Multiple-step ahead prediction for non linear dynamic systems: A Gaussian Process treatment with propagation of the uncertainty

Abstract

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y t = f(y t 1 ; : : : ; y t L ), the prediction of y at time t + k is based on the estimates ^ y t+k 1 ; : : : ; ^ y t+k L of the previous outputs.