摘要：石油价格的波动不仅影响着投资者，而且对于政府部门的决策产生重要影响，其价格变化规律的研究一直受经济学界的广泛关注。影响石油价格波动的因素众多，从形成石油和美元的联动机制以来，美元就成为影响石油价格的主导因素。本文利用石油价格及美元指数非线性非平稳的特点，采用经验模态分解方法(EMD)对其进行分解，随后使用分形插值函数对其进行模拟，最终利用蒙特卡洛法对其价格进行预测。本文具体工作及结果如下：
(1)    通过EMD方法分别对石油价格及美元指数分解，得到本征模函数(IMF)及残余项(RES)，分析各阶IMF及RES的周期性及经济学意义；
(2)    利用相关系数，对石油价格及美元指数进行相关性分析，证实石油价格与美元指数存在强负相关性，即表示美元升值，将导致石油价格下跌，相反，美元贬值，牵引油价上涨；
(3)    对原始数据进行整理筛选，采用分形插值函数迭代系统，对其进行数据拟合，并将结果与原始走势图比对，发现该方法拟合效果较好。并且利用蒙特卡洛法进行模拟预测，发现该方法的预测值偏离真实值不大，是一个可行的预测模型。
关键词：石油价格；美元指数；经验模态分解方法；分形插值函数4087
Correlation Analysis between Dollar and the international crude oil prices based on EMD method and Fractal Theory

Abstract: The fluctuation of the oil price affects not only investors, but also government departments. Attention on the study of the oil price has been affected by the economic circles.  Though many factors influence the fluctuation of oil price, the dollar is the main factor after finding the linkage mechanism of oil and the dollar. Because the characteristics of the oil price and the dollar index are nonlinear and non-stationary, the author decomposes it by Empirical Mode Decomposition (EMD). The author simulates the basic data by Fractal Interpolation Function and forecasts the price by Monte Carlo method. The following is the work content of this paper:
(1)    The author decomposes the oil prices and the dollar index by EMD, and investigates the cycle and the economical information of the IMF and RES.
(2)    The author analyses the correlation of oil prices and the dollar index by correlation coefficient. The conclusion confirms that the existence of strong negative correlation between oil prices and the dollar index. It is showed that the appreciation of the dollar will lead to the decline in oil prices, and vice versa.
(3)    The author is found that the method has a good fitting effect after screening the original data, fitting on the data and contrasting the results with the original graph. With the graph of the basic data and the results, which is using the screening of the basic data and Fractal Interpolation Function to fit the basic data, discovered a better fitting effect of this method. Then we used the Monte Carlo method to forecast the price, found the prediction value is close to the true value. So we think the Monte Carlo method is useful. Finally, it is found that the predictive value by Monte Carlo method is similar with the real value.
Keywords:    Crude oil prices; Dollar index; Empirical Mode Decomposition; Fractal Interpolation Function
 目录
1    引言    1
1.1    课题目的和意义    1
1.3    论文的结构框架及主要内容    3
2    EMD方法、分形插值函数及蒙特卡罗法简介    4
2.1 经验模态分解方法(EMD)的简介    4
2.1.1本征模函数(IMF)    4
2.1.2经验模态分解方法(EMD)    4 基于EMD和分形理论的美元与国际油价的相关分析研究:http://www.751com.cn/shuxue/lunwen_583.html