Risk-Efficient Estimation of the Parameter of an Autoregressive Process

The problem of the constructing procedures for estimation of the parameter of first-order autoregression is considered. The estimates obtained are efficient relative to the standard risk (i.e., the sum of the observation cost and estimation cost). The proposed procedures are based on the least-squares method (LSM) with a random number of observations (sequential estimates). In studying properties of the sequential modification of the LSM estimate, we obtained an expansion of the mean duration of the estimation procedure, which is an analog of the Smith theorem in the renewal theory.