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December, 1990 Estimation of Nonstationary Armax Models Based on the Hannan-Rissanen Method
Dawei Huang, Lei Guo
Ann. Statist. 18(4): 1729-1756 (December, 1990). DOI: 10.1214/aos/1176347875


We consider in this paper the estimation problems for both orders and coefficients of linear feedback control systems, described by ARMAX models. The estimation algorithms are inspired by the Hannan-Rissanen method used for the estimation of stationary ARMA models, while the convergence analyses are based on limit theorems for both double array martingales and nonnegative supermartingales, and on techniques of stochastic Lyapunov functions. Traditionally used assumptions, such as the strictly positive real condition and the requirement of known upper bounds for true orders, are not imposed here.


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Dawei Huang. Lei Guo. "Estimation of Nonstationary Armax Models Based on the Hannan-Rissanen Method." Ann. Statist. 18 (4) 1729 - 1756, December, 1990.


Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0721.62091
MathSciNet: MR1074432
Digital Object Identifier: 10.1214/aos/1176347875

Primary: 62M10
Secondary: 60F15 , 93E12

Keywords: ARMAX models , Feedback , least squares , Martingales , nonstationary , order estimation , positive real

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 4 • December, 1990
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