Recursive Estimation of Misspecified MA(1) Models: Convergence Results via a Robbins-Monro Algorithm with Nonmonotone Weights

• Activity Number: 286
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): David Findley*+ and James Cantor
• Affiliation(s): U.S. Census Bureau and SAIC
• Keywords: time series models ; pseudo-linear regression (AML, RML1) ; misconvergence

Abstract

Only Hannan (1980) seems to have undertaken to rigorously prove the convergence of recursive algorithms for an ARIMA model with a moving average term when the model is misspecified. Although Hannan's pioneering paper has various lapses, it has fruitful ideas, not always adequately formulated. One idea is to show that the parameter estimates approximate the output of a simpler recursion. We summarize how, for an MA(1) model, two standard recursive schemes, PLR and RML2, can be related to a Robbins-Monro algorithm with non-monotone weights, and how a.s. convergence of this algorithm can be proved by slightly modifying and correcting some lemmas of Fradkov (1981). In this way, it can be shown that PLR estimates converge to a value that is suboptimal for one-step forecasting, but that a variant of RML2 converges optimally.