On the asymptotic behaviour of the prediction error in the singular case

Let $\{X_j\}$ be a singular stationary in a wide sense stochastic process with the spectral density function $f(\lambda)$. Denote by $\sigma_n^2$ the mean square prediction error for the prediction of $X_0$ by linear forms depending on $X_{-1}, X_{-2},\dots X_{-n}$. The rate of convergence $\delta_n=\sigma_n^2-\sigma_\infty^2\downarrow 0$, $n\uparrow\infty$, is investigated.