The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence of these in time. The extremal index \(\theta \) (Leadbetter in Z Wahrscheinlichkeitstheor Verw Geb 65:291–306, 1983) allows to infer the tendency for clustering of high values, but does not allow to evaluate the greater or less amount of oscillations in a cluster. The estimation of \(\theta \) entails the validation of local dependence conditions regulating the distance between high levels oscillations of the process, which is difficult to implement in practice. In this work, we propose a smoothness coefficient to evaluate the degree of smoothness/oscillation in the trajectory of a process, with an intuitive reading and simple estimation. Application in some examples will be provided. We will see that, in a stationary sequence, it coincides with the tail dependence coefficient \(\lambda \) (Sibuya in Ann Inst Stat Math 11:195–210, 1960; Joe in Multivariate models and dependence concepts. Monographs on statistics and applied probability, vol 73. Chapman and Hall, London, 1997), providing a new interpretation of the latter. This relationship will inspire a new estimator for \(\lambda \), and its performance will be evaluated based on a simulation study. We illustrate with an application to financial series.

灾难的风险与发生极端价值的可能性有关。为了评估过程出现高值的倾向性以及这些值的持久性，已经开发了几种统计方法。极值指数\（\ theta \）（Z Wahrscheinlichkeitstheor Verw Geb 65：291–306，1983年的领导者）可以推断出高值聚类的趋势，但不允许评估一个或多个振荡中的更大或更小数量簇。\（\ theta \）的估计需要验证调节过程的高水平振荡之间的距离的局部依赖条件，这在实践中很难实现。在这项工作中，我们提出了一个平滑系数，以直观的读数和简单的估算来评估过程轨迹中的平滑/振动程度。将提供一些示例中的应用。我们将看到，在一个平稳序列中，它与尾部依赖系数\（\ lambda \）相符（Sibuya在Ann Inst Stat Math 11：195–210，1960年； Joe在多元模型和依赖概念中。应用概率，第73卷。Chapman和Hall，伦敦，1997年），提供了对后者的新解释。这种关系将激发\（\ lambda \）的新估计，并将根据模拟研究评估其性能。我们举例说明金融系列。