On sequential parameter estimation of a linear regression process ?

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 R with the exception of some lines. The asymptotic behavior of the duration of observations is investigated. It is shown, that the proposed general procedure may be applied to the sequential parameter estimation problem for affine stochastic delay differential equations as well as autoregressive stochastic differential equations of arbitrary order.