On sequential parameter estimation of a linear regression process

Abstract

This paper presents a sequential estimation procedure for unknown parameters of a stochastic linear regression. As examples the sequential estimation problem of two dynamic parameters in stochastic linear systems with memory and in autoregressive processes is solved. The estimation procedure is based on the least squares method with weights and yields estimators with guaranteed accuracy in the sense of the Lq–norm (q ≥ 2). The proposed procedure works in the mentioned examples for all possible values of the unknown dynamic parameters on the plane R2 with the exception of some lines. The asymptotic behavior of the duration of observations is investigated.