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.

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.

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.

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.

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.

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.

Using Extreme Value Theory to Assess the Mortality Risk of Tornado Outbreaks

The majority of tornado fatalities occur during severe thunderstorm occurrences that produce a large number of tornadoes,termed tornado outbreaks.This study used extreme value theory to estimate the impact of tornado outbreaks on fatalities while accounting for climate and demographic factors.The findings indicate that the number of fatalities increases with the increase of tornado outbreaks.Additionally,this study undertook a counterfactual analysis to determine what would have been the probability of a tornado outbreak under various climatic and demographic scenarios.The results of the counterfactual study indicate that the likelihood of increased mortality increases as the population forecast grows.Intensified El Niño events,on the other hand,reduce the likelihood of further fatalities.La Niña events are expected to increase probability of fatalities.

Statistical Modeling and Trend Detection of Extreme Sea Level Records in the Pearl River Estuary

Sea level rise has become an important issue in global climate change studies. This study investigates trends in sea level records, particularly extreme records, in the Pearl River Estuary, using measurements from two tide gauge stations in Macao and Hong Kong. Extremes in the original sea level records （daily higher high water heights） and in tidal residuals with and without the 18.6-year nodal modulation are investigated separately. Thresholds for defining extreme sea levels are calibrated based on extreme value theory. Extreme events are then modeled by peaks-over-threshold models. The model applied to extremes in original sea level records does not include modeling of their durations, while a geometric distribution is added to model the duration of extremes in tidal residuals. Realistic modeling results are recommended in all stationary models. Parametric trends of extreme sea level records are then introduced to nonstationary models through a generalized linear model framework. The result shows that, in recent decades, since the 1960s, no significant trends can be found in any type of extreme at any station, which may be related to a reduction in the influence of tropical cyclones in the region. For the longer-term record since the 1920s at Macao, a regime shift of tidal amplitudes around the 1970s may partially explain the diverse trend of extremes in original sea level records and tidal residuals.

Modeling Cyber Loss Severity Using a Spliced Regression Distribution with Mixture Components

Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.

On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures

This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations.The paper starts briefly reviewing classical univariate/multivariate extreme value theory,tail equivalence,and tail(in)dependence.New extreme value theory for heterogeneous populations is then introduced.Time series models for maxima and extreme observations are the focus of the review.These models naturally form a new system with similar structures.They can be used as alternatives to the widely used ARMA models and GARCH models.Applications of these time series models can be in many fields.The paper discusses two important applications:systematic risks and extreme co-movements/large scale contagions.

An Analysis of the Maximum Lifespan in the World and Japan

Extreme value theory provides methods to analyze the most extreme parts of data. We used the generalized extreme value (GEV) distribution to predict the human lifespan in the world and Japan. The diagnostic plots, which assessed the accuracy of the GEV model, were fitted to the human lifespan, validating the model. The human lifespan in the world and Japan had shape parameters of ?0.1623 and ?0.2949 and had an upper limit. The calculated upper limit in the world was 128.7 years. The world’s oldest record holder, Jeanne Calment’s age of 122.45 years, was close to the 260-year return level and was far from the calculated upper limit. The calculated upper limit in Japan was 120.4 years. Japan’s oldest record holder, Kane Tanaka’s age of 119 years in 2022, was the 500-year return level and was close to the upper limit. In the world, achieving the calculated limit was difficult, but the human lifespan will soon reach the upper limit in Japan.

Extreme Risk Measurement of Carbon Market Considering Multifractal Characteristics

Influenced by the global economy,politics,energy and other factors,the price of carbon market fluctuates sharply.It is of great practical significance to explore a suitable measurement method of extreme risk of carbon market.Considering that the return series of carbon market has the characteristics of leptokurtosis,fat tail,skewness and multifractal,and there maybe many extreme risk values in the carbon market,this paper introduces the Skewed-t distribution which can describe the characteristics of leptokurtosis,fat tail and skewness of return series into MSM model which can describe multifractal characteristic of return series to model volatility of carbon market.On the basis,based on the extreme value theory,this paper constructs Skewed-t-MSM-EVT model to measure extreme risk of carbon market.This paper chooses EUA market as the object to study extreme risk of carbon market,and draws the following conclusions:Skewed-t-MSM-EVT model has significantly higher prediction accuracy for carbon market's Va R than MSM-EVT models under other distributions(including normal distribution,t distribution,GED distribution);Skewed-t-MSM-EVT model is superior to traditional Skewed-t-FIGARCH-EVT and Skewed-t-GARCH-EVT models in predicting carbon market's Va R.This research has important practical significance for accurately grasping the risk of carbon market and promoting energy conservation and emission reduction.

Statistical Modeling of CMIP5 Projected Changes in Extreme Wet Spells over China in the Late 21st Century

The observed intensity, frequency, and duration（IFD） of summer wet spells, defined here as extreme events with one or more consecutive days in which daily precipitation exceeds a given threshold（the 95th percentile）, and their future changes in RCP4.5 and RCP8.5 in the late 21st century over China, are investigated by using the wet spell model（WSM） and by extending the point process approach to extreme value analysis. Wet spell intensity is modeled by a conditional generalized Pareto distribution, frequency by a Poisson distribution, and duration by a geometric distribution, respectively. The WSM is able to realistically model summer extreme rainfall spells during 1961–2005, as verified with observations at 553 stations throughout China. To minimize the impact of systematic biases over China in the global climate models（GCMs） of the Coupled Model Intercomparison Project Phase 5（CMIP5）, five best GCMs are selected based on their performance to reproduce observed wet spell IFD and average precipitation during the historical period. Furthermore, a quantile–quantile scaling correction procedure is proposed and applied to produce ensemble projections of wet spell IFD and corresponding probability distributions. The results show that in the late 21st century, most of China will experience more extreme rainfall and less low-intensity rainfall. The intensity and frequency of wet spells are projected to increase considerably, while the duration of wet spells will increase but to a much less extent. The IFD changes in RCP8.5 are in general much larger than those in RCP4.5.

Multivariate extremes and max-stable processes:discussion of the paper by Zhengjun Zhang

This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.

Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.

Extreme vocabulary learning

Regarding extreme value theory,the unseen novelclasses in the openset recognition can be seen as the extremevalues of training classes.Following this idea,we introducethe margin and coverage distribution to model the trainingclasses.A novel visual-semantic embedding framework-extreme vocabulary learning(EVoL)is proposed;the EVoL embeds the visual features into semantic space in a probabilisticway.Notably,we adopt the vast open vocabulary in the semantic space to help further constraint the margin and coverage of training classes.The learned embedding can directlybe used to solve supervised learning,zero-shot learning,andopen set recognition simultaneously.Experiments on twobenchmark datasets demonstrate the effectiveness of the proposed framework against conventional ways.

Quantitative assessment and visualization of flight risk induced by coupled multi-factor under icing conditions

Aircraft icing has been proven to be one of the most serious threats to flight safety. During the analysis of flight risk under icing conditions, quantitative assessment and visualization of flight risk are quite essential as they provide safe manipulation strategies in intricate conditions.However, they are rarely studied. Since the icing flight accidents are the result of the coupling of multiple unfavorable factors, in present study, we have proposed a method to quantitatively assess flight risk induced by multi-factor coupling under icing conditions by Monte-Carlo simulation and multivariate extreme value theory. The results demonstrate that the flight risk probability increases with the rise of unfavorable factors. Besides, a flight risk visualization method named flight safety window has been presented to build the flight risk distribution cloud maps in different complex conditions. The cloud maps show that the icing would give rise to atrophy of the safety scope, and the consequence would be even more severe when coupled with other more unfavorable factors. The proposed methods in this study would be useful in flight risk analysis under icing conditions and can enhance the pilot's situational awareness in selecting correct strategies within the safety zone to avoid unsafe manipulation.

MODELING JUMPS IN RETURNS OF FINANCIAL ASSETS AS M4 PROCESSES: MEASURED EXCHANGE RATE EXPOSURE OF ASIAN EQUITY PORTFOLIO

Previous work on the exposure of equity markets to exchange rate risk, surprisingly, found stock returns were not significantly affected by exchange rate fluctuations. In this paper, we examine the relation between China, Japan and USA MSCI （Morgan ＆ Stanley Capital International） daily equity index returns and SAFE （State Administration of Foreign Exchange） exchange rate returns of Chinese RMB and Japanese Yen in US dollar. We find a significant relation between Asian foreign equity stock retums and Chinese RMB and Japanese Yen exchange rate retums. This article incorporates foreign exchange values as partial determinants of Asian foreign equity market returns and suggests that currency risk is of hedging concern to investors with implications for portfolio management. We implement our result in portfolio＇s CaR determination under VaR constraints.