title: Prediction in projection.
abstract: Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from scalar time-series data-e.g., via delay-coordinate embedding-can be a real challenge. In this paper, we show that forecast models that employ incomplete reconstructions of the dynamics-i.e., models that are not necessarily true embeddings-can produce surprisingly accurate predictions of the state of a dynamical system. In particular, we demonstrate the effectiveness of a simple near-neighbor forecast technique that works with a two-dimensional time-delay reconstruction of both low- and high-dimensional dynamical systems. Even though correctness of the topology may not be guaranteed for incomplete reconstructions like this, the dynamical structure that they do capture allows for accurate predictions-in many cases, even more accurate than predictions generated using a traditional embedding. This could be very useful in the context of real-time forecasting, where the human effort required to produce a correct delay-coordinate embedding is prohibitive.
authors.affiliation: Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: Joshua
authors.initials: J
authors.lastname: Garland
authors.affiliation: Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA and the Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Bradley