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

Girard, A; Rasmussen, CE; Quiñonero-Candela, J; Murray-Smith, R

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

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http://papers.nips.cc/paper/2313-gaussian-process-priors-with-uncertain-inputs-application-to-multiple-step-ahead-time-series-forecasting.pdf
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Girard, A., Rasmussen, C., Quiñonero-Candela, J., & Murray-Smith, R. (2003). Gaussian Process Priors with Uncertain Inputs Application to Multiple-Step Ahead Time Series Forecasting. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in Neural Information Processing Systems 15 (pp. 529-536). Cambridge, MA, USA: MIT Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-DB49-8

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 point estimates of the previous outputs. In this paper, 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.