Abstract A large class of useful multivariate recursive time series models and estimation methods has appeared in the engineering literature. Despite the interest and utility which this recursive work has when viewed as an extension of regression analysis, little of it has reached statisticians working in regression. To overcome this we (a) present the relevant random-β regression theory as a natural extension of conventional fixed-β regression theory and (b) derive the optimal recursive estimators in terms of the extended regression theory for a typical form of the recursive model. This also opens the way for further developments in recursive estimation, which are more tractable in the regression approach and will be presented in future papers.
Duncan et al. (1972) studied this question.