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Detecting relevant changes in the spatiotemporal mean function

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  • Holger Dette
  • Pascal Quanz

Abstract

For a spatiotemporal process {Xj(s,t)∣s∈S,t∈T}j=1,…,n, where S denotes the set of spatial locations and T the time domain, we consider the problem of testing for a change in the sequence of mean functions {μj(s,t)∣s∈S,t∈T}j=1,…,n. In contrast to most of the literature, we are not interested in arbitrarily small changes but only in changes with a norm exceeding a given threshold. Asymptotically distribution free tests are proposed, which do not require the estimation of the long‐run spatiotemporal covariance structure. In particular, we consider a fully functional approach and a test based on the cumulative sum paradigm, investigate the large sample properties of the corresponding test statistics and study their finite sample properties by means of simulation study.

Suggested Citation

  • Holger Dette & Pascal Quanz, 2023. "Detecting relevant changes in the spatiotemporal mean function," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 505-532, September.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:5-6:p:505-532
    DOI: 10.1111/jtsa.12674
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    References listed on IDEAS

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    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    3. Oleksandr Gromenko & Piotr Kokoszka & Matthew Reimherr, 2017. "Detection of change in the spatiotemporal mean function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 29-50, January.
    4. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.
    5. Holger Dette & Kathrin Möllenhoff & Stanislav Volgushev & Frank Bretz, 2018. "Equivalence of Regression Curves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 711-729, April.
    6. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    7. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    8. Alexander Aue & Gregory Rice & Ozan Sönmez, 2018. "Detecting and dating structural breaks in functional data without dimension reduction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 509-529, June.
    9. Aston, John A.D. & Kirch, Claudia, 2012. "Detecting and estimating changes in dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 204-220.
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