A new method for choosing parameters in delay reconstruction-based forecast strategies

TL;DR

This paper introduces a new parameter selection method for delay-coordinate based forecasting that maximizes shared information with future states, improving forecast accuracy for nonlinear time series.

Contribution

It proposes a novel strategy for choosing delay and embedding parameters specifically optimized for forecasting, unlike previous heuristics not tailored for this purpose.

Findings

The method reliably estimates optimal parameters from short time series.

It enhances forecast accuracy by selecting parameters that maximize predictive information.

The approach is effective on both synthetic and real-world systems.

Abstract

Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding dimension. Many heuristics and strategies have been proposed in the literature for estimating these values. Few, if any, of these methods were developed with forecasting in mind, however, and their results are not optimal for that purpose. Even so, these heuristics---intended for other applications---are routinely used when building delay coordinate reconstruction-based forecast models. In this paper, we propose a new strategy for choosing optimal parameter values for forecast methods that are based on delay-coordinate reconstructions. The basic calculation involves maximizing the shared information between each delay vector and the future state of the system. We illustrate the effectiveness of this method on several synthetic and experimental systems, showing that this metric can be calculated quickly and reliably from a relatively short time series, and that it provides a direct indication of how well a near-neighbor based forecasting method will work on a given delay reconstruction of that time series. This allows a practitioner to choose reconstruction parameters that avoid any pathologies, regardless of the underlying mechanism, and maximize the predictive information contained in the reconstruction.