基于分形理论的人民币外汇市场实证研究
发布时间：2018-08-07 20:11
【摘要】：目前对外汇市场的分析研究主要基于有效市场假说和分形市场假说的理论。有效市场理论能够对外汇市场的有效性进行很好的检验,但是并不能很好的描述外汇市场时间序列的分布特征。分形市场理论能够更加系统科学地描述和刻画外汇市场时间序列的波动,分形市场理论是对传统有效市场理论的进一步拓展,并对传统有效市场理论中一些无法解释的行为和现象进行了深入的阐释。 趋势消解分析法DFA可以有效测定外汇时间序列是否遵循布朗运动。本文利用DFA单分形分析法对基于汇改前后的人民币外汇市场进行测定,发现人民币对美元,日元,欧元,港币之间的Hurst指数均不符合一般随机游走过程理论值0.5,中国外汇市场存在较为明显的分形特征。另外,实证研究表明2005年汇率改革对中国外汇市场存在一定程度的影响,表现为汇改前后Hurst指数的显著波动,外汇市场的有效性得到一定程度的提高。 单分形理论只能描述时间序列波动的宏观面貌,存在一定的缺陷性。多重分形理论能够更好地对外汇市场的局部结构特征进行更加细致的分析。本文采用基于滑动窗口的多重分形趋势消除分析法(MFDFA)研究中国外汇市场汇率中间价时间序列的多重分形特征,发现人民币汇率时间序列的广义Hurst指数h(q)均随着q的增大而减少,同时我们利用滑动窗口MFDFA计算出的h(q)值比传统MFDFA普遍都要大,且随q的值增大更快的趋向稳定值,能够更好地刻画外汇市场价格波动的持久性特征。我们对人民币外汇市场的多重分形特征进行谱分析和成因分析,可以发现汇率的多重分形谱均为单峰钟形图像,而多重分形特征是由序列的长期相关与胖尾概率分布共同作用形成,重排和替代序列的多重分形谱宽度要显著小于原始序列,而对序列进行极端值剔除,进行EV重排之后,其多重分形特征最弱,接近于一般随机游走过程。 对外汇市场时间序列进行单分形和多重分形分析,我们能够更好地理解中国外汇市场人民币汇率交易活动之间的一些内在关系,这对于我们深入研究和解释实际的汇率交易活动具有相当重要的现实意义。
[Abstract]:At present, the analysis of foreign exchange market is mainly based on the efficient market hypothesis and fractal market hypothesis. The efficient market theory can well test the effectiveness of foreign exchange market, but it can not describe the distribution characteristics of foreign exchange market time series. Fractal market theory can describe and depict the fluctuation of foreign exchange market time series more systematically and scientifically. Fractal market theory is a further development of traditional efficient market theory. And some inexplicable behaviors and phenomena in traditional efficient market theory are explained in depth. Trend resolution analysis (DFA) can effectively determine whether foreign exchange time series follow the Brownian motion. This paper uses the DFA single fractal analysis method to measure the RMB foreign exchange market before and after the exchange rate reform, and finds that the RMB is relative to the US dollar, Japanese yen, and the euro. The Hurst index between Hong Kong dollars does not accord with the theoretical value of the general random walk process. There are obvious fractal characteristics in the foreign exchange market of China. In addition, the empirical study shows that the exchange rate reform in 2005 has a certain degree of influence on China's foreign exchange market, which shows that the Hurst index fluctuates significantly before and after the exchange rate reform, and the effectiveness of the foreign exchange market is improved to a certain extent. Single fractal theory can only describe the macroscopic appearance of time series fluctuation, and it has some defects. Multifractal theory can better analyze the local structure of foreign exchange market. In this paper, the multifractal trend elimination method based on sliding window is used to study the multifractal characteristics of the intermediate price time series in China's foreign exchange market. It is found that the generalized Hurst index h (q) of the RMB exchange rate time series decreases with the increase of Q. At the same time, the value of h (q) calculated by sliding window MFDFA is larger than that of traditional MFDFA, and tends to be stable faster with the increase of Q value, which can better depict the persistent characteristics of foreign exchange market price fluctuation. We analyze the multifractal characteristics of the RMB foreign exchange market by spectrum analysis and cause analysis. We can find that the multifractal spectrum of the exchange rate is a single-peak bell image. The multifractal feature is formed by the long-term correlation of the sequence and the fat-tailed probability distribution. The multifractal spectrum width of the rearrangement and replacement sequence is significantly smaller than that of the original sequence, but the extreme value of the sequence is eliminated and the EV rearrangement is carried out. Its multifractal feature is the weakest, which is close to the general random walk process. By using single-fractal and multifractal analysis of the time series of foreign exchange market, we can better understand the internal relationship between RMB exchange rate trading activities in China's foreign exchange market. This is of great practical significance for us to study and explain the actual exchange rate trading activities.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.6;F224
本文编号：2171219
[Abstract]:At present, the analysis of foreign exchange market is mainly based on the efficient market hypothesis and fractal market hypothesis. The efficient market theory can well test the effectiveness of foreign exchange market, but it can not describe the distribution characteristics of foreign exchange market time series. Fractal market theory can describe and depict the fluctuation of foreign exchange market time series more systematically and scientifically. Fractal market theory is a further development of traditional efficient market theory. And some inexplicable behaviors and phenomena in traditional efficient market theory are explained in depth. Trend resolution analysis (DFA) can effectively determine whether foreign exchange time series follow the Brownian motion. This paper uses the DFA single fractal analysis method to measure the RMB foreign exchange market before and after the exchange rate reform, and finds that the RMB is relative to the US dollar, Japanese yen, and the euro. The Hurst index between Hong Kong dollars does not accord with the theoretical value of the general random walk process. There are obvious fractal characteristics in the foreign exchange market of China. In addition, the empirical study shows that the exchange rate reform in 2005 has a certain degree of influence on China's foreign exchange market, which shows that the Hurst index fluctuates significantly before and after the exchange rate reform, and the effectiveness of the foreign exchange market is improved to a certain extent. Single fractal theory can only describe the macroscopic appearance of time series fluctuation, and it has some defects. Multifractal theory can better analyze the local structure of foreign exchange market. In this paper, the multifractal trend elimination method based on sliding window is used to study the multifractal characteristics of the intermediate price time series in China's foreign exchange market. It is found that the generalized Hurst index h (q) of the RMB exchange rate time series decreases with the increase of Q. At the same time, the value of h (q) calculated by sliding window MFDFA is larger than that of traditional MFDFA, and tends to be stable faster with the increase of Q value, which can better depict the persistent characteristics of foreign exchange market price fluctuation. We analyze the multifractal characteristics of the RMB foreign exchange market by spectrum analysis and cause analysis. We can find that the multifractal spectrum of the exchange rate is a single-peak bell image. The multifractal feature is formed by the long-term correlation of the sequence and the fat-tailed probability distribution. The multifractal spectrum width of the rearrangement and replacement sequence is significantly smaller than that of the original sequence, but the extreme value of the sequence is eliminated and the EV rearrangement is carried out. Its multifractal feature is the weakest, which is close to the general random walk process. By using single-fractal and multifractal analysis of the time series of foreign exchange market, we can better understand the internal relationship between RMB exchange rate trading activities in China's foreign exchange market. This is of great practical significance for us to study and explain the actual exchange rate trading activities.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.6;F224
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