The Annals of Statistics

Recursive Estimation Based on ARMA Models

E. J. Hannan

Full-text: Open access

Abstract

A recursive estimate of the stochastic structure of a stationary time series is constructed based on the assumption that the true structure is ARMA, i.e., has a rational spectrum. The estimate is recursive in the sense that each successive estimate is obtained from the previous one by a relatively simple adjustment, that could be effected in a "real time" situation. The procedure is basically that of updating a regression when all variates involved are constructed from previous estimates of the parameter vector. The strong convergence of the estimate to the true value is established as well as a result relating to the rate of convergence.

Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 762-777.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345069

Digital Object Identifier
doi:10.1214/aos/1176345069

Mathematical Reviews number (MathSciNet)
MR572620

Zentralblatt MATH identifier
0447.62085

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62N15 62L12: Sequential estimation

Keywords
ARMA models recursive estimation strong convergence martingales real time calculation

Citation

Hannan, E. J. Recursive Estimation Based on ARMA Models. Ann. Statist. 8 (1980), no. 4, 762--777. doi:10.1214/aos/1176345069. https://projecteuclid.org/euclid.aos/1176345069


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