【作者】 杨妮；

【导师】 谢赤；

【作者基本信息】 湖南大学 ， 管理科学与工程， 2008， 博士

【摘要】 汇率是一国经济的重要变量,既决定着经济的对内均衡,又影响着经济的对外均衡。随着经济全球化的不断推进和国际资本流动的日益加剧,汇率对于投资者选择正确的投资策略、企业对外汇风险的规避和防范以及中央银行对外汇市场的有效干预和制定正确的货币政策,都有着非常重要的影响。因此,关于汇率的行为描述和预测问题一直是国内外理论界关注的焦点。传统的资本市场理论构建在理性投资人、有效市场假说和随机游动三大假设条件基础之上。然而,这种基于线性研究范式的均衡分析体系无法对外汇市场的一些异象给出合理的解释,如汇率收益率分布的“尖峰厚尾”特征、波动的集群性、外汇市场中汇率波动的“无链接”问题等。资本市场在其本质上是非线性的。因此,引入非线性研究范式,对金融变量进行分析和预测研究是金融市场理论发展的必然结果。本文基于非线性研究范式和投资者异质预期的假设,以5种主要货币的汇率时间序列为研究对象,检验其非线性动力学特征,研究对象包括英镑(GBP)、瑞士法郎(CHF)、日元(JPY)、瑞典克朗(SEK)和加拿大元(CAD)兑美元(USD)的日汇率数据,样本区间选自1975年1月1日至2007年5月31日。实证检验表明,在研究的汇率时间序列中,均找到了非线性依赖性、长记忆性、混沌动力学特征以及多重分形性的判据:非线性依赖性的检验借助于BDS统计量,所有汇率序列的检验结果均拒绝独立同分布(iid)的原假设,数据中存在非线性依赖特征。同时,通过对子样本序列和标准序列进行BDS检验,其结果支持“数据中的非线性依赖性可能源于低维混沌”的假设;长记忆性特征分析借助于重标极差分析方法(R/S)、对数周期图法(GPH)和高斯半参数估计法(GSP),估计长记忆参数d和Hurst指数,结果表明5种汇率序列的每日、每周和每月的数据均具有长记忆特征,在统计意义上存在标度不变的自相似结构,汇率的波动服从分形布朗运动,即有偏的随机游动,从而否定了传统线性研究范式的随机游动假说;混沌动力学特征分析借助相空间重构技术,在判定非线性依赖性特征存在的前提下,对汇率时间序列的混沌特征量进行了估计。其中,重构参数的选择借助于Kim提出的C-C算法。实证结果显示,5种汇率时间序列的最大Lyapunov指数λ1均大于0,相关维的估计值均为分数,从而得到了确定性混沌存在的判据。这一结论为运用混沌理论对汇率变量进行解释以及短期预测提供了可能;多重分形理论是分形理论的重要组成部分。本文在获取汇率时间序列存在长记忆性和分数维等分形特征的基础之上,进一步对其多重分形特征进行了分析:一方面借助配分函数分布图进行存在性的判定,另一方面通过多重分形谱对该特征进行了描述和分析比较。本文通过对汇率时间序列的非线性依赖性、长记忆性、混沌动力学特征以及多重分形特征进行检验,得到汇率时间序列存在非线性动力学特征的证据。这不仅为人们更好地认识资本市场的本质特征提供了理论依据,同时也为投资者制定投资策略、企业规避外汇风险、货币当局制定货币政策和对外汇市场进行有效干预提供了技术支持。汇率时间序列存在非线性动力学特征表明,复杂系统内部的常态波动性来源于汇率系统的内随机性,是系统内部非线性机制导致的必然结果,而不必依赖于外部随机事件的冲击。因此,将汇率变量偏离均衡的原因完全归结于外部干扰,试图通过强制干预令其回归均衡的努力是无效的。在得到汇率时间序列存在分形和混沌动力学特征的实证结果后,本文利用混沌时间序列预测方法对汇率变量进行预测研究。考虑到单个预测模型的局限性,本文利用组合预测误差最小化原理,将三种常见的非线性混沌时间序列预测模型,即基于径向基函数的神经网络模型、基于Lyapunov指数的预测模型和基于Volterra级数展开的自适应预测模型,集成构建了动态组合预测模型。D-M检验和H-M检验均表明构建的组合预测模型具有较好的市场预测能力,能取得显著优于随机游走模型的预测效果。通过误差性能指标和方向统计量指标分析可知,组合模型较之单独的预测模型均具有较明显的优势。更多还原

【Abstract】 As an important variable in the international financial field, the exchange rate could determine the inner equilibrium and also influence the outer equilibrium of the national economy. With the development of the economic globalization and the acceleration of the international capital’s movement, the exchange rate is becoming more and more important for the investor’s making correct strategies, the enterprise’s risk aversion, and the central bank’s intervention in international exchange market. So, the behavior description and the forecasting’s validity of the exchange rate variable has been becoming one of the most popular topics and focus in the financial research field.The traditional capital market theory has been established on the foundation of three hypotheses: Rational Investors, Efficient Market, and Random Walk. However, such equilibrium analysis system, which belongs to linearity methodology, couldn’t provide reliable explanation of many odds lying in exchange market. Such as the“fat tails”in returns distribution and autocorrelation in time series, the volatility clustering, and the irrelevance problem between the exchange rate and the interrelated economic variables. The intrinsic characteristic of the capital market is not linearity, but nonlinearity. Therefore, the phenomenon that a new research trend comes to being could be taken for granted, which bases the point of nonlinearity and system evolution instead of in a linear and equilibrium view.This paper investigates the intrinsic nonlinear dynamics complex behaviors of five main exchange rates thoroughly, basing on the nonlinearity methodology and the hypothesis of heterogeneous expectations. The empirical sample consists of five daily exchange rates time series, including GBP/USD, CHF/USD, JPY/USD, SEK/USD and CAD/USD. The period covers more than 30 years, from Jan 1st 1975 to May 31st 2007. Finally, empirical researches have revealed that there really existing the nonlinear dependence, the long-memory property, the chaotic dynamic characters, and the multi fractal property.The BDS testing has been applied to detect whether the nonlinearity properties existing in exchange rates time series. Luckily, all of the empirical results refuse the null hypothesis (independent and identically distributed, iid). Besides the discovering of the nonlinearities dependence lying in the time series, the testing has been also put on the sub-sample series and the normalized series, to explore an intrinsic explanation for the existence of nonlinearity. At last, the results revealed that the nonliterary lying in the data may be caused by chaos.In order to detect the Long-Memory property, this paper applies the Rescaled Range Analysis(R/S), the Log Period-gram Estimation(GPH) and the Gaussian Semi parametric Estimation(GSP) on fifteen time series, including daily, weekly and monthly data of five exchange rate time series, by estimating the parameter d and Hurst exponents. The results tell us that there has do exist the Long-Memory property in all of the chosen exchange rates. It can be concluded that there is multi-scale self-similarity structure lying in the exchange rate time series. Therefore, the variable should follow Fractal Brown Movement, not the pure random walk (hypothesizes under the traditional capital market theory).In order to judge the existence of chaotic dynamical features in exchange rate time series, this paper applies the technique of phase space reconstruction and the algorithm of small data sets on the exchange rates. The empirical results show that all of the largest Lyapunov exponentsλ1 are above zero, and all fractal dimensions are no-integer, which suggest the existence of chaos. It not only helps us for knowing the behavior of exchange rates better, but also providing the possibility for short-term forecasting.Multi fractal theory is an important composition of fractal theory. After detecting the long-memory and fractal properties in the exchange rate time series, this paper puts the multi fractal analysis on exchange rates for more details. Firstly, the distribution diagrams of partition function have been applied for diagnosing the existence of multi fractal characteristic. After then, the multi fractal spectra have been used to describe the multi fractal characteristics. The discovery of nonlinear dynamic properties lying in exchange rate time series means that the volatility of the variables should origins from the nonlinear system itself, not only depending on the outer interrupting. Therefore, it’s invalid for the national bank’s forcibly intervention in the exchange market to make the price return equilibrium.Furthermore, after detecting the nonlinear dynamic properties lying in the exchange rate time series, this paper integrates the RBF Neural Network Model, the Lyapunov Exponent Predicting Model and the Volterra Adaptive Predicting Model into an Adjustable Component Predicting Model, in order to make a good predicting of the chaotic variable of exchange rate, and the weights of which could be adjusted by the time series themselves. The results of the empirical research on five exchange rate time series show that both the forecasting errors and the direction statistics of the Component Predicting Model could obtain better results than individual models, especially for the JPY/USD and the SEK/USD time series. Moreover, a compare of the predicting performance has been taken between the Adjustable Component Predicting Model and the Random Walk Model. Luckily, both of the D-M testing and H-M testing refuse the original hypnosis and the empirical results show that the Adjustable Component Predicting Model could obtain obvious advantages over the Random Walk Model as expected.更多还原