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A NOTE ON THE GENERATION OF INDEPENDENT REALIZATIONS OF A VECTOR AUTOREGRESSIVE MOVING‐AVERAGE PROCESS
Author(s) -
Shea B. L.
Publication year - 1988
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1988.tb00479.x
Subject(s) - autoregressive–moving average model , mathematics , autoregressive model , representation (politics) , state space , series (stratigraphy) , generating function , state space representation , state vector , state (computer science) , moving average , moving average model , covariance , function (biology) , covariance matrix , matrix (chemical analysis) , algorithm , time series , autoregressive integrated moving average , statistics , mathematical analysis , paleontology , physics , classical mechanics , evolutionary biology , politics , biology , political science , law , materials science , composite material
. Barone has described a method for generating independent realizations of a vector autoregressive moving‐average (ARMA) process which involves recasting the ARMA model in state space form. We discuss a direct method of computing the initial state covariance matrix T 0 which, unless the number of time series is large, is usually faster than using the doubling algorithm of Anderson and Moore. Our numerical comparisons are particularly valuable because T 0 must also be computed when calculating the likelihood function. A number of other computational refinements are described. In particular, we advocate the use of Choleski factorizations rather than spectral decompositions. For a pure moving‐average process computational savings can be achieved by working directly with the ARMA model rather than with its state space representation.