Detecting a Structural Change in Functional Time Series Using Local Wilcoxon Statistic

TL;DR

This paper introduces a new statistical method using a local Wilcoxon statistic to detect structural changes in functional time series, aiding in the analysis of economic and financial data over time.

Contribution

It proposes a novel test for structural change detection in functional time series based on a local Wilcoxon statistic and a local depth function.

Findings

Effective detection of structural changes demonstrated

Applicable to economic and financial functional data

Advances current methods for homogeneity testing

Abstract

Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have to deal with time series of functional data, where we cannot easily decide, whether they are to be considered as homogeneous or heterogeneous. At present a discussion on adequate tests of homogenity for functional data is carried. We propose a novel statistic for detetecting 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 (2013).