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An algorithm for the exact likelihood of a stationary vector autoregressive‐moving average model

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  • JOSÉ ALBERTO MAURICIO

Abstract

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.

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  • José Alberto Mauricio, 2002. "An algorithm for the exact likelihood of a stationary vector autoregressive‐moving average model," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 473-486, July.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:4:p:473-486
    DOI: 10.1111/1467-9892.00273
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    Cited by:

    1. Alj, Abdelkamel & Jónasson, Kristján & Mélard, Guy, 2016. "The exact Gaussian likelihood estimation of time-dependent VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 633-644.
    2. Mauricio, Jose Alberto, 2008. "Computing and using residuals in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1746-1763, January.
    3. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 10-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.
    5. Dufour, Jean-Marie & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
    6. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    7. Wenbin Du & You Wu & Yunliang Zhang & Ya Gao, 2022. "The Impact Effect of Coal Price Fluctuations on China’s Agricultural Product Price," Sustainability, MDPI, vol. 14(15), pages 1-15, July.
    8. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    9. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.

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