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February, 1979 Lower Bounds for Nonlinear Prediction Error in Moving Average Processes
Marek Kanter
Ann. Probab. 7(1): 128-138 (February, 1979). DOI: 10.1214/aop/1176995153


As yet no efficiently computable algorithm for one step nonlinear prediction has been proposed for any general class of stationary processes which performs strictly better than the optimal linear predictor. In this paper it is shown that for the class of stationary moving average processes the improvement obtained by optimal nonlinear prediction versus optimal linear prediction is bounded by a constant which depends only on the distribution of the independent and identically distributed random variables $Y_j$ used to form the moving average process $X_n = \sum a_jY_{n - j}$.


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Marek Kanter. "Lower Bounds for Nonlinear Prediction Error in Moving Average Processes." Ann. Probab. 7 (1) 128 - 138, February, 1979.


Published: February, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0405.60041
MathSciNet: MR515818
Digital Object Identifier: 10.1214/aop/1176995153

Primary: 60G25
Secondary: 60G10 , 60G15 , 62M20 , 94A05 , 94A15

Keywords: differential entropy , Moving average stationary process , mutual information , one step prediction error

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 1 • February, 1979
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