Statistical Papers

, Volume 60, Issue 5, pp 1677–1698 | Cite as

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

  • Daniel Kosiorowski
  • Jerzy P. RydlewskiEmail author
  • Małgorzata Snarska
Regular Article


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.


Functional data analysis Local depth Functional depth Detecting structural change Heterogenity Wilcoxon test 

Mathematics Subject Classification

62G30 62-07 62G35 62P20 



JPR research has been partially supported by the AGH local Grant No. 15.11.420.038, MS research has been partially supported by Cracow University of Economics local Grant Nos. 045.WF.KRYF.01.2015.S.5045, 161.WF.KRYF.02.2015.M.5161, and National Science Center Grant No. NCN.OPUS.2015.17.B.HS4.02708. DK research has been supported by the CUE local Grants 2016 and 2017 for preserving scientific resources.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Daniel Kosiorowski
    • 1
  • Jerzy P. Rydlewski
    • 2
    Email author
  • Małgorzata Snarska
    • 3
  1. 1.Department of StatisticsCracow University of EconomicsKrakówPoland
  2. 2.AGH University of Science and TechnologyFaculty of Applied MathematicsKrakówPoland
  3. 3.Department of Financial MarketsCracow University of EconomicsKrakówPoland

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