Trimmed fuzzy clustering of financial time series based on dynamic time warping

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 warping 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.

[1]  N. R. Sakthivel,et al.  Clustering stock price time series data to generate stock trading recommendations: An empirical study , 2017, Expert Syst. Appl..

[2]  Alex B. McBratney,et al.  Application of fuzzy sets to climatic classification , 1985 .

[3]  Luis Angel García-Escudero,et al.  Trimming Tools in Exploratory Data Analysis , 2003 .

[4]  Fabrizio Durante,et al.  Clustering of financial time series in risky scenarios , 2013, Advances in Data Analysis and Classification.

[5]  Pierpaolo D'Urso,et al.  Fuzzy Clustering for Data Time Arrays With Inlier and Outlier Time Trajectories , 2005, IEEE Transactions on Fuzzy Systems.

[6]  Toni Giorgino,et al.  Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package , 2009 .

[7]  Ricardo J. G. B. Campello,et al.  A fuzzy extension of the silhouette width criterion for cluster analysis , 2006, Fuzzy Sets Syst..

[8]  B. Lafuente-Rego,et al.  Robust fuzzy clustering based on quantile autocovariances , 2018, Statistical Papers.

[9]  Sandra Paterlini,et al.  Clustering financial time series: an application to mutual funds style analysis , 2004, Comput. Stat. Data Anal..

[10]  Stefano Maria Iacus,et al.  Clustering of discretely observed diffusion processes , 2010, Comput. Stat. Data Anal..

[11]  Elizabeth Ann Maharaj,et al.  Time Series Clustering and Classification , 2019 .

[12]  Silvano Cincotti,et al.  Clustering of financial time series with application to index and enhanced index tracking portfolio , 2005 .

[13]  Paola Zuccolotto,et al.  A double clustering algorithm for financial time series based on extreme events , 2016 .

[14]  Pierpaolo D'Urso,et al.  Quantile autocovariances: A powerful tool for hard and soft partitional clustering of time series , 2017, Fuzzy Sets Syst..

[15]  Pierpaolo D'Urso.  Fuzzy C-Means Clustering Models For Multivariate Time-Varying Data: Different Approaches , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[16]  José Antonio Vilar,et al.  Classifying Time Series Data: A Nonparametric Approach , 2009, J. Classif..

[17]  Jorge Caiado,et al.  A GARCH-based method for clustering of financial time series: International stock markets evidence , 2007 .

[18]  Pei-Chann Chang,et al.  Evolving and clustering fuzzy decision tree for financial time series data forecasting , 2009, Expert Syst. Appl..

[19]  Pierpaolo D'Urso,et al.  Dissimilarity measures for time trajectories , 2000 .

[20]  Eamonn J. Keogh,et al.  Everything you know about Dynamic Time Warping is Wrong , 2004 .

[21]  A. Gordaliza,et al.  Robustness Properties of k Means and Trimmed k Means , 1999 .

[22]  Donald J. Berndt,et al.  Using Dynamic Time Warping to Find Patterns in Time Series , 1994, KDD Workshop.

[23]  N. G. Zagoruyko,et al.  Automatic recognition of 200 words , 1970 .

[24]  C. Hennig,et al.  Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods , 2008 .

[25]  Pierpaolo D'Urso,et al.  Clustering of financial time series , 2013 .

[26]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Elizabeth Ann Maharaj,et al.  Wavelet-based Fuzzy Clustering of Time Series , 2010, J. Classif..

[28]  Mitsuyoshi Imamura,et al.  Stock price prediction usingk-medoids clustering with indexing dynamic time warping , 2019, Electronics and Communications in Japan.

[29]  Francesco Lisi,et al.  Double clustering for rating mutual funds , 2015 .

[30]  Carlo Piccardi,et al.  Clustering Financial Time Series by Network Community Analysis , 2011 .

[31]  M. Wedel,et al.  A fuzzy clusterwise regression approach to benefit segmentation , 1989 .

[32]  Shu‐Lien Chang,et al.  Historical high and stock index returns: Application of the regression kink model , 2018 .

[33]  Stavros Degiannakis,et al.  Intra-Day Realized Volatility for European and USA Stock Indices , 2014 .

[34]  James M. Keller,et al.  Comparing Fuzzy, Probabilistic, and Possibilistic Partitions , 2010, IEEE Transactions on Fuzzy Systems.

[35]  Giovanni De Luca,et al.  A tail dependence-based dissimilarity measure for financial time series clustering , 2011, Adv. Data Anal. Classif..

[36]  Roberto Bellotti,et al.  Hausdorff Clustering of Financial Time Series , 2007 .

[37]  Pierpaolo D'Urso,et al.  Autoregressive metric-based trimmed fuzzy clustering with an application to PM10 time series , 2017 .

[38]  Tapan Kamdar,et al.  On Creating Adaptive Web Servers Using Weblog Mining , 2000 .

[39]  Roberto Bellotti.  Hausdorff Clustering , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Tomohiro Ando,et al.  Clustering Huge Number of Financial Time Series: A Panel Data Approach With High-Dimensional Predictors and Factor Structures , 2015 .

[41]  Arnon Karnieli,et al.  Linear mixture model approach for selecting fuzzy exponent value in fuzzy c-means algorithm , 2006, Ecol. Informatics.

[42]  Emma M. Iglesias,et al.  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 , 2015 .

[43]  Cem Iyigun,et al.  Temporal clustering of time series via threshold autoregressive models: application to commodity prices , 2016, Ann. Oper. Res..

[44]  Ali Dolati,et al.  A Copula Based ICA Algorithm and Its Application to Time Series Clustering , 2018, J. Classif..

[45]  Luis Angel García-Escudero,et al.  A review of robust clustering methods , 2010, Adv. Data Anal. Classif..

[46]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[47]  Chen Yang,et al.  Clustering of financial instruments using jump tail dependence coefficient , 2018, Stat. Methods Appl..

[48]  Jorge Caiado,et al.  Clustering financial time series with variance ratio statistics , 2014 .

[49]  Pierpaolo D'Urso,et al.  Robust fuzzy clustering of multivariate time trajectories , 2018, Int. J. Approx. Reason..

[50]  Qingfu Liu,et al.  Overnight returns of stock indexes: Evidence from ETFs and futures ☆ , 2017 .

[51]  Pierpaolo D'Urso,et al.  GARCH-based robust clustering of time series , 2016, Fuzzy Sets Syst..

[52]  Padmini Srinivasan,et al.  Stock Chatter: Using Stock Sentiment to Predict Price Direction , 2013, Algorithmic Finance.

[53]  José G. Dias,et al.  Clustering financial time series: New insights from an extended hidden Markov model , 2015, Eur. J. Oper. Res..

[54]  Witold Pedrycz,et al.  Fuzzy clustering of time series data using dynamic time warping distance , 2015, Eng. Appl. Artif. Intell..