Title: About the complexity of a functional data set
Authors: Enea Bongiorno - Universita del Piemonte Orientale (Italy) [presenting]
Aldo Goia - University of Eastern Piedmont Amedeo Avogadro (Italy)
Philippe Vieu - University Paul Sabatier (France)
Abstract: Consider the problem to state the compatibility of observed functional data with a reference model. Starting from the small ball probability factorization, it is possible to introduce the concept of complexity for functional data and suitable indexes measuring it. At a first stage, a descriptive approach, mainly based on a new graphical tool (namely the log-Volugram), is implemented and fruitfully applied. From an inferential perspective, a hypothesis test is implemented: the test statistic is derived, its asymptotic law is studied, a study of level and power of the test for finite sample sizes and a comparison with a competitor are carried out by Monte Carlo simulations. It turns out that the developed methodologies are fully free from assumptions on model, distribution as well as dominating measure. Applications are provided over financial time series.