Kernel Auto-Regressive Model with eXogenous Inputs for Nonlinear Time Series Prediction

In this paper we present a novel approach for nonlinear time series prediction using kernel methods. The kernel methods such as support vector machine (SVM) and support vector regression (SVR) deal with nonlinear problems assuming independent and identically distributed (i.i.d.) data, without explicit notion of time. However, the problem of prediction necessitates temporal information. In this regard, we propose a novel time series modeling technique, kernel auto-regressive model with exogenous inputs (KARX) and associated estimation methods. Amongst others the advantage of KARX model compared to the widely used nonlinear auto-regressive exogenous (NARX) model (which is implemented using artificial 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. Also, we employ online estimation schemes for estimating model noise parameters. The efficacy of the approach is demonstrated on artificial time series as well as real world time series acquired from aircraft engines