JSM 2004 - Toronto

Abstract #301919

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Activity Number: 57
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: Business and Economics Statistics Section
Abstract - #301919
Title: Recursive Estimation of Misspecified MA(1) Models: General Results
Author(s): James Cantor*+ and David F. Findley
Companies: Science Applications International Corporation and U.S. Census Bureau
Address: 1100 North Glebe Rd., Arlington, VA, 22201,
Keywords: time series models ; incorrect models ; pseudo-linear regression ; recursvie maximum likelihood ; misconvergence
Abstract:

We introduce a general algorithm for the recursive estimation of an MA(1) model. The algorithm includes as special cases both pseudo-linear regression (PLR, AML, RML1) and also recursive maximum likelihood estimation (RML2). We consider its application to data generated by an MA(1) model and by several other models. Stimulated by Hannan (1980), and generalizing results of Cantor (2001), we analyze the convergence of the sequence of recursive estimates by showing, under a stability condition, its asymptotic equivalence to a sequence that satisfies a Robbins-Monro recursion. Convergence of the latter recursion is established using results of Fradkov (1980) and Findley (2001). Under moderate restrictions on the coefficients of the generating model, the stability condition is verified for PLR and for a monitored version of RML2. The latter is proved to converge to the mean square optimal parameter in all cases, whereas PLR is proved to converge to a nonoptimal value for non-MA(1) data.

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