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

在所提出的框架中，我们首先假设存在一个事件动力系统，该系统产生观测到的复杂事件时间序列。因此，动态系统的重要和基本信息不仅是事件大小或事件时间，还包括观测到的事件大小和时间。为了在我们的建模框架下分析几个具有复杂行为的时间序列，我们使用所提出的方法和传统方法来评估事件序列的预测精度。对于评估，我们使用了从数学模型生成的人工事件序列。结果表明，该框架适用于事件序列的预测。然后，我们将所提出的方法应用于现实世界中的复杂现象。我们使用激光二极管泵浦的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。从该系统中，我们可以观察到在弱抽运功率下的单纵模振荡，其输出类似于…的尖峰振荡更多的离子。提出的方法用于预测尖峰大小和时间。作为该方案的应用，我们首先将该方法应用于连续时间序列极大值发生时刻的预测。这里，最大大小和计时分别被视为事件大小和计时的输出集。然后，我们预测了由数学模型产生的连续时间序列的极大值和现实世界复杂现象的极大值。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值来提高观测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可预测性，但我们使用的是一种简单的方法：我们预测连续时间序列的两个连续极大值，然后对这些极大值之间的值进行内插。结果表明，我们的建模方法对于提高连续时间序列的长期预测是适用的。较少

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