标题： “蝴蝶效应”与能源期货市场的混沌现象 显示英文标题

标题： "Butterfly Effect" vs Chaos in Energy Futures Markets

摘要： 在本文中，我们检验能源期货时间序列（取暖油、天然气）对初始条件的敏感依赖性（即所谓的“蝴蝶效应”，从而检验这些序列的确定性。 本文与之前的研究在以下几点有所不同：首先，我们重新阅读了能源市场文献中的现有作品，阐明了\emph{蝴蝶效应}在混沌定义中的作用（由Devaney引入），并使用这一定义来防止关于价格序列表面上的混沌性的误导性结果。 其次，我们检验时间序列对初始条件的敏感依赖性，引入了一个描述序列确定性率的系数，该系数表示其可靠性水平（以百分比表示）。 引入这一可靠性水平是基于这样一个事实，即从随机系统生成的时间序列也可能表现出对初始条件的敏感依赖性。 根据这一观点，这里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存在对初始条件的敏感依赖性。最大可靠性水平在这里是$\simeq 56\% $，太低而无法确保对初始条件的敏感依赖性的有力证据。 显示英文摘要

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.