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ESTIMATION OF THE MULTIVARIATE AUTOREGRESSIVE MOVING AVERAGE HAVING PARAMETER RESTRICTIONS AND AN APPLICATION TO ROTATIONAL SAMPLING
Author(s) -
Shin Dong Wan,
Sarkar Sahadeb
Publication year - 1995
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1995.tb00244.x
Subject(s) - mathematics , estimator , autoregressive model , estimation theory , parametric statistics , parametric model , newton's method , sampling (signal processing) , statistics , nonlinear system , computer science , physics , quantum mechanics , filter (signal processing) , computer vision
. 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.