In the article we consider the problem of linear extrapolation of zero-mean widesense-stationary random process both discrete-time and continuous-time cases under conditions of the absence of a priori information about the statistical characteristics of disturbance in the absence of measurement errors under scalar observation only the restricted disturbance is assumed. We investigate a minimax approach, which guarantees the prediction of high quality at the least favorable disturbance spectrum. The simple implementation of an optimal adaptive minimax predictor and prediction based on Kalman -Bucy filter and their comparative characteristics has been obtained. Examples are given.
In the article we consider the problem of linear extrapolation of zero-mean wide-sense-stationary random process both discrete-time and continuous-time cases under conditions of the absence of a priori information about the statistical characteristics of disturbance in the absence of measurement errors under scalar observation only the restricted disturbance is assumed. We investigate a minimax approach, which guarantees the prediction of high quality at the least favorable disturbance spectrum. The simple implementation of an optimal adaptive minimax predictor and prediction based on Kalman – Bucy filter and their comparative characteristics has been obtained. Examples are given.