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Knot-optimizing spline networks (KOSNETS) for nonparametric regression. (English) Zbl 1154.62069

Summary: We present a novel method for short term forecasts 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 \(\beta\)-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.

MSC:

62M20 Inference from stochastic processes and prediction
65K05 Numerical mathematical programming methods
41A15 Spline approximation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C60 Computational problems in statistics (MSC2010)
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