Kernel-Based Autoregressive Modeling with a Pre-Image Technique

Autoregressive (AR) modeling is a very popular method for time series analysis. Being linear by nature, it obviously fails to adequately describe nonlinear systems. In this paper, we propose a kernel-based AR modeling, by combining two main concepts in kernel machines. One the one hand, we map samples to some nonlinear feature space, where an AR model is considered. We show that the model parameters can be determined without the need to exhibit the nonlinear map, by computing inner products thanks to the kernel trick. On the other hand, we propose a prediction scheme, where the prediction in the feature space is mapped back into the input space, the original samples space. For this purpose, a pre-image technique is derived to predict the future back in the input space. The efficiency of the proposed method is illustrated on real-life time-series, by comparing it to other linear and nonlinear time series prediction techniques.