Prediction in Projection

Full and accurate reconstruction of dynamics from time-series data---e.g., via delay-coordinate embedding---is a real challenge in practice. In this talk, I will illustrate---for forecasting purposes---information can be gleaned from incomplete embeddings. In particular, I will provide a proof of concept for a stream-forecasting technique using a tau-return map embedding of the data. Even though correctness of the topology is not guaranteed for these incomplete reconstructions, near-neighbor forecasts in these reduced-order spaces are as (or more) effective than using a traditional embedding. I will illustrate the efficiency of this method on synthetic time series generated from the Lorenz-96 atmospheric model, as well as on experimental data.