  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 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 process, it
coincides with the tail dependence coefficient $\lambda$ (Sibuya 1960, Joe
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.
