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VOL. 52 | 2006 Recursive estimation of possibly misspecified MA(1) models: Convergence of a general algorithm
James L. Cantor, David F. Findley

Editor(s) Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai

## Abstract

We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses Pseudolinear Regression (PLR--also referred to as AML and $\mbox{RML}_1$) and Recursive Maximum Likelihood ($\mbox{RML}_2$) without monitoring. Stimulated by the approach of Hannan (Hannan, E. J. (1980), Recursive estimation based on ARMA models, Ann. Statist.8 (4) 762–777, MR572620), our convergence results are obtained indirectly by showing that the recursive sequence can be approximated by a sequence satisfying a recursion of simpler (Robbins-Monro) form for which convergence results applicable to our situation have recently been obtained.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62108
MathSciNet: MR2427837

Digital Object Identifier: 10.1214/074921706000000932

Subjects:
Primary: 62L20, 62M10