Stylized facts for univariate high-frequency data in finance are well known. They include scaling behaviour, volatility clustering, heavy tails and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this paper, bivariate series of high-frequency FX spot...

This article describes smooth nonstationary generalized additive modeling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. We summarize the smoothing methodology as a new tool for practical extreme value exploration in finance and...

This paper compares the shape of the level sets for two multivariate densities. The densities are positive and continuous, and have the same dependence structure. The density f is heavy-tailed. It decreases at the same rate-up to a positive constant-along all rays. The level sets {fc} for...

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...