基于混沌的神经网络与分形插值的汇率组合预测研究

发布时间：2018-06-04 04:21

本文选题：汇率预测 + 混沌　；参考：《华北电力大学》2017年硕士论文

【摘要】：汇率的有效预测不但能够影响本国与别国的经济与贸易,同时能够防范国际性金融危机的发生或减少所造成的损失。传统的研究方法和模型,不能够充分的解释汇率波动这样的复杂非线性系统,混沌在非线性研究中占有重要地位,本文试图利用混沌理论对汇率行为进行研究,充分挖掘混沌对复杂非线性系统的解释与预测能力,以期达到提高汇率预测精度的目的,以此来指导国家宏微观各主体的经济活动和行为。本文以混沌理论为基础,同时将神经网络和分形插值法应用于汇率时间序列的研究与预测中。根据货币的活跃程度不同选取三个具有代表性的货币对,美元兑人民币、英镑兑人民币、加元兑人民币。首先,借助于图示法和指标法对其进行统计性描述,并进行非线性特征分析。然后,利用C-C算法求得三个汇率时间序列的时间延迟、嵌入维数以此来重构相空间,在此基础之上,利用wolf算法和G-P算法分别求出最大Lyapunov指数和分形维数,对汇率的混沌特性进行验证。在确定汇率系统的混沌性之后,根据汇率的混沌特征来分别建立神经网络和分形插值预测模型。神经网络的构建是将混沌系统重构相空间的最佳嵌入维作为输入层的神经元数,并将重构相空间中的时序向量作为神经元的输入量;分形插值模型中的垂直比例因子则根据分形维数计算求得。最后,在分别利用两个模型进行预测的基础上,根据较大误差在组合预测模型中占比较小的原则进行动态组合预测的实证研究。本文通过对三个人民币汇率的统计性描述得出,汇率时间序列不服从正态分布,具有非线性特征。同时,求得的三个最大Lyapunov指数都为正数,而分形维数都为较小的分数,这表明三个汇率序列都为对初始条件都具有敏感性的低维混沌系统。以混沌理论为基础的汇率组合预测模型在有效利用混沌对复杂系统解释能力的同时,能将神经网络的非线性逼近能力以及分形插值对不光滑曲线的拟合能力结合应用。预测结果表明,组合预测模型能够保留单个预测模型的优势的同时降低单个模型的缺点在预测中的影响,预测精度得到有效提高。
[Abstract]:The effective prediction of exchange rate can not only affect the economy and trade between our country and other countries, but also prevent the loss caused by the international financial crisis. Traditional research methods and models can not fully explain the complex nonlinear system such as exchange rate fluctuations. Chaos plays an important role in nonlinear research. This paper attempts to use chaos theory to study exchange rate behavior. In order to improve the accuracy of exchange rate prediction, the chaotic interpretation and prediction ability of complex nonlinear systems can be fully exploited to guide the economic activities and behaviors of the national macro and micro entities. In this paper, based on chaos theory, neural network and fractal interpolation are applied to the study and prediction of exchange rate time series. Three representative pairs, the dollar versus the renminbi, the pound against the renminbi and the Canadian dollar against the yuan, are chosen depending on the currency's activity. Firstly, the statistical description and nonlinear characteristic analysis are carried out with the help of graphical method and index method. Then, the time delay of three exchange rate time series is obtained by C-C algorithm, and the embedded dimension is used to reconstruct the phase space. On this basis, the maximum Lyapunov exponent and fractal dimension are obtained by using wolf algorithm and G-P algorithm, respectively. The chaos characteristic of exchange rate is verified. After the chaos of exchange rate system is determined, neural network and fractal interpolation prediction model are established according to the chaotic characteristics of exchange rate. The optimal embedding dimension of the reconstructed phase space of the chaotic system is taken as the number of neurons in the input layer, and the time series vector in the reconstructed phase space is taken as the input quantity of the neuron. The vertical scaling factor in the fractal interpolation model is calculated according to the fractal dimension. Finally, on the basis of the two models, the dynamic combination prediction is studied based on the principle that the large error is small in the combination forecasting model. Based on the statistical description of the three RMB exchange rates, it is concluded that the time series of exchange rates are not obedient to normal distribution and have nonlinear characteristics. At the same time, the three largest Lyapunov exponents obtained are all positive numbers, while the fractal dimensions are all small fractions, which indicates that the three exchange rate sequences are all low-dimensional chaotic systems with sensitivity to initial conditions. The exchange rate combination forecasting model based on chaos theory can effectively utilize the ability of chaotic interpretation to complex system, at the same time, it can combine the nonlinear approximation ability of neural network and the ability of fractal interpolation to fit the non-smooth curve. The prediction results show that the combined prediction model can preserve the advantages of the single prediction model and reduce the influence of the shortcomings of the single model in the prediction, and the prediction accuracy is improved effectively.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183;F832.6;F224

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