Extreme value theory applied to the auroral electrojet indices

The study of extreme weather and space events has gained paramount importance in modern society owing to rapid advances in high technology.Understanding and describing exceptional occurrences plays a crucial role in making decisive assessments of their potential impact on technical,economic,and social aspects in various fields.This research focuses on analyzing the hourly values of the auroral electrojet(AE)geomagnetic index from 1957 to 2019 by using the peak over threshold method in extreme value theory.By fitting the generalized Pareto distribution to extreme AE values,shape parameter indices were derived,revealing negative values that establish an upper bound for this time series.Consequently,it became evident that the AE values had reached a plateau,suggesting that extreme events exceeding the established upper limit are rare.As a result,although the need for diligent precautions to mitigate the consequences of such extreme events persists,surpassing the upper limit of AE values becomes increasingly challenging.It is also possible to observe an aurora in the middle-and low-latitude regions during the maximum period of the AE index.

Estimation of Return Level for Maximum Daily and Hourly Precipitation in Nagano Prefecture, Japan, Using the Extreme Value Theory

The weather in Nagano Prefecture, Japan, can be roughly classified into four types according to principal component analysis and k-means clustering. We predicted the extreme values of the maximum daily and hourly precipitation in Nagano Prefecture using the extreme value theory. For the maximum daily precipitation, the vales of ξ in Matsumoto, Karuizawa, Sugadaira, and Saku were positive;therefore, it has no upper bound and tends to take large values. Therefore, it is dangerous and caution is required. The values of ξ in Nagano, Kisofukushima, and Minamishinano were determined to be zero, therefore, there was no upper limit, the probability of obtaining a large value was low, and caution was required. We predicted the maximum return levels for return periods of 10, 20, 50, and 100 years along with respective 95% confidence intervals in Nagano, Matsumoto, Karuizawa, Sugadaira, Saku, Kisofukushima, and Minamishinano. In Matsumoto, the 100-year return level was 182 mm, with a 95% CI [129, 236]. In Minamishinano, the 100-year return level was 285 mm, with a 95% CI [173, 398]. The 100-year return levels for the maximum daily rainfall were 285, 271, and 271 mm in Minamishinano, Saku, and Karuizawa, respectively, where the changes in the daily maximum rainfall were larger than those at other points. Because these values are large, caution is required during heavy rainfall. The 100-year return levels for the maximum daily and hourly precipitation were similar in Karuizawa and Saku. In Sugadaira, the 100-year return level for a maximum hourly rainfall of 107.2 mm was larger than the maximum daily rainfall. Hence, it is necessary to be careful about short-term rainfall events.

Analyzing of the ENSO Index Using Extreme Value Theory

We predicted the extreme values of the ENSO index, the Niño3.4 index, and the Southern Oscillation Index (SOI) using extreme value theory. Various diagnostic plots for assessing the accuracy of the Generalized Pareto (GP) model fitted to the Niño3.4 index and SOI are shown, and all four diagnostic plots support the fitted GP model. Because the shape parameter of the Niño3.4 was negative, the Niño3.4 index had a finite upper limit. In contrast, that of the SOI was zero, therefore the SOI did not have a finite upper limit, and there is a possibility that a significant risk will occur. 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. The 10-year, and 100-year return levels for Niño3.4 were estimated to be 2.41, and 2.62, with 95% CI [2.22, 2.59], and [2.58, 2.66], respectively. The Niño3.4 index was 2.65 in the 2015/16 super El Niño, which is a phenomenon that occurs once every 500 years. The Niño3.4 index was 2.51 in the 1982/83, and 1997/98 super El Niño, which is a phenomenon that occurs once every 20 years. Recently, a large super El Niño event with a small probability of occurrence has occurred. In response to global warming, the super El Niño events are becoming more likely to occur.

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

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.

Network Traffic Based on GARCH-M Model and Extreme Value Theory

GARCH-M ( generalized autoregressive conditional heteroskedasticity in the mean) model is used to analyse the volatility clustering phenomenon in mobile communication network traffic. Normal distribution, t distribution and generalized Pareto distribution assumptions are adopted re- spectively to simulate the random component in the model. The demonstration of the quantile of network traffic series indicates that common GARCH-M model can partially deal with the "fat tail" problem. However, the "fat tail" characteristic of the random component directly affects the accura- cy of the calculation. Even t distribution is based on the assumption for all the data. On the other hand, extreme value theory, which only concentrates on the tail distribution, can provide more ac- curate result for high quantiles. The best result is obtained based on the generalized Pareto distribu- tion assumption for the random component in the GARCH-M model.

Analysis of Japan and World Records in the 100 m Dash Using Extreme Value Theory

Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distribution. The various diagnostic plots, which assessed the accuracy of the GEV model, were well fitted to the 100 m records in the world and Japan, validating the model. The men’s world record had a shape parameter of -0.250 with a 95% confidence interval of [-0.391, -0.109]. The 100 m record had a finite limit and a calculated upper limit was 9.46 s. The return level estimates for the men’s world record were 9.74, 9.62, and 9.58 s with a 95% confidence interval of [9.69, 9.79], [9.54, 9.69], and [9.48, 9.67] for 10-, 100- and 350-year return periods, respectively. In one year, the probability of occurrence for a new world record of men, 9.58 s (Usain Bolt), was 1/350, while that for women, 10.49 s (Florence Griffith-Joyner), was about 1/100, confirming it was more difficult for men to break records than women.

Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory

One of the most important and interesting issues associated with the earthquakes is the long-term trend of the extreme events. Extreme value theory provides methods for analysis of the most extreme parts of data. We estimated the annual maximum magnitude of earthquakes in Japan by extreme value theory using earthquake data between 1900 and 2019. Generalized extreme value (GEV) distribution was applied to fit the extreme indices. The distribution was used to estimate the probability of extreme values in specified time periods. The various diagnostic plots for assessing the accuracy of the GEV model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model. The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood. Hence, the annual maximum magnitude of earthquakes has a finite upper limit. We obtained the maximum return level for the return periods of 10, 20, 50, 100 and 500 years along with their respective 95% confidence interval. Further, to get a more accurate confidence interval, we estimated the profile log-likelihood. The return level estimate was obtained as 7.83, 8.60 and 8.99, with a 95% confidence interval of [7.67, 8.06], [8.32, 9.21] and [8.61, 10.0] for the 10-, 100- and 500-year return periods, respectively. Hence, the 2011 off the Pacific coast of Tohoku Earthquake, which was the largest in the observation history of Japan, had a magnitude of 9.0, and it was a phenomenon that occurs once every 500 year.

Empirical Analysis of Value-at-Risk Estimation Methods Using Extreme Value Theory

This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.

Estimation of Dynamic VaR in Chinese Stock Markets Based on Time Scale and Extreme Value Theory

The accuracy and time scale invariance of value-at-risk （VaR） measurement methods for different stock indices and at different confidence levels are tested. Extreme value theory （EVT） is applied to model the extreme tail of standardized residual series of daily/weekly indices losses, and parametric and nonparametric methods are used to estimate parameters of the general Pareto distribution （GPD）, and dynamic VaR for indices of three stock markets in China. The accuracy and time scale invariance of risk measurement methods through back-testing approach are also examined. Results show that not all the indices accept time scale invariance; there are some differences in accuracy between different indices at various confidence levels. The most powerful dynamic VaR estimation methods are EVT-GJR-Hill at 97.5% level for weekly loss to Shanghai stock market, and EVT-GARCH-MLE （Hill） at 99.0% level for weekly loss to Taiwan and Hong Kong stock markets, respectively.

Analysis of Network Traffic with Extreme Value Theory

It is very im portant to analyze network traffic in the network control and management. In thi s paper, extreme value theory is first introduced and a model with threshold met hods is proposed to analyze the characteristics of network traffic. In this mode l, only some traffic data that is greater than threshold value is considered. Th en the proposed model with the trace is simulated by using S Plus software. The modeling results show the network traffic model constructed from the extreme va lue theory fits well with that of empirical distribution. Finally, the extreme v alue model with the FARIMA(p,d,q) modeling is compared. The anal ytical results illustrate that extreme value theory has a good application foreg round in the statistic analysis of network traffic. In addition, since only some traffic data which is greater than the threshold is processed, the computation overhead is reduced greatly.

Application of Extreme Value Theory to Generation and Analysis of Pseudorandom Samples

The article deals with the methodology of pseudorandom data analysis. As a mathematical tool for carrying out the research the extreme value theory was used that creates one of the directions in mathematical statistics, and is related to investigating the extreme deviations from the median values in probability distributions. Also, the methods for estimating unknown parameters and algorithm of random-number generation are discussed. The models of treatment the extreme values are constructed which are based on machine generated sample and approach is proposed for their future application for constructing forecasting models.

Ultimate Olympics Records in Athletics Using Extreme Value Theory

Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the ultimate 100 m, 200 m, 400 m, 4 × 100 m relay, and long jump records of male gold medalists at the Olympics. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to all event records, validating the model. The 100 m, 200 m, 400 m, 4 × 100 m, and long jump records had negative shape parameters and calculated upper limits of 9.58 s, 19.18 s, 42.97 s, 36.71 s, and 9.03 m, respectively. The calculated upper limit in the 100 m (9.58 s) was equal to the record of Usain Bolt (August 16, 2009). The 100 m and 200 m world records were close to the calculated upper limits, and achieving the calculated limit was difficult. The 400 m and 4 × 100 m relay world records were almost equal to the calculated upper limits and the 500-year return level estimate, and slight improvement was possible in both. At the Tokyo Olympics in August 2021, in the 100 m, 200 m, and 4 × 100 m, in one year the probability of occurrence for a record was about 1/30. In the 400 m and long jump, it was about 1/20. In the 100 m, 200 m, and 4 × 100 m relay, more difficult records show that a fierce battle has taken place.

An Extreme Value Approach to Test the Effect of Price Limits on Volatility

Many stock exchanges around the world enforcing daily price limits on the amount asset prices can change to prevent the market from overreacting and to reduce volatility. Price limits are artificial boundaries set by market regulators who restrict price changes of a stock to a pre-specified range during a trading day or a single trading session. The primary aim of price limit rules is to stabilize the markets during panic trading, to moderate vitality by repressing excessive speculation, and to allow stocks to be traded at prices close to their fair value. However, their impact on the market is a somewhat unresolved issue （Harris, 1998）. Using a methodology of comparing volatility based on the extreme value technique, the authors empirically investigate the impact of price limits on the volatility of the Stock Exchange of Thailand. The empirical results support price limits advocates, suggesting that price limits rules moderate stock price volatility.

基于GPD理论和百分位数阈值法的轮轨力极值估计与动力系数研究

在高速铁路无砟轨道结构设计和检算时,列车荷载设计值是关键的设计参数之一。基于GPD理论,研究全波段不平顺激励下的轮轨力极值估计方法,并与脉冲激励下的结果对比,为无砟轨道结构设计和相关规范的完善提供依据。结果表明:采用百分位数法选取阈值时,应对样本分簇以提高样本之间的独立性和轮轨力极值估计的精度;提出结合百分位数阈值的形状参数筛选法进行轮轨力极值估计,确定了每簇样本量大小和形状参数区间;样本量宜取3×10^(5)~5×10^(5)个,百分位数阈值宜取50%~98%,且以轮轨力极值估计值的均值作为最终的轮轨力极值估计值;列车速度为250~400 km/h的列车荷载设计值动力系数分别为2.2、2.4、2.6和2.8。

基于极值理论的地基增强系统完好性评估方法

针对地基增强系统(Ground Based Augmentation System,GBAS)完好性风险事件的极端性而导致的无法通过风险事件发生频率评估系统性能的问题,提出一种基于极值理论的GBAS完好性评估方法。根据机载端(位置域)输出的位置误差和保护级计算安全系数,并利用区间极大值模型对安全系数进行建模描述以获得其分布模型;利用极大似然法估计安全系数模型参数,进而利用模型外推法计算GBAS完好性风险值。给出GBAS完好性评估流程,并利用GBAS系统进行了验证实验。研究结果表明:对于C类GBAS进近服务而言,基于全球定位系统(Global Position System,GPS)增强GBAS和基于北斗卫星导航系统(Beidou Navigation Satellite System,BDS)增强GBAS可用性均大于99.9999%;对于F类GBAS进近服务而言,BDS GBAS可用性能要优于GPS GBAS;根据7 d观测数据外推得到的GPS GBAS垂直和侧向完好性风险值分别为4.557×10^(-8)/进近和5.152×10^(-8)/进近,BDS GBAS垂直和侧向完好性风险值分别为1.612×10^(-7)/进近和1.823×10^(-7)/进近,满足航空器终端区I类进近与着陆导航性能需求。

结合未知类特征生成与分类得分修正的SAR目标开集识别方法

现有合成孔径雷达(SAR)目标识别方法大多局限于闭集假定,即认为训练模板库内训练目标类别包含全部待测目标类别,不适用于库内已知类和库外未知新类目标共存的真实开放识别环境。针对训练模板库目标类别非完备情况下的SAR目标识别问题,该文提出一种结合未知类特征生成与分类得分修正的SAR目标开集识别方法。该方法在利用已知类学习原型网络保证已知类识别精度的基础上结合对潜在未知类特征分布的先验认知,生成未知类特征更新网络,进一步保证特征空间中已知类、未知类特征的鉴别性。原型网络更新完成后,所提方法挑选各已知类边界特征,并计算边界特征到各自类原型的距离(极大距离),通过极值理论对各已知类极大距离进行概率拟合确定了各已知类最大分布区域。测试阶段在度量待测样本特征与各已知类原型距离预测闭集分类得分的基础上,计算了各距离在对应已知类极大距离分布上的概率,并修正闭集分类得分,实现了拒判概率的自动确定。基于MSTAR实测数据集的实验结果表明,所提方法能够有效表征真实未知类特征分布并提升网络特征空间已知类与未知类特征的鉴别性,可同时实现对库内已知类目标的准确识别和对库外未知类新目标的准确拒判。

CVaR-EVT和BMM在极端金融风险管理中的应用研究

随着风险度量一致性原则的提出,研究发现金融机构广泛采用的VaR模型存在严重不足,尤其针对分布具有厚尾特征的极端金融风险无法有效度量。本文采用极值理论(EVT)解决VaR方法的尾部度量不足问题,利用CVaR-EVT和BMM模型分析美国、香港股票市场和我国沪深两市指数18年的日收益数据,研究发现:(1)在95%置信区间及点估计中,分位数为99%的CVaR-EVT所揭示的极端风险优于VaR的估计值,且BMM方法为实施长期极端风险管理提供了有力的决策依据,其回报率受分段时区的影响,期间越长,风险估计值越高;(2)模型采用ML和BS方法统计估值显示,我国股票市场极端风险尾部估计值高于香港和美国市场,但是,国内市场逐步稳定,并呈现出跟进国际市场且差距缩小的发展趋势。

极值理论(EVT)在汇率受险价值(VaR)计算中的应用

本文讨论根据极值理论 (EVT)计算金融市场风险重要量度——受险价值 (Va R)的一种新方法 ,给出金融资产组合收益或损失尾部分布的二阶展开式的参数估计形式 ,并以此为基础提出用确定临界值并估计Va R的“两次子样试算法”,最后用 1971- 1998年的日元 /美元汇率 6 70 0多个历史数据验证在极端条件下用EVT估计 Va R具有很高的准确性 .

基于GARCH-EVT-VaR模型的国际主要碳排放交易市场风险度量研究

选取欧洲碳排放权交易系统现货和期货数据,以及芝加哥气候环境交易所的数据,根据在险值理论、条件方差理论以及极值理论,构造GARCH-EVT-VaR模型,度量上述两个市场的正常波动和极端情况下的期望风险。对比两个市场的波动情况、市场效率以及市场风险,本文发现碳排放权交易市场下跌风险更大,并且下跌的信息对于市场的影响更明显。另外,认为强制性交易市场更适合碳排放权交易,且期货交易的引入增大了碳交易市场的不确定性。