On Some Numerical Properties of Arma Parameter Estimation Procedures

H. Joseph Newton
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H. Joseph Newton: Texas A&M University, Institute of Statistics

A chapter in Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, 1981, pp 172-177 from Springer

Abstract: Abstract This paper reviews the algorithms used by statisticians for obtaining efficient estimators of the parameters of a univariate autoregressive moving average (ARMA) time series. The connection of the estimation problem with the problem of prediction is investigated with particular emphasis on the Kalman filter and modified Cholesky decomposition algorithms. A result from prediction theory is given which provides a significant reduction in the computations needed in Ansley’s (1979) estimation procedure. Finally it is pointed out that there are many useful facts in the literature of control theory that need to be investigated by statisticians interested in estimation and prediction problems in linear time series models.

Keywords: ARMA models; Maximum likelihood estimation; Minimum mean square error prediction; Kalman filter algorithm; Modified Cholesky decomposition algorithm (search for similar items in EconPapers)
Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-9464-8_25

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DOI: 10.1007/978-1-4613-9464-8_25

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