The extremal coefficient function has been discussed as an analog of the autocovariance function for extreme values. However, as to the behavior of valid extremal coefficient functions little is known apart from their positive definite type. In particular, the reconstruction of valid processes...

The extremal coefficient function has been discussed as an analog of the autocovariance function for extreme values. However, as to the behavior of valid extremal coefficient functions little is known apart from their positive definite type. In particular, the reconstruction of valid processes...

The extremal coefficient function has been discussed as an analog of the autocovariance function for extreme values. However, as to the behavior of valid extremal coefficient functions little is known apart from their positive definite type. In particular, the reconstruction of valid processes...

The goal of this paper is two-fold: (1) We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. (2) We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes.

The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison et al. (2012) [5]). A major drawback of this max-stable model was the lack of a spectral representation such that...

Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian approaches. In this paper, we present a Bayesian approach...

We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes.