On asymptotic behaviour of the prediction error

Let $\{x_j\}$ be a wide sense stationary regular stochastic process with the sprectral density function $\varphi(x)$. Denote by $\sigma_n^2$ the mean square prediction error in predicting $x_0$ by linear forms in $x_{-1},x_{-2},\dots,x_{-n}$. Put $\delta_n=\sqrt{\sigma_n^2-\sigma^2}=\sqrt{\sigma_n^2-\sigma_\infty^2}$.
The rate of convergence $\delta_n\to0$ for different classes of spectral densities in regular and irregular (Jacobi's) cases is investigated.