能源期货市场的“蝴蝶效应”与混沌
"Butterfly Effect" vs Chaos in Energy Futures Markets
摘要：
在本文中，我们测试的敏感依赖于初始条件（所谓的“蝴蝶效应”）的能源期货时间序列（取暖油，天然气），从而确定这些系列。本文与以往研究的不同之处在于：首先，我们重新阅读了已有的关于能源市场的文献，启发了\emph{butterfly effect}在Devaney提出的混沌定义中的作用，利用该定义避免了对价格序列表面混沌性的误导。其次，我们测试的时间序列敏感的依赖于初始条件，引入一个系数，描述了一系列的确定性率，代表其可靠性水平（百分比）。引入这种可靠性水平的动机是随机系统产生的时间序列也可能对初始条件表现出敏感的依赖性。根据这一观点，此处获得的最大可靠性水平太低，无法确保有强有力的证据表明敏感性。此处获得的最大可靠性水平是$\simeq 56\% $，太低，无法确保有强有力的证据表明敏感性依赖于初始条件。
英文摘要：
In this paper we test for the sensitive dependence on initial conditions (the so called "butterfly effect") of energy futures time series (heating oil, natural gas), and thus the determinism of those series. This paper is distinguished from previous studies in the following points: first, we reread existent works in the literature on energy markets, enlightening the role of \emph{butterfly effect} in chaos definition (introduced by Devaney), using this definition to prevent us from misleading results about ostensible chaoticity of the price series. Second, we test for the time series for sensitive dependence on initial conditions, introducing a coefficient that describes the determinism rate of the series and that represents its reliability level (in percentage). The introduction of this reliability level is motivated by the fact that time series generated from stochastic systems also might show sensitive dependence on initial conditions. According to this perspective, the maximum reliability level obtained here is too low to be able to ensure that there is strong evidence of sensitive The maximum reliability level obtained here was been $\simeq 56\% $, too low to ensure strong evidence of sensitive dependence on initial conditions.
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