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A Nonlinear Dynamical System Approach for Analyzing Time Series with Event Size and Event Timing Information and its Applications

分析具有事件大小和事件时序信息的时间序列的非线性动力系统方法及其应用

基本信息

批准号：
13831002
负责人：
IKEGUCHI Tohru
金额：
$ 1.92万
依托单位：
SAITAMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13831002/
关键词：
Nonlinear Causal Relation Dynamical Systems Chaos Event Amplitude Event Timing Prediction Statistical Hypothesis Testing

项目摘要

In the proposed framework, first we assume an existence of an event dynamical system, which produces observed complex event time series. Thus, the important and essential information of the dynamical system is not only event sizes or event timings but both of observed event sizes and timings.To analyze several time series with complex behavior under our modeling framework, we evaluate prediction accuracy of event series using both the proposed method and the conventional method. For the evaluation, we use artificial event series generated from a mathematical model. As results, we show that the proposed framework is applicable for predicting event series. Then, we apply the proposed method to real world complex phenomena. We use experimental time series of a laser diode-pumped Nd:YVO_4 microchip laser, as one of the examples of possible chaotic phenomena. From this system, we can observe a single longitudinal mode oscillation at weak pumping power, whose output looks like spike oscillat … More ion. The proposed method is used for predicting the spike sizes and timings. We show that the proposed method is more effective for event prediction than the conventional methods, in such real world complex phenomena.As applications of our proposed scheme, first we apply the proposed method to predict the timings of occurrence of maxima of continuous time series. Here, maximum sizes and timings are treated as an output set of event sizes and timings, respectively. Then, we predict maxima of continuous time series produced from mathematical models and maxima of real world complex phenomena. Results of the proposed method show high accuracies of maxima prediction. Next we use the maximum prediction by the proposed method for improving long-term predictability of the observed continuous time series. Since it is widely acknowledged that one of the characteristics of deterministic chaos is long-term unpredictability, it is very interesting and important issue to remove long-term predictability of the continuous time series. Although we can take several strategies for realizing the long-term predictability, we use a simple method : we predict two successive maxima of the continuous time series, then we interpolate the values between these maxima. As results, we show that our modeling method is applicable for improving long-term prediction of the continuous time series. Less

在建议的框架中，首先，我们假设存在一个事件动力系统，它产生观察到的复杂事件的时间序列。因此，重要的和必要的信息的动力系统不仅是事件的大小或事件的时间，但观察到的事件的大小和timing.To分析几个时间序列的复杂行为下，我们的建模框架，我们评估预测精度的事件序列使用所提出的方法和传统的方法。对于评估，我们使用从数学模型生成的人工事件序列。作为结果，我们表明，所提出的框架是适用于预测事件序列。然后，我们将所提出的方法应用到真实的世界的复杂现象。我们使用激光二极管泵浦的Nd：YVO_4微片激光器的实验时间序列作为可能的混沌现象的例子之一。在弱抽运功率下，我们观察到了单纵模振荡，其输出类似于尖峰脉冲 ...更多信息离子。所提出的方法是用于预测尖峰的大小和定时。结果表明，在这种真实的世界的复杂现象中，该方法比传统方法更能有效地预测事件.作为该方法的应用，我们首先将该方法应用于连续时间序列极大值出现的时间预测.这里，最大大小和时间分别被视为事件大小和时间的输出集。然后，我们预测由数学模型产生的连续时间序列的最大值和真实的世界复杂现象的最大值。实验结果表明，该方法具有较高的极大值预测精度。接下来，我们使用所提出的方法的最大预测，以提高所观察到的连续时间序列的长期可预测性。由于人们普遍认为确定性混沌的特征之一是长期不可预测性，因此消除连续时间序列的长期可预测性是一个非常有趣和重要的问题。虽然我们可以采取几种策略来实现长期的可预测性，但我们使用一种简单的方法：我们预测连续时间序列的两个连续的最大值，然后在这些最大值之间插值。作为结果，我们表明，我们的建模方法是适用于改善连续时间序列的长期预测。少