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 of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about future regressor values, thus updating the uncertainty on the current prediction.
Accepted by NIPS*02.
Available as ps.