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Recursive estimation of possibly misspecified MA(1) models: Convergence of a general algorithm

James L. Cantor·David F. Findley
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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 $RML_1$) and Recursive Maximum Likelihood ($RML_2$) without monitoring. Stimulated by the approach of Hannan (1980), 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.

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James L. Cantor, David F. Findley. 2007-02-26. Recursive estimation of possibly misspecified MA(1) models: Convergence of a general algorithm. https://doi.org/10.1214/074921706000000932

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