  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 embeddings of the dynamics 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 embedding. Even though correctness of the topology is not
guaranteed for incomplete reconstructions like this, the dynamical structure
that they capture allows for accurate predictions---in many cases, even more
accurate than predictions generated using a full 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.

Chaotic Dynamics