Analysis of the USD/JPY and EUR/JPY Exchange Rates Using Multifractal Analysis and Extreme Value Theory  

作　　者：Fumio Maruyama Fumio Maruyama(Department of Sports and Health Science, Matsumoto University, Matsumoto, Japan)

机构地区：[1]Department of Sports and Health Science, Matsumoto University, Matsumoto, Japan

出　　处：《Journal of Applied Mathematics and Physics》2023年第10期2816-2827,共12页应用数学与应用物理（英文）

摘　　要：We performed a multifractal analysis using wavelet transform to detect the changes in the fractality of the USD/JPY and EUR/JPY exchange rates, and predicted their extreme values using extreme value theory. After the 1997 Asian financial crisis, the USD/JPY and EUR/JPY became multifractal, then the USD/JPY became monofractal and stable, and yen depreciation was observed. However, the EUR/JPY became multifractal and unstable, and a strong yen depreciation was observed. The coherence between the USD/JPY and EUR/JPY was strong between 1995 and 2000. After the 2007-2008 financial crisis, the USD/JPY became monofractal and stable, and yen appreciation was observed. However, the EUR/JPY became multifractal and unstable, and strong yen appreciation was observed. Various diagnostic plots for assessing the accuracy of the GP model fitted to USD/JPY and EUR/JPY are shown, and all the diagnostic plots support the fitted GP model. The shape parameters of USD/JPY and EUR/JPY were close to zero, therefore the USD/JPY and EUR/JPY did not have finite upper limits. We predicted the maximum return level for the return periods of 10, 20, 50, 100, 350, and 500 years and their respective 95% confidence intervals (CI). As a result, the 10-year and 100-year return levels for USD/JPY were estimated to be 149.6 and 164.8, with 95% CI [143.2, 156.0] and [149.4, 180.1], respectively.We performed a multifractal analysis using wavelet transform to detect the changes in the fractality of the USD/JPY and EUR/JPY exchange rates, and predicted their extreme values using extreme value theory. After the 1997 Asian financial crisis, the USD/JPY and EUR/JPY became multifractal, then the USD/JPY became monofractal and stable, and yen depreciation was observed. However, the EUR/JPY became multifractal and unstable, and a strong yen depreciation was observed. The coherence between the USD/JPY and EUR/JPY was strong between 1995 and 2000. After the 2007-2008 financial crisis, the USD/JPY became monofractal and stable, and yen appreciation was observed. However, the EUR/JPY became multifractal and unstable, and strong yen appreciation was observed. Various diagnostic plots for assessing the accuracy of the GP model fitted to USD/JPY and EUR/JPY are shown, and all the diagnostic plots support the fitted GP model. The shape parameters of USD/JPY and EUR/JPY were close to zero, therefore the USD/JPY and EUR/JPY did not have finite upper limits. We predicted the maximum return level for the return periods of 10, 20, 50, 100, 350, and 500 years and their respective 95% confidence intervals (CI). As a result, the 10-year and 100-year return levels for USD/JPY were estimated to be 149.6 and 164.8, with 95% CI [143.2, 156.0] and [149.4, 180.1], respectively.

关 键 词：WAVELET MULTIFRACTAL Extreme Value Theory GP USD/JPY and EUR/JPY Ex-change Rates 

分 类 号：P64[天文地球—地质矿产勘探]