AS 197

A fast algorithm for the exact likelihood of autoregressive-moving average models. 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


References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Mockus, Jonas; Katina, Joana; Katin, Igor: On autoregressive moving-average models as a tool of virtual stock-exchange: experimental investigation (2012)
  2. De Livera, Alysha M.; Hyndman, Rob J.; Snyder, Ralph D.: Forecasting time series with complex seasonal patterns using exponential smoothing (2011)
  3. Aknouche, Abdelhakim; Hamdi, Fayçal: Extension of the Chandrasekhar filter to the case of periodic state-space models (2008)
  4. Mauricio, José Alberto: Computing and using residuals in time series models (2008)
  5. Mélard, Guy; Roy, Roch; Saidi, Abdessamad: Exact maximum likelihood estimation of structured or unit root multivariate time series models (2006)
  6. Francq, Christian; Zakoïan, Jean-Michel: Covariance matrix estimation for estimators of mixing weak ARMA models (2000)
  7. Gómez, Víctor; Maravall, Agustín; Peña, Daniel: Missing observations in ARIMA models: Skipping approach versus additive outlier approach (1999)
  8. Azrak, Rajae; Mélard, Guy: The exact quasi-likelihood of time-dependent ARMA models (1998)
  9. Klein, André; Mélard, Guy; Zahaf, Toufik: Computation of the exact information matrix of Gaussian dynamic regression time series models (1998)
  10. Penzer, Jeremy; Shea, Brian: The exact likelihood of an autoregressive-moving average model with incomplete data (1997)
  11. Gómez, Víctor; Maravall, Agustín: New methods for quantitative analysis of short-term economic activity (1996)
  12. Luceño, Alberto: A fast likelihood approximation for vector general linear processes with long series: Application to fractional differencing (1996)
  13. Luceño, Alberto; Gonzalez, Francisco J.; Puig-Pey, Jaime: Computing optimal adjustment schemes for the general tool-wear problem (1996)
  14. Martin, R.J.: Some results on unilateral ARMA lattice processes (1996)
  15. Sabiti, Jacques Kiseta: A fast estimation method for ARMA processes (1996)
  16. Gómez, Víctor; Maravall, Agustín: Estimation, prediction, and interpolation for nonstationary series with the Kalman filter (1994)
  17. Luceño, Alberto: Fast optimization of the exact likelihood of AR and ARMA processes (1994)
  18. Luceño, Alberto: A fast algorithm for the exact likelihood of stationary and partially nonstationary vector autoregressive-moving average processes (1994)
  19. Pawitan, Yudi; O’Sullivan, Finbarr: Nonparametric spectral density estimation using penalized Whittle likelihood (1994)
  20. Azrak, R.; Mélard, G.: Exact maximum likelihood estimation for extended ARIMA models (1993)

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