Smoothness of time series: a new approach to estimation

Abstract

The assessment of the risk of occurrence of extreme phenomena is inherently linked to the theory of extreme values. In the context of a time series, the analysis of its trajectory toward a greater or lesser smoothness, i.e. presenting a lesser or greater propensity for oscillations, respectively, constitutes another contribution in the assessment of the risk associated with extreme observations. For example, a financial market index with successive oscillations between high and low values shows investors a more unstable and uncertain behavior. In stationary time series, the upper tail smoothness coefficient is described by the tail dependence coefficient, a well-known concept first introduced by Sibuya. This work focuses on an inferential analysis of the upper tail smoothness coefficient, based on subsampling techniques for time series. In particular, we propose an estimator with reduced bias. We also analyze the estimation of confidence intervals through a block bootstrap methodology and a test procedure to prior detect the presence or absence of smoothness. An application to real data is also presented.