• Corpus ID: 248496720

Tail Adversarial Stability for Regularly Varying Linear Processes and their Extensions

  title={Tail Adversarial Stability for Regularly Varying Linear Processes and their Extensions},
  author={Shuyang Bai and Ting Zhang},
The recently introduced notion of tail adversarial stability has been proven useful in studying tail dependent time series and obtaining their limit theorems. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes, but not yet studied for additive linear processes that have also been commonly used in modeling extremal clusters and tail dependence in time series. In this article, we fill this gap by verifying the tail adversarial… 



High-quantile regression for tail-dependent time series

Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly

Extreme value theory for suprema of random variables with regularly varying tail probabilities

Structural break tests for extremal dependence in β-mixing random vectors

We derive a structural break test for extremal dependence in β-mixing random vectors whose marginals may be (asymptotically) dependent or independent. Extant tests require independent observations

The extremogram: a correlogram for extreme events

We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes among

Regularly varying multivariate time series

On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures

ABSTRACT This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations. The paper starts briefly reviewing

Basic properties and prediction of max-ARMA processes

A max-autoregressive moving average (MARMA(p, q)) process {Xt } satisfies the recursion for all t where φ i , , and {Zt } is i.i.d. with common distribution function Φ1,σ (X): = exp {–σ x –1} for .

Bivariate tail estimation: dependence in asymptotic independence

In the classical setting of bivariate extreme value theory, the procedures for estimating the probability of an extreme event are not applicable if the componentwise maxima of the observations are

On closure and factorization properties of subexponential and related distributions

  • P. EmbrechtsC. Goldie
  • Mathematics
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
  • 1980
Abstract For a distribution function F on [0, ∞] we say F ∈ if {1 – F(2)(x)}/{1 – F(x)}→2 as x→∞, and F∈, if for some fixed γ > 0, and for each real , limx→∞ {1 – F(x + y)}/{1 – F(x)} ═ e– n.