Nonlinear Time-Series Prediction with Missing and Noisy Data

We derive solutions for the problem of missing and noisy data in nonlinear timeseries prediction from a probabilistic point of view. We discuss different approximations to the solutions, in particular approximations which require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and we show how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sun-spot data set. In particular, we show that for K-step prediction stochastic simulation is superior to simply iterating the predictor.

• Type: Journal
• Year: 1998
• Where: NECO
• Authors: Volker Tresp, Reimar Hofmann
• Keywords: NECO 1998, Nonlinear Timeseries Prediction, Prediction, Solutions