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On The Relationship Between Generalized Least Squares And Gaussian Estimation Of Vector Arma Models

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  • D. S. Poskitt
  • M. O. Salau

Abstract

. This paper investigates theoretical aspects of the relationship between the generalized least squares and Gaussian estimation schemes for vector autoregressive moving‐average models. The asymptotic convergence of the generalized least squares estimator to the Gaussian estimator is established and an alternative numerical method for implementing the generalized least squares scheme is proposed. Finally, some simulation results are presented to illustrate the theory.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:6:p:617-645
    DOI: 10.1111/j.1467-9892.1995.tb00259.x
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    References listed on IDEAS

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    1. Poskitt, D. S. & Salau, M. O., 1994. "On the Asymptotic Relative Efficiency of Gaussian and Least Squares Estimators for Vector ARMA Models," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 294-317, November.
    2. D. S. Poskitt & A. R. Tremayne, 1986. "Some Aspects Of The Performance Of Diagnostic Checks In Bivariate Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 217-233, May.
    3. 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.
    4. 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.
    5. Piero Barone, 1987. "A METHOD FOR GENERATING INDEPENDENT REALIZATIONS OF A MULTIVARIATE NORMAL STATIONARY AND INVERTIBLE ARMA(p, q) PROCESS," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 125-130, March.
    6. E. J. Hannan & L. Kavalieris, 1986. "Regression, Autoregression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 27-49, January.
    7. B. L. Shea, 1987. "Estimation Of Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 95-109, January.
    8. Sergio Koreisha & Tarmo Pukkila, 1990. "A Generalized Least‐Squares Approach For Estimation Of Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 139-151, March.
    9. Gwilym M. Jenkins & Athar S. Alavi, 1981. "Some Aspects Of Modelling And Forecasting Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(1), pages 1-47, January.
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    Cited by:

    1. Pierre Duchesne & Pierre Lafaye de Micheaux, 2013. "Distributions for residual autocovariances in parsimonious periodic vector autoregressive models with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 496-507, July.
    2. Poskitt, D. S., 2003. "On the specification of cointegrated autoregressive moving-average forecasting systems," International Journal of Forecasting, Elsevier, vol. 19(3), pages 503-519.
    3. 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.
    4. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    5. Salau, M. O., 1998. "Efficient computation of zeros of the moving average operator with real matricial coefficients," SFB 373 Discussion Papers 1998,46, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. M. Salau, 2003. "The effects of different choices of order for autoregressive approximation on the Gaussian likelihood estimates for ARMA models," Statistical Papers, Springer, vol. 44(1), pages 89-105, January.
    7. Ursu, Eugen & Duchesne, Pierre, 2009. "On multiplicative seasonal modelling for vector time series," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2045-2052, October.

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