Advertisement

Journal of Mathematical Sciences

, Volume 237, Issue 6, pp 754–765 | Cite as

VAR Model Based Clustering Method for Multivariate Time Series Data

Article
  • 1 Downloads

In this study, we develop a clustering method for multivariate time series data. In practical situations, such problems can arise in finance, economics, control theory, and health science. First, we propose to use a simulation based approximation to the test statistic and develop a method to test if two multivariate time series are coming from same VAR process. Then, the testing method is extended to a group of multivariate time series objects. Finally, a new clustering algorithm is developed using the testing method. The proposed algorithm does not use a predetermined number of clusters and finds the best possible clustering from the data. Empirical studies are provided in this paper, and they establish the accuracy of the algorithm. Finally, as a practical example, the algorithm is implemented to identify activities of different persons from a real-life data obtained from single chest-mounted accelerometers worn by different individuals.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Abraham, P. A. Cornillon, E. Matzner-Løber, and N. Molinari, “Unsupervised curve clustering using B-splines,” Scand. J. Stat., 30, No. 3, 581–595 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. Antoniadis, J. Bigot, and R. von Sachs, “A multiscale approach for statistical characterization of functional images,” J. Comput. Graph. Stat., 18, No. 1, 216–237 (2009).MathSciNetCrossRefGoogle Scholar
  3. 3.
    L. Bao and S. Intille, “Activity recognition from user-annotated acceleration data,” Pervasive Computing, 1–17 (2004).Google Scholar
  4. 4.
    P. Bloomfield, Fourier Analysis of Time Series: An Introduction, John Wiley & Sons, New York (2004).zbMATHGoogle Scholar
  5. 5.
    G. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time Series Analysis: Forecasting and Control, John Wiley and Sons, New York (2015).zbMATHGoogle Scholar
  6. 6.
    P. Casale, P. Pujol, and P. Radeva, “Personalization and user verification in wearable systems using biometric walking patterns,” Persow. Ubiq. Comput., 16, No. 5, 563–580 (2012).CrossRefGoogle Scholar
  7. 7.
    J.-M. Chiou and P.-L. Li, “Functional clustering and identifying substructures of longitudinal data,” J. R. Stat. Soc. Ser. B, 69, No. 4, 679–699 (2007).MathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Degras, Z. Xu, T. Zhang, and W. B. Wu, “Testing for parallelism among trends in multiple time series,” IEEE Trans. Signal Process., 60, No. 3, 1087–1097 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    A. P. Dempster, N. M. Laird, and D. B. Rubin. “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B, 39, No. 1, 1–38 (1977).MathSciNetzbMATHGoogle Scholar
  10. 10.
    D.A. Dickey and W.A. Fuller, “Distribution of the estimators for autoregressive time series with a unit root,” J. Am. Stat. Assoc., 74, No. 366a, 427–431 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Z. Gao, Y. Yang, P. Fang, Y. Zou, C. Xia, and M. Du, “Multiscale complex network for analyzing experimental multivariate time series,” Europhys. Let., 109, No. 3, 30005 (2015).CrossRefGoogle Scholar
  12. 12.
    L. A. Garcia-Escudero and A. Gordaliza, “A proposal for robust curve clustering,” J. Classif., 22, No. 2, 185–201 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    P. Hall, Y. K. Lee, and B. U. Park, “A method for projecting functional data onto a low-dimensional space,” J. Comput. Graph. Stat., 16, No. 4, 799–812 (2007).MathSciNetCrossRefGoogle Scholar
  14. 14.
    J.D. Hamilton, Time Series Analysis, Vol. 2, Princeton University Press, Princeton (1994).zbMATHGoogle Scholar
  15. 15.
    H. Izakian, W. Pedrycz, and I. Jamal, “Fuzzy clustering of time series data using dynamic time warping distance,” Eng. Appl. Artif. Intell., 39, 235–244 (2015).CrossRefGoogle Scholar
  16. 16.
    Y. Kakizawa, R. H. Shumway, and M. Taniguchi, “Discrimination and clustering for multivariate time series,” J. Am. Stat. Assoc., 93, No. 441, 328–340 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    T. W. Liao, “Clustering of time series data — a survey,” Pattern Recognit., 38, No. 11, 1857–1874 (2005).CrossRefzbMATHGoogle Scholar
  18. 18.
    S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inform. Theor., 28, No. 2, 129–137 (1982).MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    H. Lütkepohl, New Introduction to Multiple Time Series Aanalysis, Springer, New York (2005).CrossRefzbMATHGoogle Scholar
  20. 20.
    J. MacQueen, “Some methods for classification and analysis of multivariate observations,” in: Proc. Fifth Berkeley Sympos. Math. Stat. and Probability, Vol. I: Statistics, University of California Press, Berkeley (1967), pp. 281–297.Google Scholar
  21. 21.
    A. Mannini and A.M. Sabatini, “Machine learning methods for classifying human physical activity from on-body accelerometers,” Sensors, 10, No. 2, 1154–1175 (2010).CrossRefGoogle Scholar
  22. 22.
    T. Oates, L. Firoiu, and P. Cohen, “Clustering time series with hidden Markov models and dynamic time warping,” in: Proceedings of the IJCAI-99 Workshop on Neural, Symbolic and Reinforcement Learning Methods for Sequence Learning, Stockholm (1999), pp. 17–21.Google Scholar
  23. 23.
    T. Santos and R. Kern, “A literature survey of early time series classification and deep learning,” SAMI@ iKNOW (2016).Google Scholar
  24. 24.
    A. Singhal and D. E. Seborg, “Clustering multivariate time-series data,” J. Chemomet., 19, No. 8, 427–438 (2005).CrossRefGoogle Scholar
  25. 25.
    P. Smyth et al., “Clustering sequences with hidden Markov models,” Adv. Neur. Inform. Process Syst., 648–654 (1997).Google Scholar
  26. 26.
    T. Tarpey and K. K. J. Kinateder, “Clustering functional data,” J. Classif., 20, No. 1, 93–114 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    J. H. Ward Jr., “Hierarchical grouping to optimize an objective function,” J. Am. Stat. Assoc., 58, 236–244 (1963).MathSciNetCrossRefGoogle Scholar
  28. 28.
    W. B. Wu, “Nonlinear system theory: Another look at dependence,” Proc. Natl. Acad. Sci. USA, 102, No. 40, 14150–14154 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    K. Yang and C. Shahabi, “A PCA-based similarity measure for multivariate time series,” in: Proceedings of the 2nd ACM International Workshop on Multimedia Databases, ACM (2004), pp. 65–74.Google Scholar
  30. 30.
    T. Zhang, “Clustering high-dimensional time series based on parallelism,” J. Am. Stat. Assoc., 108, No. 502, 577–588 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    E. Zivot and J. Wang, “Vector autoregressive models for multivariate time series,” Modeling Financial Time Series with S-PLUS, 385–429 (2006).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ChicagoChicagoUSA

Personalised recommendations