Simulation of time series using periodic gamma autoregressive models

Abstract

AbstractPeriodic autoregressive models are frequently used to model hydrologic series. In the literature, annual streamflow series are approximated by normal distribution. However, for short periods (daily, weekly, monthly) this is no longer the case, particularly due to the data skewness. A new class of first‐order model was, therefore, studied in an attempt to overcome this problem. The model has an autoregressive structure and can be additive, multiplicative, or hybrid, but with gamma marginal distribution. Furthermore, the classical model assumes that the method of moments is effective for parameters estimation. For the first time, this paper undertakes a complete analysis of the hybrid model for this context and the novelty lies in the parameter estimation via maximization of the likelihood function. For an application in the Brazilian case, the additive model proved to be more effective than previously reported and the method allows high orders and skewed distributions.