开放高维混沌系统预测的简单统计方法
A simple statistical approach to prediction in open high dimensional chaotic systems
摘要：
最近两篇关于混沌系统预测的论文，一篇关于多视图嵌入1，另一篇关于投影预测2，提供了支持混沌系统特定预测方法的经验证据。多视图嵌入1是一种使用多个多变量时间序列来提出混沌时间序列的改进的基于嵌入的预测器的方法。预测中的投影2讨论了小得多的嵌入可以提供有用的预测，即使它们可能无法解决系统的动力学。这两篇论文都引用了最近邻3或Lorenz方法（LMA）4来估计。然而，对于开放的高维混沌系统，在历史中可能没有非常接近的最近邻轨迹，因此在本文中，我们加入了线性响应理论5的线程，尽管我们的方法很简单，假设多个嵌入5上的线性回归6就足够了。因此，该方法是创建多个1低维嵌入2的线性响应模型5，以提供预测高维开放混沌系统的实用方法。一些理论发展起来，主要是围绕两个未经证实的理论来提出预测方法，并将其应用于地球气候系统的预测（预测一个小地区的区域降雨量）提前多个季节，并为应用于三个股票指数（道琼斯工业平均指数、道琼斯运输平均指数和道琼斯公用事业平均指数）的模拟自动交易程序提供动力，基于1929年至2007年的数据7
英文摘要：
Two recent papers on prediction of chaotic systems, one on multi-view embedding1 , and the second on prediction in projection2 provide empirical evidence to support particular prediction methods for chaotic systems. Multi-view embedding1 is a method of using several multivariate time series to come up with an improved embedding based predictor of a chaotic time series. Prediction in projection2 discusses how much smaller embeddings can provide useful prediction even though they may not be able to resolve the dynamics of the system. Both papers invoke a nearest neighbor3, or Lorenz method of Analogue (LMA)4 approach to estimation. However with open high dimensional chaotic systems there may be no very close nearest neighbor trajectories in a history, so in this paper we add in the thread of linear response theory5, although our approach is quite simple assuming that linear regressions6 on multiple embeddings5 will be sufficient. The approach is thus to create linear response models5 of multiple1 low dimensional embeddings2 to provide practical methods of predicting in high dimensional, open chaotic systems. Some theory is developed, mostly around two unproven conjectures to suggest methods of prediction, and they are applied to prediction in the earth's climate system (predicting regional rainfall in a small region) multiple seasons ahead and to power a simulated automated trading program applied to three stock indexes, the Dow Jones industrial average, the Dow Jones transportation average, and the Dow Jones utility average, based on data from 1929 through 20077
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
