随机数序列局部极值间距离的概率分布

Extremal Indices in the Series Scheme and their Applications

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices through two definitions generalizing the basic properties of the classical extremal index. We prove some useful properties of the new extremal indices. We show how the behavior of aggregate activity maxima on random graphs (in information network models) and the behavior of maxima of random particle scores in branching processes (in biological population models)…

Statistical inference for heavy tailed series with extremal independence

We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to infinity, the conditional distribution of $X_h$ suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the normalization and of the limiting distribution.

基于极值图的单变量和多变量时间序列的极值相关估计

Estimating Extremal Dependence in Univariate and Multivariate Time Series via the Extremogram

Davis和Mikosch [7]介绍了极值图作为一种灵活的定量工具，用于测量平稳时间序列中各种类型的极值相关性。在那里，我们展示了样本极值图的一些标准统计特性。一个主要的困难是为极值图建立可信的置信带。在本文中，我们采用平稳的引导，以克服这个问题。此外，我们引入交叉极值图作为两个或多个时间序列之间的极值序列相关性的度量。我们还研究了极值事件之间的返回时间的极值图。平稳引导的极值图和由此产生的解释的使用说明在几个单变量和多变量的金融时间序列的例子。

Method of moments estimators for the extremal index of a stationary time series

The extremal index $θ$, a number in the interval $[0,1]$, is known to be a measure of primal importance for analyzing the extremes of a stationary time series. New rank-based estimators for $θ$ are proposed which rely on the construction of approximate samples from the exponential distribution with parameter $θ$ that is then to be fitted via the method of moments. The new estimators are analyzed both theoretically as well as empirically through a large-scale simulation study. In specific scenarios, in particular for time series models with $θ\approx 1$, they are found to be superior to recent …

序列极值相关测度及其估计

Measures of serial extremal dependence and their estimation

本文的目标是双重的：1。我们回顾了经典的和最近的措施序列极值依赖在严格的平稳时间序列以及他们的估计。2.我们讨论了最近的重尾时间序列的概念，包括定期变化和最大稳定过程。序列极值依赖的典型特征是序列中高阈值的不一致性簇。我们首先讨论的概念极值指数的一个单变量序列，即倒数的预期集群大小，这引起了极大的关注极值文献。然后，我们继续通过引入极值图，这是一个渐进的自相关函数序列的极值事件在时间序列。在这种情况下，我们讨论了时间序列的规则变化。这个概念对于描述严格平稳序列中的序列极值依赖和重尾是有用的。我们简要讨论了由Basrak和Segers提出的用概率的方式描述规则变化序列的依赖结构的尾过程。具有Frechet边缘的极大稳定过程是一类重要的正则变化序列。最近，这个类引起了建模和统计目的的关注。我们将极值图应用于最大稳定过程。最后讨论了时域和频域极值的估计。

滑动平均过程误差项局部极值间距离的渐近概率分布

Asymptotic probability distribution of distances between local extrema of error terms of a moving average process

考虑移动平均过程MA（q）的误差项x（i），其中x（i）=e（i）+ e（i-1）+.+ e（i-q）和e（i）-独立同分布（i.i.d.）随机变量。如果下列条件成立，则我们将项x（i）识别为局部极大值：x（i-1）< x（i）> x（i+1）。如果局部极大值x（i）之后是下一个局部极大值x（k），则d=k-i是局部极大值之间的距离。距离d（j）本身是随机变量。本文研究距离d（j）的概率分布。特别地，我们证明了对于任何q>0，平均距离E[d（j）]=4，并且渐近方差也等于4。