Extreme Value Theory Methods Research Articles

Forecasting VaRs via hybrid EVT with normal and non-normal filters: A comparative analysis from the Chinese stock market

This paper studies the performance of hybrid methods combining normal and non-normal GARCH-type filters with extreme value theory (EVT) in predicting Value-at-Risk (VaR) for four major stock indices in the Chinese stock market. Based on the out-of-sample VaR forecasts results over the 24 models considered, we find that the hybrid EVT approaches illustrate substantial advantage over the corresponding GARCH-type models with parametric distributions, especially in the lower tail and extremal VaR evaluations (1% and 0.5% VaRs). Overall, the hybrid EVT methods with heavy-tailed filters (std-EVT, sstd-EVT) perform the best, followed by the hybrid EVT approaches with light-tailed filters (norm-EVT, snorm-EVT), and then the GARCH-type models with skewed student-t distribution. The conditional normal, skewed normal and student-t models are rejected and excluded from the Model Confidence Set (MCS) in predicting extremal VaRs for most cases, particularly for the lower tail. Additionally, we find that the results for alternative models in predicting VaRs vary sharply among alternative innovation specifications, but present trivial differences across the volatility models. Furthermore, our results based on the MCS tests and comparative backtests also indicate that the scoring function effectively discriminates predictive performance across methods for the lower tail, in contrast to showing less disparity for the upper tail. This emphasizes the importance of model selection in VaR forecasting performance for the lower tail. The above findings are robust to alternative threshold selections and the rolling-step chosen to update parameters. Similar analyses concerning the out-of-sample performance of the 24 models in predicting the Expected Shortfall (ES) show consistent results overall.

RD-OpenMax: Rethinking OpenMax for Robust Realistic Open-Set Recognition.

Open-set recognition (OSR) toward a practical open-world setting has attracted increasing research attention in recent years. However, existing OSR settings are either too idealized or focus on specific scenes such as long-tailed distribution and few-shot samples, which fail to capture the complexity of real-world scenarios. In this article, we propose a realistic OSR (ROSR) setting that covers a diverse range of challenging and real-world scenarios, including fine-grained cases with strong semantic correlation and a large number of species, few-shot samples, long-tailed sample distribution, dynamic inputs (e.g., images, spatio-temporal, and multimodal signals) and cross-domain adaptation. In particular, we rethink the simple and basic OpenMax for the ROSR setting and introduce a novel method, regularized discriminative OpenMax (RD-OpenMax), to handle the challenges in the ROSR setting. RD-OpenMax improves upon the basic OpenMax approach by introducing a covariance attention-based covariance pooling (CACP) module as a global aggregation step before the deep architecture's classifier. This module explores rich statistical information on features and provides discriminative distance scores for OpenMax. To address the instability of extreme value theory (EVT) estimation due to insufficient training samples under few-shot and long-tailed scenarios, we propose a regularized EVT (REVT) method based on Monte Carlo sampling to recalibrate the distribution of distance scores. As such, our RD-OpenMax performs a REVT model of distance scores generated by discriminative CACP representations to distinguish known classes and recognize unknown ones effectively and robustly. Extensive experiments are conducted on more than ten visual benchmarks across several scenarios, and the empirical comparisons show that the ROSR setting challenges existing state-of-the-art OSR approaches. Moreover, our RD-OpenMax clearly outperforms its counterparts under the ROSR setting while performing favorably against state-of-the-arts under the traditional OSR setting.

Estimation of the Probability of Earthquakes Return Period in Zimbabwe Using Gumbel’s Extreme Value Theory Method

Using Gumbel's extreme value theory method, this study looked into the probability of the largest earthquakes for different return periods in Zimbabwe. The Advanced National Seismic System (ANSS), the Northern California Earthquake Data Centre website, and UC Berkeley in the United States provided the data used for this study. The natural earthquakes with Mb ≥ 4.0 that occurred in the study area between January 1, 1901 and December 31, 2001 (a period of 100 years) with a focal depth ranging from 0 to 700 km made up the selected data. The study area is between 150S - 220S and 250E -340E in coordinates. A total of 81 events were used in the investigation. According to the results, there is a 100% chance that earthquakes with a magnitude between 4.5 and 5.5 will occur during the time interval of approximately 1 to 14 years and a 9.5% chance that within the next 100 years, there will be an earthquake with a magnitude of Mb = 6.0 or higher. For magnitudes Mb = 6.0 and above, the return period is relatively long - roughly 50 – 701 years. This suggests that there is little chance that Zimbabwe will experience earthquakes larger than magnitude 6.0. Despite being low, it is impossible to forecast with certainty because earthquake forecasting and prediction is still a complex topic.

Extreme Value Theory Modelling of the Behaviour of Johannesburg Stock Exchange Financial Market Data

Financial market data are abundant with outliers, and the search for an appropriate extreme value theory (EVT) approach to apply is an endless debate in the statistics of extremes research. This paper uses EVT methods to model the five-year daily all-share total return index (ALSTRI) and the daily United States dollar (USD) against the South African rand (ZAR) exchange rate of the Johannesburg stock exchange (JSE). The study compares the block maxima approach and the peaks-over-threshold (POT) approach in terms of their ability to model financial market data. The 100-year return levels for the block maxima approach were found to be almost equal to the maximum observations of the financial markets of 10,860 and R18.99 for the ALSTRI and the USD–ZAR, respectively. For the peaks-over-threshold (POT) approach, the results show that the ALSTRI and the USD–ZAR exchange rate will surpass 17,501.63 and R23.72, respectively, at least once in 100 years. The findings in this study reveal a clear distinction between block maxima and POT return level estimates. The POT approach return level estimates were comparably higher than the block maxima estimates. The study further revealed that the blended generalised extreme value (bGEVD) is more suitable for relatively short-term forecasting, since it cuts off at the 50-year return level. Therefore, this study will add value to the literature and knowledge of statistics and econometrics. In the future, more studies on bGEVD, vine copulas, and the r-largest-order bGEVD can be conducted in the financial markets.

Analyzing spillover effects of selected cryptocurrencies on gold and brent crude oil under COVID-19 pandemic: Evidence from GJR-GARCH and EVT copula methods

This study examines the dependence structure and estimates the Value at Risk (VaR) and risk spillover between cryptocurrencies, oil, and Gold market data. In this paper, we estimate VaR by applying a hybrid approach of extreme value theory (EVT), copula functions, and GARCH models. We implement this method in a dual pair of selected data: the cryptocurrencies (Bitcoin and Ripple) and the Brent crude oil and gold markets. To estimate the VaR structure of these combinations, we initially employ asymmetric GARCH and EVT methods to model the marginal distributions of each return series and subsequently apply Copula functions (Gaussian, Student's t, Clayton, and Frank) to connect the marginal distributions into a multivariate distribution. Based on the results, we infer that, generally, the GARCH-EVT-Copula approach works well and is better than traditional methods (e.g., Historical Simulation (HS) and variance-covariance (VC)). These results show that the GARCH-EVT-Copula model is the best method for examining the dependence structure. Finally, we implement the technique of Diebold-Yilmaz to compute the spillover index between four data before and during the COVID-19 pandemic. From this part, we conclude that cryptocurrencies have spillovers on each other, but their spillovers on Gold and oil are very small. This phenomenon implies that cryptocurrencies are tough to hedge against other financial assets but are appropriate diversifiers in an investor's portfolio. The current study's findings benefit all investors and financial market professionals who want to learn about the cryptocurrency market as a new asset class or incorporate it into their investment strategies or portfolios.

A Conceptual Model of Investment-Risk Prediction in the Stock Market Using Extreme Value Theory with Machine Learning: A Semisystematic Literature Review

The COVID-19 pandemic has been an extraordinary event, the type of event that rarely occurs but that has major impacts on the stock market. The pandemic has created high volatility and caused extreme fluctuations in the stock market. The stock market can be characterized as either linear or nonlinear. One method that can detect extreme fluctuations is extreme value theory (EVT). This study employed a semisystematic literature review on the use of the EVT method to estimate investment risk in the stock market. The literature used was selected by applying the preferred reporting items for systematic review and meta-analyses (PRISMA) guidelines, sourced from the ScienceDirect.com, ProQuest, and Scopus databases. A bibliometric analysis was conducted to determine the study characteristics and identify any research gaps. The results of the analysis show that studies on this topic are rarely carried out. Research in this field is generally performed only in univariate cases and is very complicated in multivariate cases. Given these limitations, further research could focus on developing a conceptual model that is dynamic and sensitive to extreme fluctuations, with multivariable inputs, in order to predict investment risk. The model developed here considered the variables that affect stock price fluctuations as the input data. The combination of VaR–EVT and machine-learning methods is effective in increasing model accuracy because it combines linear and nonlinear models.

Daily Precipitation and Temperature Extremes in Southern Italy (Calabria Region)

We apply extreme value theory (EVT) to study the daily precipitation and temperature extremes in the Calabria region (southern Italy) mainly considering a long-term observational dataset (1990–2020) and also investigating the possible use of the ERA5 (ECMWF Reanalysis v5) fields. The efficiency of the EVT applied on the available observational dataset is first assessed—both through a punctual statistical analysis and return-level maps. Two different EVT methods are adopted, namely the peak-over-threshold (POT) approach for the precipitation and the block-maxima (BM) approach for the temperature. The proposed methodologies appear to be suitable for describing daily extremes both in quantitative terms, considering the punctual analysis in specific points, and in terms of the most affected areas by extreme values, considering the return-level maps. Conversely, the analysis conducted using the reanalysis fields for the same time period highlights the limitations of using these fields for a correct quantitative reconstruction of the extremes while showing a certain consistency regarding the areas most affected by extreme events. By applying the methodology on the observed dataset but focusing on return periods of 50 and 100 years, an increasing trend of daily extreme rainfall and temperature over the whole region emerges, with specific areas more affected by these events; in particular, rainfall values up to 500 mm/day are predicted in the southeastern part of Calabria for the 50-year-return period, and maximum daily temperatures up to 40 °C are expected in the next 100 years, mainly in the western and southern parts of the region. These results offer a useful perspective for evaluating the exacerbation of future extreme weather events possibly linked to climate change effects.

EVT-Based Methods as Support for the Construction of a Synthetic Index of Socio-Economic Development for Territorial Units

Socio-economic development is an important multidimensional issue and its measurement is complex. This process reveals many problems that need to be resolved, such as data availability, selection of indicators and their measurement, selection of appropriate methods for normalization, weighing and aggregation of indicators. The main problem with the real data are atypical observations. In our research, we deal with the solution of this problem. We propose a comprehensive linear ordering procedure to assess the level of socio-economic development of various types of territorial units. It is based on the positional version of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and methods of Extreme Value Theory (EVT). In the first stage, we propose to use a two-step procedure based on six automatic methods to identify the tail of the data distribution (atypical observations). In the second stage, we suggest to use the positional TOPSIS method to aggregate indicators and eliminate the impact of asymmetry, mainly in the central part of the data distribution.

Evaluating the safety of autonomous vehicle–pedestrian interactions: An extreme value theory approach

With the increasing advancements in autonomous vehicle (AV) technologies, the forecasts of AV market shares seem to follow an ever-growing trend. This leads to the inherent need for proactive safety evaluations of AV impacts on other road users. To that end, this study proposes a modeling framework for the proactive assessment of pedestrian safety in AV environments. The proposed framework relies on the Extreme Value Theory (EVT), with the peak over threshold modeling technique, to develop an estimate of AV-pedestrian collisions using AV-pedestrian conflicts. The proposed framework was applied to two AV datasets, collected from three locations in the US and Singapore, using the operating AV fleets of two developers, Motional and Lyft. Both datasets included trajectory data for the subject AV, as well as LiDAR point clouds and annotated video data from AV cameras to capture the trajectories of surrounding road users. The datasets were processed to extract the AV-pedestrian conflicts along with the corresponding conflict indicators, mainly the post-encroachment time (PET) and time-to-collision (TTC). Relevant covariates were introduced to the proposed models to enhance their performance and prediction accuracy, including turning movements and conflict speeds. The results indicate an alarming risk to pedestrians when interacting with AVs, especially at the early stages of AV adoption. The expected number of collisions ranged from 4 to 5.5 per million vehicle kilometers travelled (VKT) of the AVs. With the addition of the covariates, the expected number of collisions went down to a range of 2.3–3.7 per million VKT, but with a narrower confidence interval of the resulting estimate and a better fit. The introduced approach shows promising prospects for the application of EVT methods to address AV safety impacts. It also invites future applications to address issues of concern for pedestrian safety in different conditions of urban traffic.

Value at Risk with Performing Exponential Generalized Autoregressive Conditional Heteroscedasticity–Generalized Pareto Distribution

Stocks are an investment that many investors are interested in but often have a high risk. Value at Risk (VaR) is one tool that is often used in risk measurement. In general, financial data fluctuate rapidly so that the variants of the residuals are not constant or heteroscedasticity. The condition of heteroscedasticity is modeled using the ARCH/GARCH model. If there is an asymmetric effect on the data, it is modeled using an asymmetric GARCH model, namely Exponential GARCH (EGARCH). In addition to the impacts of heteroscedasticity and asymmetric events, extreme events in fat distribution tails are modeled using the Extreme Value Theory method, namely the Peaks Over Threshold method with the Generalized Pareto Distribution (GPD) approach. The data in this study is the return data of PT. Indocement Tunggal Prakarsa Tbk (INTP) for the period of March 1, 2013 - October 31, 2018. It was found that the data was heteroscedasticity, asymmetric, and there were also fat distribution tails, so it was modeled using a combination of EGARCH-GPD models. ARIMA ([2], 0, [2,13]) EGARCH (1,1) has the smallest AIC compared to other models, and then we choose it as the best model. The amount of risk with a 95% confidence level obtained with the GPD approach is 0.333% of current investment.

Extreme Value Modelling of the Monthly South African Industrial Index (J520) Returns

This study uses Extreme Value Theory (EVT), Value-at-Risk (VaR) and Expected Shortfall (ES) analysis as a unified tool for managing extreme financial risk. The study extends the application of the generalised Pareto distribution (GPD) by modelling monthly South African Industrial Index (J520) returns (years: 1995C2018) to quantify the tail-related risk measures. The GPD is used to estimate the tail-related risk measures using the Peak over Threshold (PoT) method. Maximum Likelihood Estimates (MLE) of model parameters were obtained and the models goodness of fit was assessed graphically using Quantile-Quantile (QCQ) plots, Probability (PCP) plots, scatter plots, residuals, return levels and density plots. The findings are that the GPD provides an adequate fit to the data of excesses (extreme losses or gains). Low frequency but very high or very low returns impact on investment decisions. Calculations of the VaR and ES tail-related risk measures based on the fitted GPD model are given. The results reveal that for an investment in the South African Industrial Index (J520), the prospect of potential extreme losses is less than the prospect of potential extreme gains. There seems to be an upper bound where losses do not seem to exceed easily. The study concluded that EVT, together with VaR and ES analysis are useful tools that can be applied in practice to manage index/stock price risk and help investors improve their investment decisions and trading strategies through better quality information derived from the tools. This study contributes to empirical evidence on EVT methods that help to protect financial systems against unpredictable fluctuations and losses of extreme nature.

The Risk Analysis and Modeling of Byco Petroleum in Pakistan Using Extreme Value Theory

The extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. This paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution. L-moment ratio diagram is being used to find the appropriate distributions among the distributions. L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pakistan Limited. Thereafter, the probability weighted moment (PWM) method has been used in order to estimate the parameters of probability distributions. Furthermore, Anderson–Darling (AD) goodness-of-fit test is employed to test the goodness of fit among GEV and GL distributions, and it is clear from the results that the GL distribution is more reliable and applicable for extreme minima of Byco Petroleum Company in the Pakistan stock exchange market. EVT and traditional methods are used for value-at-risk (VaR) analysis. The analysis indicates that EVT methods are more suitable for risk measurement in comparison with traditional methods.

Towards a statistically robust determination of minimum water potential and hydraulic risk in plants

Minimum water potential (Ψmin ) is a key variable for characterizing dehydration tolerance and hydraulic safety margins (HSMs) in plants. Ψmin is usually estimated as the absolute minimum tissue Ψ experienced by a species, but this is problematic because sample extremes are affected by sample size and the underlying probability distribution. We compare alternative approaches to estimate Ψmin and assess the corresponding uncertainties and biases; propose statistically robust estimation methods based on extreme value theory (EVT); and assess the implications of our results for the characterization of hydraulic risk. Our results show that current estimates of Ψmin and HSMs are biased, as they are strongly affected by sample size. Because sampling effort is generally higher for species living in dry environments, the differences in current Ψmin estimates between these species and those living under milder conditions are partly artefactual. When this bias is corrected using EVT methods, resulting HSMs tend to increase substantially with resistance to embolism across species. Although data availability and representativeness remain the main challenges for proper determination of Ψmin , a closer look at Ψ distributions and the use of statistically robust methods to estimate Ψmin opens new ground for characterizing plant hydraulic risks.

Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

Determining the premium of paddy insurance using the extreme value theory method and the operational value at risk approach

Paddy farming is a source of livelihood for most rural communities in Indonesia. Indonesia as an agrarian country with a tropical climate, where the sun shines all the time and farmers can grow crops throughout the season. However, changes in air temperature, weather, and annual rainfall which sometimes change uncertainly cause changes in cropping patterns, which are caused by minimal water supplies in the dry season and flooding in the rainy season. This uncertainty will certainly increase the risk of crop failure. In addition to the risk of weather, other disturbances from plant pests and plant pests also cause the risk of crop failure, which results in greater losses to farmers. One way to transfer this risk is through a rice agricultural insurance program. This study aims to calculate the premium price using the Extreme Value Theory (EVT) method with the Operational Value at Risk (OpVaR) approach based on weather, pests and plant diseases. In this study, the data used are weather data Pests and plant diseases disturbance in West Java in 2009-2019. The stages in this research, the first step is to determine the estimated threshold value to obtain extreme data, then estimate the parameters using the likelihood method. Data suitability test with Generalized Pareto Distribution (GPD) was performed using the QQplot test. Risk is determined by the Operational Value at Risk (OpVaR) approach, the results of which are used to calculate the appropriate premium for paddy agricultural insurance.

Safety analysis of unsignalized intersections: a bivariate extreme value approach

ABSTRACT Application of extreme value theory (EVT) to road safety analysis is gaining interest, thanks to its ability to produce quick and reliable safety evaluations without the use of crash data. Traditionally applied to single collision types and single extreme variables (i.e. surrogate measures of safety), EVT can be further exploited to simultaneously model multiple collision types, with the use of multiple extreme variables. In this paper two bivariate EVT approaches are applied for the safety evaluation of a three-leg unsignalized intersection, considering: (i) two conflict points and a single surrogate measure of safety; (ii) two surrogate measures of safety collected in a single conflict point. Each bivariate analysis was applied with two EVT methods: Component-wise Maxima (CM) and Excesses Over a Threshold (EOT). Bivariate models produced good results, especially with the EOT method, and were able to significantly improve the univariate benchmark results when the two estimation datasets were correlated.

Estimation of the Occurrence Probability of Extreme Geomagnetic Storms by Applying Extreme Value Theory to Aa Index

AbstractIn this work, the occurrence probability of extreme geomagnetic storms is estimated by applying extreme value theory to the geomagnetic activity Aa index. The Aa index has 172 years observation time span, which is much longer than other geomagnetic indices, and thus is more suitable for analysis for rarely occurred extreme geomagnetic storms. We use two newly developed extreme value theory methods, block maxima method and peak over threshold, and find that the extreme geomagnetic storm that happened in March 1989 may happen once per century. This result implies that we should pay more attention to such extreme geomagnetic storms that can cause space weather hazards.

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.

PERHITUNGAN VALUE AT RISK DENGAN PENDEKATAN THRESHOLD AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY-GENERALIZED EXTREME VALUE

Stock is the most popular type of financial asset investment. Before buying a stock, an investor must estimate the risks which will be received. Value at Risk (VaR) is one of the methods that can be used to measure the level of risk. When investing in stock, if an investor wants to earn high returns, then he must be prepared to face higher risks. Most of stock return data have volatility clustering characteristic or there are cases of heteroscedasticity and the distribution of stock returns has heavy tail. One of the time series models that can be used to overcome the problem of heteroscedasticity is the ARCH/GARCH model, while the method for analyzing heavy tail data is Extreme Value Theory (EVT). In this study used an asymmetrical ARCH model with the Threshold ARCH (TARCH) and EVT methods with Generalized Extreme Value (GEV) to calculate VaR of the stock return from PT Bumi Serpong Damai Tbk for the period of September 2012 to October 2018. The best chosen model is AR([3])–TARCH(1). At the 95% confidence level, the maximum loss an investor will be received within the next day by using the TARCH-GEV calculation is 0.18%.

Exchange market pressure in South Africa and Kenya: An analysis using parametric and non-parametric extreme value theory

Orientation: Exchange market pressure (EMP) is the selling pressure of domestic currency or excess demand needed for foreign currency. Research purpose: The purpose of this study was to analyse EMP using extreme value theory (EVT) and to compare two commonly used EVT methods. Motivation for the study: To determine whether the EMP of two African countries can be modelled with EVT, and if so, which method would be best suited. To determine periods of extreme pressure or currency crisis by using these methods. Lastly, to study the individual components of the EMP index during these periods of stress of crises. Research design/approach and method: The monthly data of the three components of the EMP index for two African countries (Republic of South Africa [RSA] and Kenya) were studied for a period of 19 years (1999–2017). The data were modelled using the generalised Pareto distribution (GPD) with the peak over threshold (POT) method using maximum likelihood estimation. Moreover, the data were also modelled using the non-parametric Hill estimate. Appropriate estimated and empirical quantiles are reported in order to determine periods of extreme pressure or crises. The components of the EMP RSA data set were modelled with appropriate autoregressive moving averages and/or autoregressive conditional heteroscedasticity/generalised autoregressive conditional heteroscedasticity (ARMA/ARCH/GARCH) processes to ensure independent and identically distributed variables. Main findings: Reliable and accurate estimates were obtained for the scale and shape parameter using the GPD POT method for both countries. Positive shape parameters confirmed generalised extreme value distributions with heavy tails of the Frechet type. Similarly, accurate and reliable shape estimates were computed using the non-parametric Hill estimator for both countries. Practical/managerial implications: The GPD POT method more closely reflected estimates to the empirical qauntiles compared to the Hill method. It is feasible to model the EMP data of two African countries with EVT using both POT estimation methods. However, the GPD method using maximum likelihood estimation was more accurate compared to the non-parametric Hill estimate. Contribution/value-add: It is feasible to model the EMP data of two African countries using EVT using both POT methods. As a consequence periods of extreme pressure could be identified. Therefore the individual components of the EMP at those periods of extreme pressure could be studied more closely.