Journal of Classification

, Volume 31, Issue 3, pp 325–350 | Cite as

Robust Functional Supervised Classification for Time Series

  • Andrés M. Alonso
  • David Casado
  • Sara López-Pintado
  • Juan Romo


We propose using the integrated periodogram to classify time series. The method assigns a new time series to the group that minimizes the distance between the series integrated periodogram and the group mean of integrated periodograms. Local computation of these periodograms allows the application of this approach to nonstationary time series. Since the integrated periodograms are curves, we apply functional data depth-based techniques to make the classification robust, which is a clear advantage over other competitive procedures. The method provides small error rates for both simulated and real data. It improves existing approaches and presents good computational behavior.


Time series Supervised classification Integrated periodogram Functional data depth 


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  1. ABRAHAM, C., CORNILLON, P.A., MATZNER-LØBER, E. and MOLINARI, N. (2003), “Unsupervised Curve Clustering Using B-Splines”, Scandinavian Journal of Statistics, 30(3), 581–595.CrossRefzbMATHMathSciNetGoogle Scholar
  2. ALONSO, A.M., CASADO, D., LÓPEZ-PINTADO, S. and ROMO, J. (2008), “A Functional Data Based Method for Time Series Classification”, Working Paper, Departamento de Estadística. Universidad Carlos III deMadrid, available at
  3. BIAU, G., BUNEA, F., andWEGKAMP, M.H. (2003), “Functional Classification in Hilbert Spaces”, IEEE Transactions on Information Theory, 1(11), 1–8.Google Scholar
  4. BLANDFORD, R.R. (1993), “Discrimination of Earthquakes and Explosions at Regional Distances Using Complexity”, Report AFTAC-TR-93-044 HQ, Air Force Technical Applications Center, Patrick Air Force Base, FL.Google Scholar
  5. CASADO, D. (2013), StatisCLAS: Methods for Statistical Classification, Package of code, available at
  6. CHANDLER, G., and POLONIK, W. (2006), “Discrimination of Locally Stationary Time Series Based on the Excess Mass Functional”, Journal of the American Statistical Association, 101(473), 240–253.CrossRefzbMATHMathSciNetGoogle Scholar
  7. CLEVELAND, R.B., CLEVELAND, W.S., MCRAE, J.E., and TERPENNING, I. (1990), “STL: A Seasonal-Trend Decomposition Procedure Based on Loess”, Journal of Official Statistics, 6, 2–73.Google Scholar
  8. DAHLHAUS, R. (1996), “Asymptotic Statistical Inference for Nonstationary Processes with Evolutionary Spectra”, in Athens Conference on Applied Probability and Time Series Analysis, eds. P.M. Robinson and M. Rosenblatt, New York: Springer.Google Scholar
  9. DAHLHAUS, R. (1997), “Fitting Time Series Models to Nonstationary Processes”, The Annals of Statistics, 25(1), 1–37.CrossRefzbMATHMathSciNetGoogle Scholar
  10. DIGGLE, P.J., and FISHER, N.I. (1991), “Nonparametric Comparison of Cumulative Periodograms”, Journal of the Royal Statistical Society, Series C (Applied Statistics), 40(3), 423–434.zbMATHMathSciNetGoogle Scholar
  11. FERRATY, F., and VIEU, P. (2003), “Curves Discrimination: A Nonparametric Functional Approach”, Computational Statistics and Data Analysis, 44, 161–173.CrossRefzbMATHMathSciNetGoogle Scholar
  12. HALL, P., POSKITT, D.S., and PRESNELL, B. (2001), “A Functional Data-Analytic Approach to Signal Discrimination”, Technometrics, 43(1), 1–9.CrossRefzbMATHMathSciNetGoogle Scholar
  13. HASTIE, T., BUJA, A., and TIBSHIRANI, R.J. (1995), “Penalized Discriminant Analysis”, The Annals of Statistics, 23(1), 73–102.CrossRefzbMATHMathSciNetGoogle Scholar
  14. HIRUKAWA, J. (2004), “Discriminant Analysis for Multivariate Non-Gaussian Locally Stationary Processes”, Scientiae Mathematicae Japonicae, 60(2), 357–380.zbMATHMathSciNetGoogle Scholar
  15. HODRICK, R., and PRESCOTT, E.C. (1997), “Postwar U.S. Business Cycles: An Empirical Investigation”, Journal of Money, Credit, and Banking, 29(1), 1–16.CrossRefGoogle Scholar
  16. HUANG, H., OMBAO, H. and STOFFER, D.S. (2004), “Discrimination and Classification of Nonstationary Time Series Using the SLEX Model”, Journal of the American Statistical Association, 99(467), 763–774.CrossRefzbMATHMathSciNetGoogle Scholar
  17. JAMES, G.M., and HASTIE, T. (2001), “Functional Linear Discriminant Analysis for Irregularly Sampled Curves”, Journal of the Royal Statistical Society, Series B, 63, 533–550.CrossRefzbMATHMathSciNetGoogle Scholar
  18. JAMES, G.M., and SUGAR, C.A. (2003), “Clustering for Sparsely Sampled Functional Data”, Journal of the American Statistical Association, 98(462), 397–408.CrossRefzbMATHMathSciNetGoogle Scholar
  19. KAKIZAWA, Y., SHUMWAY, R.H., and TANIGUCHI, M. (1998), “Discrimination and Clustering for Multivariate Time Series”, Journal of the American Statistical Association, 93(441), 328–340.CrossRefzbMATHMathSciNetGoogle Scholar
  20. LIAO, T.W. (2005), “Clustering of Time Series Data Survey”, Pattern Recognition, 38, 1857–1874.CrossRefzbMATHGoogle Scholar
  21. LÓPEZ-PINTADO, S., and ROMO, J. (2006), “Depth-Based Classification for Functional Data”, DIMACS Series in Discrete Mathematics and Theoretical Computer Science (Vol. 72), Providence RI: American Mathematical Society.Google Scholar
  22. LÓPEZ-PINTADO, S., and ROMO, J. (2009), “On the Concept of Depth for Functional Data”, Journal of the American Statistical Association, 104(486), 704–717.CrossRefMathSciNetGoogle Scholar
  23. MAHARAJ, E.A., and ALONSO, A.M. (2007), “Discrimination of Locally Stationary Time Series Using Wavelets”, Computational Statistics and Data Analysis, 52, 879–895.CrossRefzbMATHMathSciNetGoogle Scholar
  24. OMBAO, H.C., RAZ, J.A., VON SACHS, R., and MALOW, B.A. (2001), “Automatic Statistical Analysis of Bivariate Nonstationary Time Series”, Journal of the American Statistical Association, 96(454), 543–560.CrossRefzbMATHMathSciNetGoogle Scholar
  25. PRIESTLEY, M. (1981), Spectral Analysis and Time Series. Volume 1: Univariate Series, London: Academic Press, Inc.zbMATHGoogle Scholar
  26. SAKIYAMA, K., and TANIGUCHI, M. (2004), “Discriminant Analysis for Locally Stationary Processes”, Journal of Multivariate Analysis, 90, 282–300.CrossRefzbMATHMathSciNetGoogle Scholar
  27. SHUMWAY, R.S. (2003), “Time-Frequency Clustering and Discriminant Analysis”, Statistics & Probability Letters, 63, 307–314.CrossRefzbMATHMathSciNetGoogle Scholar
  28. SHUMWAY, R.H., and STOFFER, D.S. (2000), Time Series Analysis and Its Applications, New York: Springer.CrossRefzbMATHGoogle Scholar
  29. TANIGUCHI, M., and KAKIZAWA, Y. (2000), Asymptotic Theory of Statistical Inference for Time Series, New York: Springer.CrossRefzbMATHGoogle Scholar

Copyright information

© Classification Society of North America 2014

Authors and Affiliations

  • Andrés M. Alonso
    • 1
    • 2
  • David Casado
    • 3
  • Sara López-Pintado
    • 4
  • Juan Romo
    • 1
  1. 1.Universidad Carlos III de MadridMadridSpain
  2. 2.INAECUMadridSpain
  3. 3.Universidad Complutense de MadridMadridSpain
  4. 4.Columbia UniversityNew YorkUSA

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