Prediction of time series using Yule-Walker equations with kernels

The autoregressive (AR) model is a well-known technique to analyze time series. The Yule-Walker equations provide a straightforward connection between the AR model parameters and the covariance function of the process. In this paper, we propose a nonlinear extension of the AR model using kernel machines. To this end, we explore the Yule-Walker equations in the feature space, and show that the model parameters can be estimated using the concept of expected kernels. Finally, in order to predict once the model identified, we solve a pre-image problem by getting back from the feature space to the input space. We also give new insights into the convexity of the pre-image problem. The relevance of the proposed method is evaluated on several time series.