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Initialization for generating single‐site and multisite low‐order periodic autoregressive and moving average processes
Author(s) -
Salas Jose D.,
Abdelmohsen Magdy W.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/93wr00371
Subject(s) - initialization , autoregressive model , univariate , moving average , autoregressive–moving average model , multivariate statistics , covariance , variance (accounting) , computer science , process (computing) , moving average model , mathematics , autoregressive integrated moving average , statistics , time series , accounting , business , programming language , operating system
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 to t = 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 approach.