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
RML1β) and Recursive Maximum Likelihood (RML2β) 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.Comment: Published at http://dx.doi.org/10.1214/074921706000000932 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org