Quite a number of works is devoted to the problem of estimation of parameters of an autoregression process (AR) which is of particular importance both for applications and theory. The main part of them consists of results related to asymptotic estimation theory and is connected with the least squares method (LSM). The case of a nonstable AR process was considered by the authors in Autom. Remote Control 49, No. 11, 1495-1504 (1988); translation from Avtom. Telemekh. 1988, No. 11, 130-141 (1988; Zbl 0699.93089), with an additional requirement: all the roots of a characteristic polynomial should lie either inside or outside of the unit disc.
In the present paper a sequential plan of guaranteed estimation of AR parameters is proposed for a more general case when roots of the characteristic polynomial may be both inside and outside the unit disc and the vector of unknown parameters may take any value outside of a certain surface in parametric space. The sequential plan is constructed on the basis of estimates obtained by means of a correlational criterion. Note that estimates of such a type were first employed by V. V. Konev and V. A. Vasil’ev [Izv. Akad. Nauk SSSR Ser. Tekhn. Kibern. 6, 145-154 (1982)] to construct the guaranteed estimates, where the problem of parameter estimation for a stable AR with incomplete observations was studied.
For the entire collection see [Zbl 0839.00010].