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A randomness test for functional panels

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  • Kokoszka, Piotr
  • Reimherr, Matthew
  • Wölfing, Nikolas

Abstract

Functional panels are collections of functional time series, and arise often in the study of high frequency multivariate data. We develop a portmanteau style test to determine if the cross-sections of such a panel are independent and identically distributed. Our framework allows the number of functional projections and/or the number of time series to grow with the sample size. A large sample justification is based on a new central limit theorem for random vectors of increasing dimension. With a proper normalization, the limit is standard normal, potentially making this result easily applicable in other FDA context in which projections on a subspace of increasing dimension are used. The test is shown to have correct size and excellent power using simulated panels whose random structure mimics the realistic dependence encountered in real panel data. It is expected to find application in climatology, finance, ecology, economics, and geophysics. We apply it to Southern Pacific sea surface temperature data, precipitation patterns in the South-West United States, and temperature curves in Germany.

Suggested Citation

  • Kokoszka, Piotr & Reimherr, Matthew & Wölfing, Nikolas, 2016. "A randomness test for functional panels," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 37-53.
    • Handle: RePEc:eee:jmvana:v:151:y:2016:i:c:p:37-53
    DOI: 10.1016/j.jmva.2016.07.002
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    References listed on IDEAS

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    1. Aghoukeng Jiofack, Jean Gérard & Nkiet, Guy Martial, 2010. "Testing for lack of dependence between functional variables," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1210-1217, August.
    2. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    3. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    4. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    5. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    6. Gabrys, Robertas & Kokoszka, Piotr, 2007. "Portmanteau Test of Independence for Functional Observations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1338-1348, December.
    7. Liebl, Dominik, 2013. "Modeling and Forecasting Electricity Spot Prices: A Functional Data Perspective," MPRA Paper 50881, University Library of Munich, Germany.
    8. Bo Fu, 2002. "Testing model adequacy for dynamic panel data with intercorrelation," Biometrika, Biometrika Trust, vol. 89(3), pages 591-602, August.
    9. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 313-332.
    10. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 100-119.
    11. Thomas J. Fisher & Colin M. Gallagher, 2012. "New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 777-787, June.
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