Geodesic
On asymptotic behaviour of the prediction error
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 724-739

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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. 
@article{TVP_1974_19_4_a4,
     author = {B. L. Golinskii},
     title = {On asymptotic behaviour of the prediction error},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {724--739},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a4/}
}
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B. L. Golinskii. On asymptotic behaviour of the prediction error. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 724-739. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a4/