| Abstract: |
| Support vector machines (SVMs) are a recent supervised learning approach towards function estimation. They combine several results from statistical learning theory, optimisation theory, and machine learning, and employ kernels as one of their most important ingredients. In this regard we propose a novel methodologie to derives a formal test from the nonparametric support vector regression estimator of the Lyapunov exponent in a noisy system with Kalman filtering (SVREKF). Amongst others the advantage of SVREKF compared to the widely used estimators (which is implemented using Artifcial Neural Network (ANN)) is, implicit nonlinear mapping and better regularization capability. In this work, we make use of Kalman recursions instead of quadratic programming which is generally used in kernel methods. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. We apply our test to some of the standard chaotic systems and the financial time series. The performance of the test is very satisfactory in the presence of noise as well as with limited number of observations.We also discuss some of the limitations of our fndings. |
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