Log in

Trimmed fuzzy clustering of financial time series based on dynamic time war**

  • S.I.: Recent Developments in Financial Modeling and Risk Management
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In finance, cluster analysis is a tool particularly useful for classifying stock market multivariate time series data related to daily returns, volatility daily stocks returns, commodity prices, volume trading, index, enhanced index tracking portfolio, and so on. In the literature, following different methodological approaches, several clustering methods have been proposed for clustering multivariate time series. In this paper by adopting a fuzzy approach and using the Partitioning Around Medoids strategy, we suggest to cluster multivariate financial time series by considering the dynamic time war** distance. In particular, we proposed a robust clustering method capable to neutralize the negative effects of possible outliers in the clustering process. The clustering method achieves its robustness by adopting a suitable trimming procedure to identify multivariate financial time series more distant from the bulk of data. The proposed clustering method is applied to the stocks composing the FTSE MIB index to identify common time patterns and possible outliers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. http://finance.yahoo.com.

  2. Results are available upon request.

References

  • Anderson, D. T., Bezdek, J. C., Popescu, M., & Keller, J. M. (2010). Comparing fuzzy, probabilistic, and possibilistic partitions. IEEE Transactions on Fuzzy Systems, 18(5), 906–918.

    Google Scholar 

  • Ando, T., & Bai, J. (2017). Clustering huge number of financial time series: A panel data approach with high-dimensional predictors and factor structures. Journal of the American Statistical Association, 112(519), 1182–1198.

    Google Scholar 

  • Aslan, S., Yozgatligil, C., & Iyigun, C. (2018). Temporal clustering of time series via threshold autoregressive models: Application to commodity prices. Annals of Operations Research, 260(1–2), 51–77.

    Google Scholar 

  • Basalto, N., Bellotti, R., De Carlo, F., Facchi, P., Pantaleo, E., & Pascazio, S. (2007). Hausdorff clustering of financial time series. Physica A: Statistical Mechanics and its Applications, 379(2), 635–644.

    Google Scholar 

  • Basalto, N., Bellotti, R., De Carlo, F., Facchi, P., Pantaleo, E., & Pascazio, S. (2008). Hausdorff clustering. Physical Review E, 78(4), 046112.

    Google Scholar 

  • Bastos, J. A., & Caiado, J. (2014). Clustering financial time series with variance ratio statistics. Quantitative Finance, 14(12), 2121–2133.

    Google Scholar 

  • Berndt, D.J., & Clifford, J. (1994). Using dynamic time war** to find patterns in time series. In Proceedings of the AAAI-94 workshop knowledge discovery in databases (pp. 359–370). Seattle, WA.

  • Caiado, J., & Crato, N. (2007). A GARCH-based method for clustering of financial time series: International stock markets evidence. In C. Skiadas (Ed.), Recent Advances in Stochastic Modeling and Data Analysis (pp. 542–551). Singapore: World Scientific.

    Google Scholar 

  • Campello, R. J. G. B., & Hruschka, E. R. (2006). A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Sets and Systems, 157, 2858–2875.

    Google Scholar 

  • Chang, S.-L., Chien, C.-Y., Lee, H.-C., & Lin, C. (2018). Historical high and stock index returns: Application of the regression kink model. Journal of International Financial Markets, Institutions and Money, 52, 48–63.

    Google Scholar 

  • Davé, R. N., & Krishnapuram, R. (1997). Robust clustering methods: A unified view. IEEE Transactions on Fuzzy Systems, 5(2), 270–293.

    Google Scholar 

  • De Gregorio, A., & Iacus, S. M. (2010). Clustering of discretely observed diffusion processes. Computational Statistics & Data Analysis, 54(2), 598–606.

    Google Scholar 

  • De Luca, G., & Zuccolotto, P. (2011). A tail dependence-based dissimilarity measure for financial time series clustering. Advances in Data Analysis and Classification, 5(4), 323–340.

    Google Scholar 

  • De Luca, G., & Zuccolotto, P. (2017). A double clustering algorithm for financial time series based on extreme events. Statistics & Risk Modeling, 34(1–2), 1–12.

    Google Scholar 

  • Degiannakis, S., & Floros, C. (2016). Intra-day realized volatility for European and USA stock indices. Global Finance Journal, 29, 24–41.

    Google Scholar 

  • Dias, J. G., Vermunt, J. K., & Ramos, S. (2015). Clustering financial time series: New insights from an extended hidden Markov model. European Journal of Operational Research, 243(3), 852–864.

    Google Scholar 

  • Dose, C., & Cincotti, S. (2005). Clustering of financial time series with application to index and enhanced index tracking portfolio. Physica A: Statistical Mechanics and its Applications, 355(1), 145–151.

    Google Scholar 

  • Durante, F., Pappadà, R., & Torelli, N. (2014). Clustering of financial time series in risky scenarios. Advances in Data Analysis and Classification, 8(4), 359–376.

    Google Scholar 

  • D’Urso, P. (2000). Dissimilarity measures for time trajectories. Statistical Methods & Applications, 9(1–3), 53–83.

    Google Scholar 

  • D’Urso, P. (2004). Fuzzy C-Means clustering models for multivariate time-varying data: Different approaches. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03), 287–326.

    Google Scholar 

  • D’Urso, P. (2005). Fuzzy clustering for data time arrays with inlier and outlier time trajectories. IEEE Transactions on Fuzzy Systems, 13(5), 583–604.

    Google Scholar 

  • D’Urso, P., Cappelli, C., Di Lallo, D., & Massari, R. (2013). Clustering of financial time series. Physica A: Statistical Mechanics and its Applications, 392(9), 2114–2129.

    Google Scholar 

  • D’Urso, P., De Giovanni, L., & Massari, R. (2016). GARCH-based robust clustering of time series. Fuzzy Sets and Systems, 305, 1–28.

    Google Scholar 

  • D’Urso, P., De Giovanni, L., & Massari, R. (2018). Robust fuzzy clustering of multivariate time trajectories. International Journal of Approximate Reasoning, 99, 12–38.

    Google Scholar 

  • D’Urso, P., Massari, R., Cappelli, C., & De Giovanni, L. (2017). Autoregressive metric-based trimmed fuzzy clustering with an application to \(\text{ PM }_{10}\) time series. Chemometrics and Intelligent Laboratory Systems, 161, 15–26.

    Google Scholar 

  • García-Escudero, L. Á., & Gordaliza, A. (1999). Robustness properties of k means and trimmed k means. Journal of the American Statistical Association, 94, 956–969.

    Google Scholar 

  • García-Escudero, L. A., Gordaliza, A., & Matrán, C. (2003). Trimming tools in exploratory data analysis. Journal of Computational and Graphical Statistics, 12, 434–449.

    Google Scholar 

  • García-Escudero, L. A., Gordaliza, A., Matrán, C., & Mayo-Iscar, A. (2010). A review of robust clustering methods. Advances in Data Analysis and Classification, 4, 89–109.

    Google Scholar 

  • Giorgino, T., et al. (2009). Computing and visualizing dynamic time war** alignments in R: The dtw package. Journal of Statistical Software, 31(7), 1–24.

    Google Scholar 

  • Hennig, C., et al. (2008). Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods. Journal of Multivariate Analysis, 99(6), 1154–1176.

    Google Scholar 

  • Iglesias, E. M. (2015). Value at Risk and expected shortfall of firms in the main European Union stock market indexes: A detailed analysis by economic sectors and geographical situation. Economic Modelling, 50, 1–8.

    Google Scholar 

  • Izakian, H., Pedrycz, W., & Jamal, I. (2015). Fuzzy clustering of time series data using dynamic time war** distance. Engineering Applications of Artificial Intelligence, 39, 235–244.

    Google Scholar 

  • Kamdar, T., & Joshi, A. (2000). On creating adaptive Web servers using Weblog Mining. Technical report TR-CS- 00-05, Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County.

  • Lafuente-Rego, B., D’Urso, P., & Vilar, J. (in press 2019). Robust fuzzy clustering based on quantile autocovariances. Statistical Papers.

  • Lai, R. K., Fan, C.-Y., Huang, W.-H., & Chang, P.-C. (2009). Evolving and clustering fuzzy decision tree for financial time series data forecasting. Expert Systems with Applications, 36(2), 3761–3773.

    Google Scholar 

  • Liu, Q., & Tse, Y. (2017). Overnight returns of stock indexes: Evidence from ETFs and futures. International Review of Economics & Finance, 48, 440–451.

    Google Scholar 

  • Maharaj, E. A., D’Urso, P., & Caiado, J. (2019). Time series clustering and classification. Boca Raton: CRC Press.

    Google Scholar 

  • Maharaj, E. A., D’Urso, P., & Galagedera, D. U. (2010). Wavelet-based fuzzy clustering of time series. Journal of Classification, 27(2), 231–275.

    Google Scholar 

  • McBratney, A., & Moore, A. (1985). Application of fuzzy sets to climatic classification. Agricultural and Forest Meteorology, 35(1–4), 165–185.

    Google Scholar 

  • Menardi, G., & Lisi, F. (2015). Double clustering for rating mutual funds. Electronic Journal of Applied Statistical Analysis, 8(1), 44–56.

    Google Scholar 

  • Nair, B. B., Kumar, P. S., Sakthivel, N., & Vipin, U. (2017). Clustering stock price time series data to generate stock trading recommendations: An empirical study. Expert Systems with Applications, 70, 20–36.

    Google Scholar 

  • Nakagawa, K., Imamura, M., & Yoshida, K. (2019). Stock price prediction using k-medoids clustering with indexing dynamic time war**. Electronics and Communications in Japan, 102, 3–8.

    Google Scholar 

  • Okeke, F., & Karnieli, A. (2006). Linear mixture model approach for selecting fuzzy exponent value in fuzzy c-means algorithm. Ecological Informatics, 1(1), 117–124.

    Google Scholar 

  • Pattarin, F., Paterlini, S., & Minerva, T. (2004). Clustering financial time series: An application to mutual funds style analysis. Computational Statistics & Data Analysis, 47(2), 353–372.

    Google Scholar 

  • Piccardi, C., Calatroni, L., & Bertoni, F. (2011). Clustering financial time series by network community analysis. International Journal of Modern Physics C, 22(01), 35–50.

    Google Scholar 

  • Rahmanishamsi, J., Dolati, A., & Aghabozorgi, M. R. (2018). A copula based ICA algorithm and its application to time series clustering. Journal of Classification, 35(2), 230–249.

    Google Scholar 

  • Ratanamahatana, C. A., & Keogh, E. (2004). Everything you know about dynamic time war** is wrong. In Third workshop on mining temporal and sequential data. Citeseer.

  • Rechenthin, M., Street, W. N., & Srinivasan, P. (2013). Stock chatter: Using stock sentiment to predict price direction. Algorithmic Finance, 2(3–4), 169–196.

    Google Scholar 

  • Velichko, V., & Zagoruyko, N. (1970). Automatic recognition of 200 words. International Journal of Man-Machine Studies, 2(3), 223–234.

    Google Scholar 

  • Vilar, J. A., Lafuente-Rego, B., & D’Urso, P. (2018). Quantile autocovariances: A powerful tool for hard and soft partitional clustering of time series. Fuzzy Sets and Systems, 340, 38–72.

    Google Scholar 

  • Vilar, J. M., Vilar, J. A., & Pértega, S. (2009). Classifying time series data: A nonparametric approach. Journal of classification, 26(1), 3–28.

    Google Scholar 

  • Wedel, M., & Steenkamp, J. (1989). A fuzzy clusterwise regression approach to benefit segmentation. International Journal of Research in Marketing, 6(4), 241–258.

    Google Scholar 

  • **e, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis & Machine Intelligence, 13(8), 841–847.

    Google Scholar 

  • Yang, C., Jiang, W., Wu, J., Liu, X., & Li, Z. (2018). Clustering of financial instruments using jump tail dependence coefficient. Statistical Methods & Applications, 27(3), 491–513.

    Google Scholar 

Download references

Acknowledgements

The authors thank Editor-in-Chief, and the referees for their useful comments and suggestions which helped to improve the quality and presentation of this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Riccardo Massari.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

D’Urso, P., De Giovanni, L. & Massari, R. Trimmed fuzzy clustering of financial time series based on dynamic time war**. Ann Oper Res 299, 1379–1395 (2021). https://doi.org/10.1007/s10479-019-03284-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03284-1

Keywords

Navigation