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July, 1980 Recursive Estimation Based on ARMA Models
E. J. Hannan
Ann. Statist. 8(4): 762-777 (July, 1980). DOI: 10.1214/aos/1176345069

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.

Citation

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E. J. Hannan. "Recursive Estimation Based on ARMA Models." Ann. Statist. 8 (4) 762 - 777, July, 1980. https://doi.org/10.1214/aos/1176345069

Information

Published: July, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0447.62085
MathSciNet: MR572620
Digital Object Identifier: 10.1214/aos/1176345069

Subjects:
Primary: 62M10
Secondary: 62L12 , 62N15

Keywords: ARMA models , Martingales , real time calculation , recursive estimation , strong convergence

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 4 • July, 1980
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