基于延迟重构的预测策略中参数选择的新方法
A new method for choosing parameters in delay reconstruction-based forecast strategies
摘要：
延迟坐标重构是一种行之有效的建模策略，用于建立非线性时间序列的有效预测。这个过程的第一步是估计两个参数的好值，即时间延迟和嵌入维数。在文献中已经提出了许多方法和策略来估计这些值。然而，这些方法中很少有（如果有的话）是在考虑预测的情况下开发的，它们的结果对于这一目的来说并不是最佳的。即便如此，这些用于其他应用程序的预测学在建立基于延迟坐标重建的预测模型时经常使用。在本文中，我们提出了一种新的策略，选择最佳的参数值的预测方法，是基于延迟坐标重建。基本的计算涉及最大化每个延迟向量和系统的未来状态之间的共享信息。我们说明了这种方法在几个合成和实验系统的有效性，表明这种度量可以快速，可靠地计算从一个相对较短的时间序列，它提供了一个直接的指示，以及如何基于近邻的预测方法将工作在一个给定的延迟重建的时间序列。这允许从业者选择避免任何病理的重建参数，而不管潜在的机制如何，并且最大化重建中包含的预测信息。
英文摘要：
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.
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