Detecting a structural change in functional time series using local Wilcoxon statistic

Functional data analysis is a part of modern multivariate statistics that analyzes data that provide information regarding curves, surfaces, or anything that varies over a certain continuum. In economics and empirical finance, we often have to deal with time series of functional data, where decision cannot be made easily, for example whether they are to be considered as homogeneous or heterogeneous. A discussion on adequate tests of homogenity for functional data is carried out in literature nowadays. We propose a novel statistic for detecting a structural change in functional time series based on a local Wilcoxon statistic induced by a local depth function proposed by Paindaveine and Van Bever, and where a point of the hypothesized structural change is assumed to be known.