Let $\{ {x_j } \}$ be a stationary stochastic process in the wide sense which is regular, with spectral density function $f(\lambda )$. Denote by $\sigma _n^2 $ the mean square prediction error in predicting $x_0 $ by linear forms in $x_{ - 1} ,x_{ - 2} , \cdots ,x_{ - n} $. Let $\delta _n = \sigma _n^2 - \sigma _\infty ^2 = \sigma _n^2 - \sigma ^2 $. The rate of convergence $\delta _n \downarrow 0$ is investigated in this article.