The Annals of Statistics

The Estimation of Arma Models

E. J. Hannan

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 3, Number 4 (1975), 975-981.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343200

Digital Object Identifier
doi:10.1214/aos/1176343200

Mathematical Reviews number (MathSciNet)
MR391446

Zentralblatt MATH identifier
0311.62056

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62M15: Spectral analysis 62E20: Asymptotic distribution theory

Keywords
Autoregressive-moving average process identification strongly consistent estimation

Citation

Hannan, E. J. The Estimation of Arma Models. Ann. Statist. 3 (1975), no. 4, 975--981. doi:10.1214/aos/1176343200. https://projecteuclid.org/euclid.aos/1176343200


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