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Fast Linear Estimation Methods For Vector Autoregressive Moving‐Average Models

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  • Sergio Koreisha
  • Tarmo Pukkila

Abstract

. Three linear methods for estimating parameter values of vector auto‐regressive moving‐average (VARMA) models which are in general at least an order of magnitude faster than maximum likelihood estimation are developed in this paper. Simulation results for different model structures with varying numbers of component series and observations suggest that the accuracy of these procedures is in most cases comparable with maximum likelihood estimation. Procedures for estimating parameter standard error are also discussed and used for identification of nonzero elements in the VARMA polynomial structures. These methods can also be used to establish the order of the VARMA structure. We note, however, that the primary purpose of these estimates is to generate initial estimates for the nonzero parameters in order to reduce subsequent computational time of more efficient estimation procedures such as exact maximum likelihood.

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  • Sergio Koreisha & Tarmo Pukkila, 1989. "Fast Linear Estimation Methods For Vector Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 325-339, July.
    • Handle: RePEc:bla:jtsera:v:10:y:1989:i:4:p:325-339
    DOI: 10.1111/j.1467-9892.1989.tb00032.x
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    Cited by:

    1. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.
    2. 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.
    3. Yifan Li & Yao Rao, 2021. "A simple nearly unbiased estimator of cross‐covariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 240-266, March.
    4. McKenzie, C.R., 1997. "The properties of some two step estimators of ARMA Models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 451-456.
    5. Hosoya, Yuzo & Terasaka, Takahiro, 2009. "Inference on transformed stationary time series," Journal of Econometrics, Elsevier, vol. 151(2), pages 129-139, August.
    6. Flores de Frutos, Rafael & Serrano, Gregorio R., 1997. "A generalized least squares estimation method for invertible vector moving average models," Economics Letters, Elsevier, vol. 57(2), pages 149-156, December.
    7. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    8. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    9. Alfredo García Hiernaux & José Casals Carro & Miguel Jerez, 2005. "Fast estimation methods for time series models in state-space form," Documentos de Trabajo del ICAE 0504, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    10. Basistha, Arabinda & Kurov, Alexander & Wolfe, Marketa Halova, 2019. "Volatility Forecasting: The Role of Internet Search Activity and Implied Volatility," MPRA Paper 111037, University Library of Munich, Germany.
    11. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    12. D. S. Poskitt & M. O. Salau, 1995. "On The Relationship Between Generalized Least Squares And Gaussian Estimation Of Vector Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 617-645, November.
    13. Dong Wan Shin & Sahadeb Sarkar, 1995. "Estimation Of The Multivariate Autoregressive Moving Average Having Parameter Restrictions And An Application To Rotational Sampling," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 431-444, July.
    14. José Alberto Mauricio Arias, 1993. "Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models," Documentos de Trabajo del ICAE 9316, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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