Limit properties of exceedances point processes of scaled stationary Gaussian sequences

We derive the limiting distributions of exceedances point processes of randomly scaled weakly dependent stationary Gaussian sequences under some mild asymptotic conditions. In the literature analogous results are available only for contracted stationary Gaussian sequences. In this paper, we include additionally the case of randomly inflated stationary Gaussian sequences with a Weibullian type random scaling. It turns out that the maxima and minima of both contracted and inflated weakly dependent stationary Gaussian sequences are asymptotically independent.Comment: 1

Expectile-based conditional tail moments with covariates

Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing quantiles by expectiles, called expectile-based conditional tail moment, and focus on the estimation of this new risk measure as the conditional survival function of the risk, given the risk exceeding the expectile and given a value of the covariates, is heavy tail. Under some regular conditions, asymptotic properties of this new estimator are considered. The extrapolated estimation of the conditional tail moments is also investigated. These results are illustrated both on simulated data and on a real insurance data.Comment: 17 pages, 7 figure