Gamma‐Autoregressive Models for Stream‐Flow Simulation

Abstract

Since hydrologic time series in general, and stream‐flow series, in particular, are dependent and not normally distributed, use of the classical autoregressive and moving average (ARMA) models to represent such series requires transformation of the original series into normal before applying the model. On the other hand, gamma‐autoregressive (GAR) models assume that the underlying series is dependent with a gamma marginal distribution and the models do not require variable transformation. However, the models require the estimation of certain statistics generally leading to biased estimates of the model parameters. This paper presents a procedure for bias correction, based on computer simulation studies, applicable for estimating parameters of GAR(l) models. Applications of the proposed procedure to annual stream‐flow series of several rivers are included. The GAR(l) model, when used in conjunction with the proposed estimation procedure, is an attractive alternative for synthetic stream‐flow simulation, is simple to use, and does not require any transformation of the original data.