Asymptotic behavior of the prediction error

Let {X_n}_– be a random process, stationary in the broad sense, with spectral density f() satisfying the singularity condition: · We denote _n² the mean square prediction error at the prediction of _o by linear forms in X_–1, ... , X_–n. In the paper one investigates the rate of decrease of _n to zero.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.