The Helson-Sarason-Szegő theorem and the Abel summability of the series for the predictor

Pourahmadi, Mohsen

doi:10.1090/S0002-9939-1984-0740191-7

The Helson-Sarason-Szegő theorem and the Abel summability of the series for the predictor
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Proc. Amer. Math. Soc. 91 (1984), 306-308 Request permission

Abstract:

It is shown that the best linear least squares predictor of a stationary stochastic process has a mean Abel summable series representation in the time domain if its density satisfies the condition of the Helson-Sarason-Szego theorem. This provides an answer to an open question of Wiener and Masani (1958) in prediction theory.

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Stationary sequences in a Hilbert space

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