On the Asymptotic Behavior of the Prediction Error

Let \ xⱼ \ be a stationary stochastic process in the wide sense which is regular, with spectral density function f(λ ). Denote by σ ₙ² the mean square prediction error in predicting x₀ by linear forms in x- 1 ,x- 2 , ⋯ ,x- n. Let δ ₙ = σ ₙ² - σ _∞ ² = σ ₙ² - σ ². The rate of convergence δ ₙ ↓ 0 is investigated in this article.