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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.

MSC:

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

Software:

AS 154; AS 197
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