scholarly journals Chinese Sunspot Drawings and Their Digitizations-(VI) Extreme Value Theory Applied to the Sunspot Number Series from the Purple Mountain Observatory

Atmosphere ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1176
Author(s):  
Yan-Qing Chen ◽  
Sheng Zheng ◽  
Yan-Shan Xiao ◽  
Shu-Guang Zeng ◽  
Tuan-Hui Zhou ◽  
...  
Keyword(s):  
Sunspot Number ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Threshold Value ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Block Maxima ◽  
First Time

Based on the daily sunspot number (SN) data (1954–2011) from the Purple Mountain Observatory, the extreme value theory (EVT) is employed for the research of the long-term solar activity. It is the first time that the EVT is applied on the Chinese SN. Two methods are used for the research of the extreme events with EVT. One method is the block maxima (BM) approach, which picks the maximum SN value of each block. Another one is the peaks-over-threshold (POT) approach. After a declustering process, a threshold value (here it is 300) is set to pick the extreme values. The negative shape parameters are obtained by the two methods, respectively, indicating that there is an upper bound for the extreme SN value. Only one value of the N-year return level (RL) is estimated: N = 19 years. For N = 19 years, the RL values of SN obtained by two methods are similar with each other. The RL values are found to be 420 for the POT method and the BM method. Here, the trend of 25th solar cycle is predicted to be stronger, indicating that the length of meridional forms of atmospheric circulation will be increased.

scholarly journals Return Levels Approach and Periods of Currency Crises

2018 ◽  
Vol 10 (3) ◽  
pp. 77
Author(s):  
Mouridi HAMIDOU ◽  
Joseph Mung'atu ◽  
George Orwa
Keyword(s):  
Currency Crises ◽  
Currency Crisis ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Sample Mean ◽  
New Approach ◽  
Gev Distribution ◽  
Return Levels ◽  
Block Maxima

Dating and observing currency crisis periods lie at the heart of much international researchers. This is due to the lack of agreement in one research methodology. Until today, there does not exist a single theory or specific international policy regulation that can explain this phenomenon in global. To identify the periods of currency crisis, many methods have been brought out. Literature first employed a combination of sample mean and standard deviation. Some recent studies have attempted to use extreme value theory (EVT). Although these procedures have been more criticized in most of the literature. These drawbacks of existing approaches give rise to a new approach which is the main goal of this research. The main purpose of this study is to employ return levels technique to date currency crisis periods. The study will discuss only one method the block maxima approach. The stress losses i.e the generalized extreme value (GEV) distribution will be fitted to the annual block maxima to estimate the T-year return levels of extreme exchange market pressure index (EMPI). The parameters of the GEV distribution are estimated using the ML estimator method. Beside, a detailed procedure of the new approach is implemented. A comparison study between our identification approach and the existing conventional approach in the most literature is also conducted. We further illustrate the method by an empirical study on identifying periods of currency crisis of Kenya as case study. For practical implement the study focuses only on one single currency crisis model known as the alternative EMP index model for the intent of arbitrating the performance among various techniques. Results suggest that our new approach (RLDT) is performing better than the conventional method when the return period is considered big. Nonetheless, our technique appears to dominate the existing conventional approaches. This paper covers only a small area of this growing field of research. Hopefully, our investigations to contribute to these efforts by showing that return level dating technique derived from stress-losses model may have a place in the toolbox of economists looking for more accurate techniques in predicting currency crises.

scholarly journals Analysing extreme value theory efficiency in probabilistic wcet estimation with block maxima

2021 ◽  
pp. 131-154
Author(s):  
Guilherme Isaias Debom Machado ◽  
Fabian Luis Vargas ◽  
Celso Maciel da Costa
Keyword(s):  
Extreme Value Theory ◽  
Execution Time ◽  
Value Theory ◽  
Extreme Value ◽  
System Delay ◽  
Worst Case ◽  
Worst Case Execution Time ◽  
Real Behavior ◽  
Block Maxima ◽  
Time Systems

The execution time is a requirement as much important as the computed result when designing real-time systems for critical applications. It is imperative to know the possible execution times, especially when some system delay may incur in equipment damages or even in crew injuries. With that in mind, the current work analyzes different techniques to define the Probabilistic Worst Case Execution Time (pWCET) using the Extreme Value Theory (EVT). Since probabilistic methodologies have been widely explored, this study aims to assure how accurate the pWCET estimations are when applying EVT knowledge. This analysis aims to compare system pWCET estimations to this real behavior, predicting the upper bound execution limits of two algorithms on MIPS processor. Further, this work regards the Block Maxima technique, which select the highest measured values to define a probabilistic distribution that represents the analyzed system. Based on the outcomes the Block Maxima technique points some limitations as requiring a large number of samples to get a reliable analysis. The obtained results have shown that EVT is a useful and trustworthy technique to define pWCET estimations.

scholarly journals Risk Analysis of Gold Prices in Pakistan Using Extreme Value Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ghulam Raza Khan ◽  
Alanazi Talal Abdulrahman ◽  
Osama Alamri ◽  
Zahid Iqbal ◽  
Maqsood Ahmad
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Risk Measures ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Extreme Stress ◽  
Daily Data ◽  
Peak Over Threshold ◽  
The Impact

Extreme value theory (EVT) is useful for modeling the impact of crashes or situations of extreme stress on investor portfolios. EVT is mostly utilized in financial modeling, risk management, insurance, and hydrology. The price of gold fluctuates considerably over time, and this introduces a risk on its own. The goal of this study is to analyze the risk of gold investment by applying the EVT to historical daily data for extreme daily losses and gains in the price of gold. We used daily gold prices in the Pakistan Bullion Market from August 1, 2011 to July 30, 2021. This paper covers two methods such as Block Maxima (BM) and Peak Over Threshold (POT) modeling. The risk measures which are adopted in this paper are Value at Risk (VaR) and Expected Shortfall (ES). The point and interval estimates of VaR and ES are obtained by fitting the Generalized Pareto (GPA) distribution. Moreover, in this paper, return-level forecasting is also included for the next 5 and 10 years by analyzing the Generalized Extreme Value (GEV) distribution.

scholarly journals Extreme value theory in emerging markets: Evidence from the Montenegrin stock exchange

2015 ◽  
Vol 60 (206) ◽  
pp. 87-116 ◽  
Author(s):  
Julija Cerovic ◽  
Vesna Karadzic
Keyword(s):  
At Risk ◽  
Stock Market ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Emerging Market ◽  
Value Theory ◽  
Extreme Value ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

The concept of Value at Risk(VaR) estimates the maximum loss of a financial position at a given time for a given probability. This paper considers the adequacy of the methods that are the basis of extreme value theory in the Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether the peaks-over-threshold method outperforms the block maxima method in evaluation of Value at Risk in emerging stock markets such as the Montenegrin market. The daily return of the Montenegrin stock market index MONEX20 is analyzed for the period January 2004 - February 2014. Results of the Kupiec test show that the peaks-over-threshold method is significantly better than the block maxima method, but both methods fail to pass the Christoffersen independence test and joint test due to the lack of accuracy in exception clustering when measuring Value at Risk. Although better, the peaks-over-threshold method still cannot be treated as an accurate VaR model for the Montenegrin frontier stock market.

A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

2007 ◽  
Vol 10 (06) ◽  
pp. 1043-1075 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Value Theory ◽  
Extreme Value ◽  
Expected Shortfall ◽  
Stable Laws ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Frequentist and Bayesian extreme value analysis on the wildfire events in Greece

2020 ◽  
Author(s):  
Nikos Koutsias ◽  
Frank A. Coutelieris
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Burned Area ◽  
Accurate Assessment ◽  
Peaks Over Threshold ◽  
Bayesian Approaches ◽  
Value Analysis

<p>A statistical analysis on the wildfire events, that have taken place in Greece during the period 1985-2007, for the assessment of the extremes has been performed. The total burned area of each fire was considered here as a key variable to express the significance of a given event. The data have been analyzed through the extreme value theory, which has been in general proved a powerful tool for the accurate assessment of the return period of extreme events. Both frequentist and Bayesian approaches have been used for comparison and evaluation purposes. Precisely, the Generalized Extreme Value (GEV) distribution along with Peaks over Threshold (POT) have been compared with the Bayesian Extreme Value modelling. Furthermore, the correlation of the burned area with the potential extreme values for other key parameters (e.g. wind, temperature, humidity, etc.) has been also investigated.</p>

scholarly journals Has fire policy decreased the return period of the largest wildfire events in France? A Bayesian assessment based on extreme value theory

2018 ◽  
Vol 18 (10) ◽  
pp. 2641-2651 ◽  
Author(s):  
Guillaume Evin ◽  
Thomas Curt ◽  
Nicolas Eckert
Keyword(s):  
Return Period ◽  
Extreme Value Theory ◽  
Fire Suppression ◽  
Value Theory ◽  
Extreme Value ◽  
Ecological Impacts ◽  
Return Level ◽  
Burned Area ◽  
Return Periods ◽  
Fire Policy

Abstract. Very large wildfires have high human, economic, and ecological impacts so that robust evaluation of their return period is crucial. Preventing such events is a major objective of the new fire policy set up in France in 1994, which is oriented towards fast and massive fire suppression. Whereas this policy is probably efficient for reducing the mean burned area (BA), its effect on the largest fires is still unknown. In this study, we make use of statistical extreme value theory (EVT) to compute return periods of very large BAs in southern France, for two distinct periods (1973 to 1994 and 1995 to 2016) and for three pyroclimatic regions characterized by specific fire activities. Bayesian inference and related predictive simulations are used to fairly evaluate related uncertainties. Results demonstrate that the BA corresponding to a return period of 5 years has actually significantly decreased, but that this is not the case for large return periods (e.g., 50 years). For example, in the most fire-prone region, which includes Corsica and Provence, the median 5-year return level decreased from 5000 to 2400 ha, while the median 50-year return level decreased only from 17 800 to 12 500 ha. This finding is coherent with the recent occurrence of conflagrations of large and intense fires clearly far beyond the suppression capacity of firemen. These fires may belong to a new generation of fires promoted by long-term fuel accumulation, urbanization into the wildland, and ongoing climate change. These findings may help adapt the operational system of fire prevention and suppression to ongoing changes. Also, the proposed methodology may be useful for other case studies worldwide.

Extreme values of non-stationary random sequences

1986 ◽  
Vol 23 (04) ◽  
pp. 937-950 ◽  
Author(s):  
Jürg Hüsler
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extremal Index ◽  
Stationary Case ◽  
Random Sequences ◽  
Similar Role ◽  
High Level

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.

scholarly journals Extreme Value Theory and Large Fire Losses

1974 ◽  
Vol 7 (3) ◽  
pp. 293-310 ◽  
Author(s):  
G. Ramachandran
Keyword(s):  
Statistical Theory ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Large Fire ◽  
Fire Insurance ◽  
Reinsurance Treaty

The statistical theory of extreme values well described by Gumbel [1] has been fruitfully applied in many fields, but only in recent times has it been suggested in connection with fire insurance problems. The idea originally stemmed from a consideration of the ECOMOR reinsurance treaty proposed by Thepaut [2]. Thereafter, a few papers appeared investigating the usefulness of the theory in the calculation of an excess of loss premium. Among these, Beard [3, 4], d'Hooge [5] and Jung [6] have made contributions which are worth studying. They have considered, however, only the largest claims during a succession of periods. In this paper, generalized techniques are presented which enable use to be made of all large losses that are available for analysis and not merely the largest. These methods would be particularly useful in situations where data are available only for large losses.

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