Abstract
Let {Xn} ∞−∞ be a random process, stationary in the broad sense, with spectral density f(λ) satisfying the singularity condition:\(\mathop \smallint \limits_{ - \pi }^\pi \ln f \left( \lambda \right)d\lambda = - \infty \) · We denote σ 2n the mean square prediction error at the prediction of χo by linear forms in X−1, ... , X−n. In the paper one investigates the rate of decrease of σn to zero.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 11–24, 1983.
In conclusion, the author wishes to express his gratitude to I. A. Ibragimov for his constant interest and help.
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Babayan, N.M. Asymptotic behavior of the prediction error. J Math Sci 27, 3170–3181 (1984). https://doi.org/10.1007/BF01850663
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DOI: https://doi.org/10.1007/BF01850663