A fast algorithm for the exact likelihood of autoregressive-moving average models. (English) Zbl 0548.65098

This algorithm has the same purpose as algorithm AS 154 of G. Gardner, A. C. Harvey and G. D. A. Phillips [ibid. 29, 311-322 (1980; Zbl 0471.62098)], namely to compute the exact likelihood function of a stationary autoregressive-moving average process of order (p,q). That algorithm appears to be slower, and requires more storage than is necessary, particularly for large p and q. The computer program described here is a combination of an improved version of an algorithm due to J. G. Pearlman [Biometrika 67, 232-233 (1980; Zbl 0425.62078)] with the quick recursion switching suggested by Gardner et al. and an algorithm of G. T. Wilson [J. Stat. Comput. Simulation 8, 301-309 (1979; Zbl 0414.62067)]. The program is extremely efficient both in terms of computing time and amount of storage.


65C99 Probabilistic methods, stochastic differential equations
62A01 Foundations and philosophical topics in statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


AS 154; AS 197
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