Confidence Estimation of Autoregressive Parameters Based on Noisy Data

We consider the problem of estimating the parameters of an autoregressive process based on observations with additive noise. A sequential method has been developed for constructing a fixed-size confidence domain with a given confidence factor for a vector of unknown parameters based on a finite sample. Formulas are obtained for the duration of a procedure that achieves the required performance of estimates of unknown parameters in the case of Gaussian noise. Confidence parameter estimates are constructed using a special sequential modification of the classic Yule–Walker estimates; this permits one to estimate the confidence factor for small and moderate sample sizes. The results of numerical modeling of the proposed estimates are presented and compared with the Yule–Walker estimates using the example of confidence estimation of spectral density.