Agathe Girard, Carl Rasmussen, Joaquin Quiñonero Candela, Roderick Murray-Smith
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. -step ahead forecasting of a discrete-time non-linear dynamic system can be per- formed by doing repeated one-step ahead predictions. For a state-space at time model of the form is based on the point estimates of the previous outputs. In this pa- per, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction.