基于多重分形的中国外汇市场效率分析  

Analysis of Chinese Exchange Market Efficiency Based on Multifractal

作　　者：杨雷鑫 王海英 顾长贵 

机构地区：[1]上海理工大学管理学院,上海

出　　处：《应用数学进展》2023年第4期1549-1566,共18页Advances in Applied Mathematics

摘　　要：探究外汇市场效率变动演化规律对于提高汇率市场的韧性具有指导意义。本文选择欧元、英镑、日元和美元兑人民币四种外汇货币汇率序列构建滑动窗口,利用多重分形去趋势波动分析法(MFDFA)和多重分形去趋势互相关分析法(MFDCCA)先后进行计算分析,发现中国外汇市场在疫情和俄乌冲突(以下简称阶段I、阶段II)突然发生时均存在显著的多重分形现象。欧元市场的多重分形程度在阶段I先增后减,但在阶段II整体降低;英镑市场的多重分形特征在两个阶段的表现相反,而日元在阶段II的多重分形水平整体较阶段I差别最大,美元市场在不同窗口下多重分形程度持续波动。两个阶段下四个市场间的幂律交叉关系一直保持多重分形的特征,阶段I汇率间存在不断增长的正向长期幂律关系,但在阶段II这种正向幂律关系不再那么稳定。最后本文为汇率市场出现多重分形的原因做出了解释,即序列波动的肥尾分布特性是主要影响源。总体研究结果为外汇市场调控提供理论指导以提高外汇市场效率。Exploring dynamic evolution law of foreign exchange market efficiency has guiding significance for improving the resilience of the exchange rate market. In this paper, four exchange rate series of foreign currencies, including the EUR, GBP, 100JPY and USD against RMB, are selected to construct sliding windows, and Multifractal Detrended Fluctuation Analysis (MFDFA) and Multifractal Detrend Cross Correlation Analysis (MFDCCA) are used to calculate and analyze. We generally find that sig-nificant multifractal phenomena existed in the four markets when the epidemic and the Rus-sia-Ukraine conflict (hereinafter referred to as period I and period II) suddenly occurred. Specifi-cally, the multifractal degree of the EUR shows increase pattern during period I then decreases with time, but decreases overall period II. The performance of the GBP is opposite in the two stages, while the overall multifractal level of the 100JPY decreases the most in period II compared with the period I. The multifractal degree of the USD continuously fluctuates under different windows. The power-law cross relationships among the four markets always have multifractal property during period I and the period II. And there is a growing positive long-term power law relationship be-tween the exchange rates in stage I, but this kind of relationship is no longer so stable in stage II. Finally, this paper explains the reasons for the emergence of multifractality in the exchange rate market, in which the fat tail distribution characteristics of series fluctuations are the main source. The above research results may provide theoretical guidance for the regulation of the foreign ex-change market to improve the efficiency of the foreign exchange market.

关 键 词：外汇汇率 滑动窗口 多重分形 长期幂律关系 

分 类 号：F83[经济管理—金融学]