A New Parameter Estimator for the Generalized Pareto Distribution under the Peaks over Threshold Framework

A Comparative Assessment of Five Different Distributions Based on Five Different Optimization Methods for Modeling Wind Speed Distribution

Determining wind regime distribution patterns is essential for many reasons; modelling wind power potential is one of the most crucial. In that regard, Weibull, Gamma, and Rayleigh functions are the most widely used distributions for describing wind speed distribution. However, they could not be the best for describing all wind systems. Also, the used estimation methods play a significant role in deciding which distribution can achieve the best matching. Consequently, alternative distributions and estimation methods are required to be studied. An extensive analysis of five different distributions to describe the wind speeds distribution, namely Rayleigh, Weibull, Inverse Gaussian, Burr Type XII, and Generalized Pareto, are introduced in this study. Further, five metaheuristic optimization methods, Grasshopper Optimization Algorithm, Grey Wolf Optimization, Moth-Flame Optimization, Salp Swarm Algorithm, and Whale Optimization Algorithm, are utilized to specify the best parameter values of each distribution. To compare the good-of-fitness of the introduced distributions, five error criteria and seven statistical descriptors are utilized.

Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables

A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal distribution, heavy tails, and dynamic changes over time. Hence, they cannot generate highly accurate information. To overcome this issue, this study proposes a combination of the Generalized Autoregressive Conditional Heteroskedasticity model, Generalized Pareto distribution, and stochastic copulas as a tool to investigate the dependence structure between the PM10 variable and other pollutant variables, including CO, NO2, O3, and SO2. Results indicate that the dynamic dependence structure between PM10 and other pollutant variables can be described with a ranking of PM10–CO > PM10–SO2 > PM10–NO2 > PM10–O3 for the overall time paths (δ) and the upper tail (τU) or lower tail (τL) dependency measures. This study reveals an evident correlation among pollutant variables that changes over time; such correlation reflects dynamic dependency.

Introduction to Extreme Seeking Entropy

Recently, the concept of evaluating an unusually large learning effort of an adaptive system to detect novelties in the observed data was introduced. The present paper introduces a new measure of the learning effort of an adaptive system. The proposed method also uses adaptable parameters. Instead of a multi-scale enhanced approach, the generalized Pareto distribution is employed to estimate the probability of unusual updates, as well as for detecting novelties. This measure was successfully tested in various scenarios with (i) synthetic data, (ii) real time series datasets, and multiple adaptive filters and learning algorithms. The results of these experiments are presented.

Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection

A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold.