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Title: Evaluating the complexity of a functional time series Authors:  Enea Bongiorno - Universita del Piemonte Orientale (Italy)
Kwo Lik Lax Chan - Università degli Studi del Piemonte Orientale (Italy) [presenting]
Aldo Goia - University of Eastern Piedmont Amedeo Avogadro (Italy)
Abstract: Consider a functional time series taking values in a general topological space and assume that its Small-Ball Probability (SmBP) factorizes into two terms that play the role of a surrogate density and of a volume term. The latter is a means for studying the complexity of the underlying process, since it may reveal some latent feature of it. In some cases, it can be analytically specified in a parametric form: a special situation is given when the process belongs to the monomial family, like in the finite-dimensional and fractal case, for which the volumetric term has monomial form depending on the SmBP radius and a parameter named complexity index. The aim is to present some results concerning the study of a nonparametric estimator for the volume term based on a U-statistic in the beta-mixing framework. Weak consistency of this estimator is provided. In the particular case of a monomial family, it is possible to estimate the complexity index by minimizing a suitable dissimilarity measure. For this estimator asymptotic Gaussianity is shown, providing theoretical support to build confidence interval for the complexity index. A Monte Carlo simulation is carried out in order to assess the performance of the methodology for finite sample sizes. Finally, the new method is applied to detect the complexity of a real-world dataset.