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

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Agathe Girard, Carl Rasmussen, Joaquin QuiƱonero 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.