Stationary Reversible Processes of a Moving Average and Autorepression with Residuals as a Moving Average

In this paper, we show how to select an adequate model of a stationary reversible moving-average process of finite order, given the appropriate number of sample correlations. We find the admissibility conditions, under which, for a reversible model of a moving-average process of no higher than the fifth order, a one-to-one correspondence between the coefficients and correlations of the process is established. If the admissibility conditions for sample correlations are met, it is possible to select a reversible stationary model. For higher-order moving-average processes, a mixed autoregression and moving-average model of no higher than the fifth order preliminarily approaches the initial data. This variant also has independent significance since even at small orders of the mixed model, good agreement between the correlations of the model and the sample correlations of the process is obtained. Particular attention is paid to the reversibility of the process since the prediction formulas assume fulfillment of this condition.