Eur. Phys. J. Special Topics 143, 261-264 (2007)
https://doi.org/10.1140/epjst/e2007-00099-5

Haar basis and nonlinear modeling of complex systems

¹ Departamento de Física Aplicada, Facultad de Ingeniería, Universidad Central de Venezuela A.P., 48110 Caracas, Venezuela
² Departamento de Matemática Aplicada, Facultad de Ingeniería, Universidad Central de Venezuela, 48110 Caracas, Venezuela

Abstract

In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.