Dynamical Modeling with Kernels for Nonlinear Time Series Prediction

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Liva Ralaivola, Florence d'Alché-Buc


We consider the question of predicting nonlinear time series. Kernel Dy- namical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.