Initialization for generating single‐site and multisite low‐order periodic autoregressive and moving average processes

摘要

Single‐site and multisite periodic autoregressive and moving average (PARMA) processes have been suggested for modeling and simulation of hydrologic processes. Generation of synthetic samples based on such models requires knowledge of the initial conditions, i.e., the values of the process at times prior tot= 1. In this paper an initialization procedure for generating univariate and multivariate PAR (1), PAR (2), and PARMA (1, 1) processes is described. The procedure is based on generating the initial values of the process in such a way that the variance‐covariance structure of the process is preserved. The initialization procedure introduced herein is exact and easy to use. Examples are included to explain the applicability of the proposed appro