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Estimation Of The Multivariate Autoregressive Moving Average Having Parameter Restrictions And An Application To Rotational Sampling

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  • Dong Wan Shin
  • Sahadeb Sarkar

Abstract

. The vector autoregressive moving average model with nonlinear parametric restrictions is considered. A simple and easy‐to‐compute Newton‐Raphson estimator is proposed that approximates the restricted maximum likelihood estimator which takes full advantage of the information contained in the restrictions. In the case when there are no parametric restrictions, our Newton‐Raphson estimator is equivalent to the estimator proposed by Reinsel et al. (Maximum likelihood estimators in the multivariate autoregressive moving‐average model from a generalized least squares view point. J. Time Ser. Anal. 13 (1992), 133–45). The Newton‐Raphson estimation procedure also extends to the vector ARMAX model. Application of our Newton‐Raphson estimation method in rotational sampling problems is discussed. Simulation results are presented for two different restricted models to illustrate the estimation procedure and compare its performance with that of two alternative procedures that ignore the parametric restrictions.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:4:p:431-444
    DOI: 10.1111/j.1467-9892.1995.tb00244.x
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    References listed on IDEAS

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    1. Dong Wan Shin, 1993. "Maximum Likelihood Estimation For Autoregressive Processes Disturbed By A Moving Average," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 629-643, November.
    2. 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.
    3. Marc Hallin, 1984. "Spectral factorization of nonstationary moving average processes," ULB Institutional Repository 2013/2001, ULB -- Universite Libre de Bruxelles.
    4. Reinsel, Greg, 1979. "FIML estimation of the dynamic simultaneous equations model with ARMA disturbances," Journal of Econometrics, Elsevier, vol. 9(3), pages 263-281, February.
    5. 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.
    6. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, vol. 47(4), pages 1005-1030, July.
    7. 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.
    8. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
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