In this paper we study the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce...

In this paper we study the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce...

We examine the asymptotic properties of the coefficient of determination, R2, in models with α-stable   random variables. If the regressor and error term share the same index of stability α2, we show that the R2  statistic does not converge to a constant but has a nondegenerate distribution...

Many econometric quantities such as long-term risk can be modeled by Pareto-like distributions and may also display long-range dependence. If Pareto is replaced by Gaussian, then one can consider fractional Brownian motion whose increments, called fractional Gaussian noise, exhibit long-range...

α-stable distributions are utilized as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate α-stable models admit closed form densities which can be evaluated pointwise. This complicates...

Abstract In this paper, we study the change point test for the tail index of scale-shifted processes. To this task, we propose two tests. The first is designed via examining the discrepancy between the two Hill estimators obtained from the observations before and after a preliminary change point...

In applications to finance, insurance, physics andmany other fields, statisticians are often faced with high qualitydatasets that exhibit deviations from the "normal behavior", causedby the extremes in the sample. As a consequence in recent years agreat deal of research has been done in...

Electricity prices in competitive markets are extremely volatile with salient features such as mean-reversion and jumps and spikes. Modeling electricity spot prices is essential for asset and project valuation as well as risk management. I introduce the mean-reversion feature into a classical...