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An algorithm for the exact likelihood of a stationary vector autoregressive‐moving average model
Author(s) -
MAURICIO JOSÉ ALBERTO
Publication year - 2002
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 - 10.1111/1467-9892.00273
Subject(s) - univariate , autoregressive model , mathematics , likelihood function , representation (politics) , star model , autoregressive–moving average model , multivariate statistics , algorithm , moving average model , state space representation , state vector , moving average , state space , autoregressive integrated moving average , mathematical optimization , estimation theory , statistics , time series , physics , classical mechanics , politics , political science , law
The so‐called innovations form of the likelihood function implied by a stationary vector autoregressive‐moving average model is considered without directly using a state–space representation. Specifically, it is shown in detail how to compute the exact likelihood by an adaptation to the multivariate case of the innovations algorithm of Ansley (1979) for univariate models. Comparisons with other existing methods are also provided, showing that the algorithm described here is computationally more efficient than the fastest methods currently available in many cases of practical interest.