Knot-optimizing spline networks (KOSNETS) for nonparametric regression

Song Wang; Quanxi Shao; Xian Zhou

doi:10.3934/jimo.2008.4.33

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2008, Volume 4, Issue 1: 33-52. Doi: 10.3934/jimo.2008.4.33

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Knot-optimizing spline networks (KOSNETS) for nonparametric regression

1.
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009
2.
CSIRO Mathematical and Information Sciences, Private Bag 5, Wembley, WA 6913
3.
Department of Actuarial Studies, Macquarie University, Sydney

Received: July 2006

Revised: November 2007

Published: January 2008

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we present a novel method for short term forecast of time series based on Knot-Optimizing Spline Networks (KOSNETS). The time series is first approximated by a nonlinear recurrent system. The resulting recurrent system is then approximated by feedforward $B$-spline networks, yielding a nonlinear optimization problem. In this optimization problem, both the knot points and the coefficients of the $B$-splines are decision variables so that the solution to the problem has both optimal coefficients and partition points. To demonstrate the usefulness and accuracy of the method, numerical simulations and tests using various model and real time series are performed. The numerical simulation results are compared with those from a well-known regression method, MARS. The comparison shows that our method outperforms MARS for nonlinear problems.

Keywords:

Nonlinear time series; Nonparametric method; Regression; Spline method; Feedforward networks.

Mathematics Subject Classification: Primary: 62M10, 65K05; Secondary: 41A15, 37M10.

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