An evaluation of the practicality and complexity of some rainfall and runoff time series models

The fundamental issue of what level of complexity is needed in stochastic models for generating or forecasting hydrologic events is studied by comparing the properties of autoregressive, moving average, and mixed models of increasing complexity for annual, monthly, weekly, and daily series. Several methods of removing seasonal nonhomogeneity of monthly series are compared, and the seasonality of monthly model coefficients is investigated. For small time increments a harmonic analysis of the coefficients is necessary to limit the number of parameters. The relative goodness of fit of several models of monthly and daily series are determined by diagnostic checks applied to the residuals, and their probability distributions are investigated. The issue of long-range versus short-range dependence is analyzed by comparing the statistics describing the span of dependence of several time series models. The need for compatible models for different time resolutions is discussed. The merits of the disaggregation model and its level of complexity are discussed and compared with those of other models.

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