Slight Misspecifications of Linear Systems

Abstract

In the parametric analysis of linear systems, one usually assumes that for one parameter the prognosis error is uncorrelated with the past of the process (“right specification”). Under additional assumptions it is known that with this the predictor determined by the true parameter has (in some sense) minimal prediction error and is uniquely determined by this property. In this paper it is shown that for every spectral measure that is right specified in the above sense there exists a neighbourhood in the weak topology such that for processes with spectral measures from this neighbourhood (“slight misspecifications”) holds: There exists one and only one predictor determined by the model that has minimal expected prediction error in the class of predictors described by the model. Then a Newton-type algorithm for the computation of this predictor is constructed that needs only local parametrisations of the model.