The problem of automatic prediction of a certain class of deterministic signals is considered. Such problems arise both in the theory of automatic control and in various applications where it is required to obtain a forecast for the observed realization. The class of signals considered in the article is quite wide. To solve this problem we use a Bourman-Lagrange series of the exponential transfer function in terms of the powers of the transfer function of the realized differentiating plant. The approximated transfer function is transcendental and infinite-dimensional. The Burman-Lagrange series allows the regularization of an incorrect problem. The prediction accuracy can be increased due to the regularization parameter, as well as by increasing the number of terms of the Burman-Lagrange series. The results of modeling of the automatic predictor constructed in the article are presented. These results show good prediction accuracy. The proposed method of synthesis of automatic predictors can be applied to other classes of signals, including the prediction of noisy signals.