Gaussian Process Priors with Uncertain Inputs Application to Multiple-Step Ahead Time Series Forecasting

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. 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.