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A functional data based method for time series classification

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  • Alonso Fernández, Andrés Modesto
  • Casado, David
  • López Pintado, Sara
  • Romo, Juan

Abstract

We propose using the integrated periodogram to classify time series. The method assigns a new element to the group minimizing the distance from the integrated periodogram of the element to the group mean of integrated periodograms. Local computation of these periodograms allows the application of the approach to non- -stationary time series. Since the integrated periodograms are functional data, we apply depth-based techniques to make the classification robust. The method provides small error rates with both simulated and real data, and shows good computational behaviour.

Suggested Citation

  • Alonso Fernández, Andrés Modesto & Casado, David & López Pintado, Sara & Romo, Juan, 2008. "A functional data based method for time series classification," DES - Working Papers. Statistics and Econometrics. WS ws087427, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws087427
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    References listed on IDEAS

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    1. Ombao H. C & Raz J. A & von Sachs R. & Malow B. A, 2001. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 543-560, June.
    2. James G.M. & Sugar C.A., 2003. "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 397-408, January.
    3. Shumway, Robert H., 2003. "Time-frequency clustering and discriminant analysis," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 307-314, July.
    4. Sakiyama, Kenji & Taniguchi, Masanobu, 2004. "Discriminant analysis for locally stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 282-300, August.
    5. Maharaj, Elizabeth A. & Alonso, Andres M., 2007. "Discrimination of locally stationary time series using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 879-895, October.
    6. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    7. Chandler, Gabriel & Polonik, Wolfgang, 2006. "Discrimination of Locally Stationary Time Series Based on the Excess Mass Functional," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 240-253, March.
    8. Hsiao-Yun Huang & Hernando Ombao & David S. Stoffer, 2004. "Discrimination and Classification of Nonstationary Time Series Using the SLEX Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 763-774, January.
    9. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
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    Cited by:

    1. Andrés Alonso & David Casado & Sara López-Pintado & Juan Romo, 2014. "Robust Functional Supervised Classification for Time Series," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 325-350, October.

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    More about this item

    Keywords

    Time series;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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