Open Access
July, 1975 The Estimation of Arma Models
E. J. Hannan
Ann. Statist. 3(4): 975-981 (July, 1975). DOI: 10.1214/aos/1176343200


In estimating a vector model, $\Sigma B(j)x(n-j)=\Sigma A(j)\epsilon(n-j), A(0)=I_r, E(\epsilon(m)\epsilon(n)')=\delta_{mn}K$ it is suggested that attention be confined to cases where $g(z) =\Sigma A(j)z^j, h(z)=\Sigma B(j)z^j$ have determinants with no zeroes inside the unit circle and have $I_r$ as greatest common left divisor and where $\1brack A(p)\vdots B(q) \rbrack$ is of rank r, where p, q are the degrees of g, h, respectively. It is shown that these conditions ensure that a certain estimation procedure gives strongly consistent estimates and the last of the conditions is probably necessary for this to be so, when the first two are satisfied. The strongly consistent estimation procedure may serve to initiate an iterative maximisation of a likelihood.


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E. J. Hannan. "The Estimation of Arma Models." Ann. Statist. 3 (4) 975 - 981, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0311.62056
MathSciNet: MR391446
Digital Object Identifier: 10.1214/aos/1176343200

Primary: 62M10
Secondary: 62E20 , 62M15

Keywords: Autoregressive-moving average process , Identification , strongly consistent estimation

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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