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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Statistics, Cracow University of Economics, Kraków, Poland

    Daniel Kosiorowski

  2. AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059, Kraków, Poland

    Jerzy P. Rydlewski

  3. Department of Financial Markets, Cracow University of Economics, Kraków, Poland

    Małgorzata Snarska

Authors
  1. Daniel Kosiorowski
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  2. Jerzy P. Rydlewski
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  3. Małgorzata Snarska
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Correspondence to Jerzy P. Rydlewski.

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Kosiorowski, D., Rydlewski, J.P. & Snarska, M. Detecting a structural change in functional time series using local Wilcoxon statistic. Stat Papers 60, 1677–1698 (2019). https://doi.org/10.1007/s00362-017-0891-y

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  • DOI: https://doi.org/10.1007/s00362-017-0891-y

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