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.
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