Titlebook: Extreme Value Theory for Time Series; Models with Power-La Thomas Mikosch,Olivier Wintenberger Book 2024 The Editor(s) (if applicable) and

花束

抱怨

欢乐中国

Regularly Varying Random Variables and VectorsIn this chapter we introduce regular variation for random variables, random vectors and their distributions. These notions are important for the study of . in Chap. .: there we define the regular variation of these processes via regular variation of their finite-dimensional distributions.

Panther

战胜

Ischemia

河潭

Self-Normalization, Sample Autocorrelations and the ExtremogramIn this chapter we first present some consequences of the .-stable limit theory developed in the previous chapter. In particular, we derive results about the joint convergence of sums and maxima of regularly varying stationary sequences, and distributional limits of . sums.

BRIBE

Introduction,h and nineteenth centuries, for example the law or large numbers, the central limit theorem with Gaussian limit distribution, and Poisson’s limit theorem. The limit law in the latter result was considered of little practical value, very much in contrast to the Gaussian law.

神圣在玷污

大炮

Examples of Regularly Varying Stationary Processes In this chapter we consider various important classes of time series models which have the regular variation property. We focus on the derivation of the corresponding tail measures and the spectral tail process. In the presence of serial dependence the tail measures and spectral tail processes ofte