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 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.

13 pages, 7 figures, 3 tables

References in corpus (4)

• Nonlinear time-series analysis revisited
• Model-free quantification of time-series predictability
• A new method for choosing parameters in delay reconstruction-based forecast strategies
• On the importance of nonlinear modeling in computer performance prediction

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• A new method for choosing parameters in delay reconstruction-based forecast strategies
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• Incomplete Phase-Space Method to Reveal Time Delay From Scalar Time-series
• Using scaling-region distributions to select embedding parameters
• Optimal Neural Network Feature Selection for Spatial-Temporal Forecasting
• Towards automated extraction and characterization of scaling regions in dynamical systems
• Prediction in Projection: A new paradigm in delay-coordinate reconstruction
• Dynamical systems theory for causal inference with application to synthetic control methods
• Asymptotically consistent prediction of extremes in chaotic systems:1 stationary case
• Statistical inference for Axiom A attractors
• Statistical Failure Mechanism Analysis of Earthquakes Revealing Time Relationships
• A simple statistical approach to prediction in open high dimensional chaotic systems
• Rethinking animal social complexity measures with the help of complex systems concepts