregation approach.