An asymptotic behaviour of the prediction error

The rate of convergence $\sigma_n\downarrow0$ of the mean square prediction error $\sigma_n^2$ of predicting $X_n$, by linear forms in $X_{-1},\dots, X_{-n}$ is investigated for stationary in the wide sence stochastic process $X_k$ with tbe spectral density satisfying the condition of singularity.