Detecting a structural change in functional time series using local Wilcoxon statistic
- 242 Downloads
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.
KeywordsFunctional data analysis Local depth Functional depth Detecting structural change Heterogenity Wilcoxon test
Mathematics Subject Classification62G30 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.
- Flores R, Lillo R, Romo J (2015) Homogenity test for functional data. arXiv:1507.01835v1
- Hyndman R, Einbeck J, Wand M (2013) The R package hdrcdeGoogle Scholar
- Kosiorowski D, Zawadzki Z (2014) DepthProc: an R package for robust exploration of multidimensional economic phenomena. http://arxiv.org/pdf/1408.4542. Accessed 5 April 2016
- López-Pintado S, Jörnsten R (2007) Functional analysis via extensions of the band depth. IMS lecture notes–monograph series complex datasets and inverse problems: tomography, networks and beyond, vol 54. Institute of Mathematical Statistics, Hayward, pp 103–120Google Scholar
- Mosler K (2013) Depth statistics. Robustness and complex data structures. Springer, Heidelberg, pp 17–34Google Scholar
- Serfling R (2006) Depth functions in nonparametric multivariate inference. In: Liu R, Serfling R, Souvaine D (eds) Series in discrete mathematics and theoretical computer science, vol 72. AMS, Providence, pp 1–15Google Scholar
- Sguera C, Galeano P, Lillo RE (2016) Global and local functional depths. arXiv:1607.05042v1
- Shang HL (2016) Bootstrap methods for stationary functional time series. Stat Comput (to appear)Google Scholar