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A comparison of linear versus non-linear prediction for polynomial functions of the Ornstein-Uhlenbeck process

Published online by Cambridge University Press:  14 July 2016

John Donelson III  and
Fred Maltz
Fred Maltz
Affiliation:
Lockheed Palo Alto Research Laboratory, Palo Alto, California
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Abstract

The general minimum mean square error prediction problem is studied for the class of processes defined by polynomial functions of the Ornstein-Uhlenbeck process. In particular, the relative error difference for non-linear prediction compared with optimal linear prediction is calculated. Limiting values are determined, including an upper bound for the maximal relative error difference. These results show no difference over the entire class for both long and short prediction lead times. For a single Hermite polynomial, the relative error difference is zero. An analytical solution for the maximal difference for lead times below a given threshold is derived. This latter result has been verified numerically on a digital computer for polynomials up to 17th degree.

Keywords

NON-LINEAR PREDICTIONLINEAR PREDICTIONHERMITE POLYNOMIAL; ORNSTEIN-UHLENBECK PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 725 - 744
Copyright
Copyright © Applied Probability Trust 1972 

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