IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v19y2017i3d10.1007_s11009-016-9528-1.html
   My bibliography  Save this article

Clustering Nonlinear, Nonstationary Time Series Using BSLEX

Author

Listed:
  • Jane L. Harvill

    (Baylor University)

  • Priya Kohli

    (Connecticut College)

  • Nalini Ravishanker

    (University of Connecticut)

Abstract

Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.

Suggested Citation

  • Jane L. Harvill & Priya Kohli & Nalini Ravishanker, 2017. "Clustering Nonlinear, Nonstationary Time Series Using BSLEX," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 935-955, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9528-1
    DOI: 10.1007/s11009-016-9528-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9528-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-016-9528-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Juárez, Miguel A. & Steel, Mark F. J., 2010. "Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 52-66.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. L. Bauwens & J. V. K. Rombouts, 2007. "Bayesian Clustering of Many Garch Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 365-386.
    4. Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
    5. Bohm, Hilmar & Ombao, Hernando & von Sachs, Rainer & Sanes, J., 2010. "Classification of multivariate non-stationary signals : the SLEX-shrinkage approach," LIDAM Reprints ISBA 2010036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    7. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    8. Richard A. Ashley & Douglas M. Patterson & Melvin J. Hinich, 1986. "A Diagnostic Test For Nonlinear Serial Dependence In Time Series Fitting Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 165-178, May.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Heard, Nicholas A. & Holmes, Christopher C. & Stephens, David A., 2006. "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 18-29, March.
    11. 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.
    12. Fruhwirth-Schnatter, Sylvia & Kaufmann, Sylvia, 2008. "Model-Based Clustering of Multiple Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 78-89, January.
    13. Corduas, Marcella & Piccolo, Domenico, 2008. "Time series clustering and classification by the autoregressive metric," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1860-1872, January.
    14. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    15. 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.
    16. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Harvill, Jane L. & Ravishanker, Nalini & Ray, Bonnie K., 2013. "Bispectral-based methods for clustering time series," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 113-131.
    2. Sylvia Frühwirth-Schnatter, 2011. "Panel data analysis: a survey on model-based clustering of time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 251-280, December.
    3. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    5. J. Fernando Vera & Rodrigo Macías, 2021. "On the Behaviour of K-Means Clustering of a Dissimilarity Matrix by Means of Full Multidimensional Scaling," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 489-513, June.
    6. Last, Michael & Shumway, Robert, 2008. "Detecting abrupt changes in a piecewise locally stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 191-214, February.
    7. Yi Peng & Yong Zhang & Gang Kou & Yong Shi, 2012. "A Multicriteria Decision Making Approach for Estimating the Number of Clusters in a Data Set," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    8. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    9. Z. Volkovich & Z. Barzily & G.-W. Weber & D. Toledano-Kitai & R. Avros, 2012. "An application of the minimal spanning tree approach to the cluster stability problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 119-139, March.
    10. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    11. Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.
    12. Ahn, Eun S. & Lee, Jin Man, 2012. "The Performance Of Nonlinearity Tests On Asymmetric Nonlinear Time Series," The Journal of Economic Asymmetries, Elsevier, vol. 9(2), pages 11-44.
    13. Koltcov, Sergei, 2018. "Application of Rényi and Tsallis entropies to topic modeling optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1192-1204.
    14. Małgorzata Just & Aleksandra Łuczak, 2020. "Assessment of Conditional Dependence Structures in Commodity Futures Markets Using Copula-GARCH Models and Fuzzy Clustering Methods," Sustainability, MDPI, vol. 12(6), pages 1-22, March.
    15. Pietro Coretto & Michele La Rocca & Giuseppe Storti, 2020. "Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters," JRFM, MDPI, vol. 13(4), pages 1-23, March.
    16. Robert Darkins & Emma J Cooke & Zoubin Ghahramani & Paul D W Kirk & David L Wild & Richard S Savage, 2013. "Accelerating Bayesian Hierarchical Clustering of Time Series Data with a Randomised Algorithm," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-9, April.
    17. Lingsong Meng & Dorina Avram & George Tseng & Zhiguang Huo, 2022. "Outcome‐guided sparse K‐means for disease subtype discovery via integrating phenotypic data with high‐dimensional transcriptomic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 352-375, March.
    18. Burghardt, Elliot & Sewell, Daniel & Cavanaugh, Joseph, 2022. "Agglomerative and divisive hierarchical Bayesian clustering," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    19. Fujita, André & Takahashi, Daniel Y. & Patriota, Alexandre G., 2014. "A non-parametric method to estimate the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 27-39.
    20. Zhelin Huang & Ngai Hang Chan, 2020. "Walsh Fourier Transform of Locally Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 312-340, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9528-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.