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Rainbow plots, Bagplots and Boxplots for Functional Data

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  • Rob J. Hyndman
  • Han Lin Shang

Abstract

We propose new tools for visualizing large numbers of functional data in the form of smooth curves or surfaces. The proposed tools include functional versions of the bagplot and boxplot, and make use of the first two robust principal component scores, Tukey's data depth and highest density regions. By-products of our graphical displays are outlier detection methods for functional data. We compare these new outlier detection methods with exiting methods for detecting outliers in functional data and show that our methods are better able to identify the outliers.

Suggested Citation

  • Rob J. Hyndman & Han Lin Shang, 2008. "Rainbow plots, Bagplots and Boxplots for Functional Data," Monash Econometrics and Business Statistics Working Papers 9/08, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2008-9
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2008/wp9-08.pdf
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    References listed on IDEAS

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    7. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
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    Citations

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    Cited by:

    1. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    2. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    3. Weiyi Xie & Sebastian Kurtek & Karthik Bharath & Ying Sun, 2017. "A Geometric Approach to Visualization of Variability in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 979-993, July.
    4. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    5. Barrow, Devon & Kourentzes, Nikolaos, 2018. "The impact of special days in call arrivals forecasting: A neural network approach to modelling special days," European Journal of Operational Research, Elsevier, vol. 264(3), pages 967-977.
    6. Francesca Ieva & Anna Maria Paganoni, 2020. "Component-wise outlier detection methods for robustifying multivariate functional samples," Statistical Papers, Springer, vol. 61(2), pages 595-614, April.
    7. repec:cte:wsrepe:24606 is not listed on IDEAS
    8. Han Lin Shang & Yang Yang & Fearghal Kearney, 2019. "Intraday forecasts of a volatility index: functional time series methods with dynamic updating," Annals of Operations Research, Springer, vol. 282(1), pages 331-354, November.
    9. Farah Yasmeen & Rob J Hyndman & Bircan Erbas, 2010. "Forecasting age-related changes in breast cancer mortality among white and black US women: A functional approach," Monash Econometrics and Business Statistics Working Papers 9/10, Monash University, Department of Econometrics and Business Statistics.
    10. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    11. Epifanio, Irene & Ventura-Campos, Noelia, 2011. "Functional data analysis in shape analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2758-2773, September.
    12. Ana Arribas-Gil & Juan Romo, 2015. "Discussion of “Multivariate functional outlier detection”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 263-267, July.
    13. Zafar, Raja Fawad & Qayyum, Abdul & Ghouri, Saghir Pervaiz, 2015. "Forecasting Inflation using Functional Time Series Analysis," MPRA Paper 67208, University Library of Munich, Germany.
    14. Graciela Boente & Matías Salibian-Barrera, 2015. "S -Estimators for Functional Principal Component Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1100-1111, September.
    15. Fraiman, Ricardo & Pateiro-López, Beatriz, 2012. "Quantiles for finite and infinite dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 1-14.
    16. Montes, Francisco & Sala, Ramón, 2012. "Equilibrio competitivo en Liga española de futbol de Primera División: Un test de Montecarlo basado en datos funcionales/Competitive Balance in the First Division Spanish Soccer League: A Montecarlo T," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 30, pages 513-526, Agosto.
    17. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    18. Yuan Yan & Marc Genton, 2015. "Discussion of “Multivariate functional outlier detection” by Mia Hubert, Peter Rousseeuw and Pieter Segaert," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 245-251, July.

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    More about this item

    Keywords

    Highest density regions; Robust principal component analysis; Kernel density estimation; Outlier detection; Tukey's halfspace depth;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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