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New approximation for ARMA parameters estimate

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  • Boularouk, Y.
  • Djeddour, K.

Abstract

This paper presents a new approach for the optimization of autoregressive moving average parameters estimation. We prove that the log likelihood function of the process is almost surely equal to a polynomial of order two. Thereafter, using the methods of least squares, our function will be approximated by a polynomial of order two which will be used to calculate an estimation of the maximum.

Suggested Citation

  • Boularouk, Y. & Djeddour, K., 2015. "New approximation for ARMA parameters estimate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 116-122.
    • Handle: RePEc:eee:matcom:v:118:y:2015:i:c:p:116-122
    DOI: 10.1016/j.matcom.2015.01.004
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    References listed on IDEAS

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    1. 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.
    2. A. I. McLeod & P. R. Holanda Sales, 1983. "An Algorithm for Approximate Likelihood Calculation of Arma and Seasonal Arma Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 211-223, June.
    3. Gregory C. Reinsel & Sabyasachi Basu & Sook Fwe Yap, 1992. "Maximum Likelihood Estimators In The Multivariate Autoregressive Moving‐Average Model From A Generalized Least Squares Viewpoint," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 133-145, March.
    4. Solo, Victor, 1984. "The exact likelihood for a multivariate ARMA model," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 164-173, October.
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    Cited by:

    1. Manuel D. Ortigueira, 2022. "A New Look at the Initial Condition Problem," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    2. Celina Pestano-Gabino & Concepción González-Concepción & María Candelaria Gil-Fariña, 2024. "VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification," Mathematics, MDPI, vol. 12(2), pages 1-15, January.

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