Recursive Estimation of Misspecified MA(1) Models: Convergence Results Via a Robbins-Monro Algorithm

Abstract

We consider the properties of two recursive estimation schemes, Pseudolinear Regression (PLR) and Recursive Maximum Likelihood Estimation (RML2), in estimating the coefficient of a first-order Moving average model when the data generating process is, say, a first order autoregression. Many convergence results are available for PLR for correct models, but there have been no mathematically complete results for a truly recursive implementation of RML2 for a Moving average model, correct or not. For the incorrect MA(1) case, we show that PLR converges, but to a suboptimal value. Under an additional condition, we show that a fully recursive implementation of RML2 converges to an optimal value. When there are several optimal values, then on any realization of the time series, RML2 does not oscillate forever between optimal values but converges to one of them. The limit can be different for different realizations. This is a joint work with Dr. James Cantor.