Abstract: A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution of the rescaled series given that, at a fixed time instant, its distance to the origin exceeds a threshold tending to infinity. The limi...

Taking daily return of international crude oil spot and futures as sample, this paper analyzed the time varying and asymmetric dependence structure of them by time varying Copula-GARCH model based on sliding window and semi parameter estimation. This paper analyzed the regular changing between dependence structure of crude oil spot and futures and the return fluctuation, and confirmed that ther...

Using a suite of 3D hydrodynamical simulations star-forming molecular clouds, we investigate how the density probability distribution function (PDF) changes when including gravity, turbulence, magnetic fields, and protostellar outflows heating. We find that PDF is not lognormal self-gravity are considered. Self-gravity produces power-law tail at high densities inclusion stellar feedback from he...

The tail behaviour of stationary R-valued Markov-Switching ARMA processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, the feasible stationarity condition given in Stelzer (2006) is extended to a criterion for regular variation. Our results complement in particul...

This paper investigates the role of domestic and global determinants core inflation in euro area. We analyse entire conditional distribution by estimating a Phillips curve type relationship with method expectile regression, here extended to capture time-varying effects. Both foreign output gap appear drive area inflation. Domestic has bigger influence right tail than left tail, providing eviden...

To recover the topology of a manifold in presence heavy tailed or exponentially decaying noise, one must understand behavior geometric complexes whose points lie tail these noise distributions. This study advances this line inquiry, and demonstrates functional strong laws large numbers for Euler characteristic process random formed by outside an expanding ball \(\mathbb {R}^{d}\). When are draw...

We study the behavior of tail a measure μ⊠t, where ⊠t is t-fold free multiplicative convolution power for t≥1. focus on case μ probability positive half-line with regularly varying right i.e. form x−αL(x), L slowly varying. obtain phase transition in μ⊞t between regimes α<1 and α>1. Our main tool description regular variation terms corresponding S-transform at 0−. also describe tails ⊠ infinite...

We consider a dynamical system in R driven by a vector field −U ′, where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy noise of small intensity and such that the heaviest tail of its Lévy measure is regularly varying. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it reminds of...

We provide a necessary and sufficient condition for the ratio of two jointly α-Fréchet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As...