Multiple-step ahead prediction for non linear dynamic systems: A Gaussian Process treatment with propagation of the uncertainty
We consider the problem of multi-step ahead prediction in ti me series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system c an be performed by doing repeated one-step ahead predictions. For a s tate-space model of the formyt = f(yt 1; : : : ; yt L), the prediction ofy at time t+ k is based on the estimates ŷt+k 1; : : : ; ŷt+k L of the previous outputs. In this paper, we show how, using an analytical Gaussia n approximation, we can formally incorporate the uncertainty about f uture regressor values, thus updating the uncertainty on the current pre diction.