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中文摘要：
通过相空间重构技术，对Brent和WTI原油价格增长率的时间序列分别进行相空间重构，将若干固定时间延迟点上的数据作为新维处理，形成相点，应用Wolf方法得出了最大的Lyapunov指数，从而给出了系统混沌存在的证据；利用关联函数求出了关联维度和Kolmogorov熵，从而给出了对系统的混沌程度的估计和对Brent和WTI原油价格进行有效性预测的时间尺度．
英文摘要：
Using the Phase Space Reconstruction Technique （PSRT） and correlation dimension method, the evidences of the existence of chaos are found in the time series of the monthly and daily Brent and WTI crude oil price fluctuations in the markets. We analyse the time series of Brent and WTI crude oil prices of the markets, attain the correlation dimensions and positive Lyapunov exponents, thus identify the existence of chaos in all 4 systems under study. Furthermore, we also obtain Kolmogorov entropies which can be used for estimating the effectiveness of prediction of Brent and WTI crude oil prices in markets.
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