Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.

[1]  Wen-Gang Che,et al.  Fuzzy time series forecasting for RMB's exchange rate based on FCM , 2010, Proceedings of the 29th Chinese Control Conference.

[2]  P. Cizeau,et al.  Statistical properties of the volatility of price fluctuations. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  D. Piccolo.  A DISTANCE MEASURE FOR CLASSIFYING ARIMA MODELS , 1990 .

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

[5]  Peter J. Rousseeuw,et al.  Clustering by means of medoids , 1987 .

[6]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[7]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[8]  Pierpaolo D'Urso,et al.  Fuzzy C-medoids clustering models for time-varying data , 2006 .

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

[10]  H. E. Stanley,et al.  Comparison between volatility return intervals of the S&P 500 index and two common models , 2008 .

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

[12]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

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

[14]  Elizabeth Ann Maharaj,et al.  A coherence-based approach for the pattern recognition of time series , 2010 .

[15]  Elizabeth Ann Maharaj,et al.  Cluster of Time Series , 2000, J. Classif..

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

[17]  Anupam Joshi,et al.  Low-complexity fuzzy relational clustering algorithms for Web mining , 2001, IEEE Trans. Fuzzy Syst..

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

[19]  R. Cont.  Empirical properties of asset returns: stylized facts and statistical issues , 2001 .

[20]  Ivo Grosse,et al.  ARCH–GARCH approaches to modeling high-frequency financial data , 2004 .

[21]  T. Warren Liao,et al.  Clustering of time series data - a survey , 2005, Pattern Recognit..

[22]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[23]  Pierpaolo D’Urso,et al.  Autocorrelation-based fuzzy clustering of time series , 2009, Fuzzy Sets Syst..

[24]  Thomas A. Runkler,et al.  Alternating cluster estimation: a new tool for clustering and function approximation , 1999, IEEE Trans. Fuzzy Syst..

[25]  Ivo Grosse,et al.  Time-lag cross-correlations in collective phenomena , 2010 .

[26]  Rosario N. Mantegna,et al.  Modeling of financial data: Comparison of the truncated Lévy flight and the ARCH(1) and GARCH(1,1) processes , 1998 .

[27]  H. Stanley,et al.  Cross-correlations between volume change and price change , 2009, Proceedings of the National Academy of Sciences.

[28]  Fabrizio Durante,et al.  Clustering of financial time series in extreme scenarios , 2012 .

[29]  H. Stanley,et al.  Linking agent-based models and stochastic models of financial markets , 2012, Proceedings of the National Academy of Sciences.

[30]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[31]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[32]  C. Granger,et al.  Varieties of long memory models , 1996 .

[33]  Kevin James Daly,et al.  Financial volatility : issues and measuring techniques , 2008 .

[34]  Asset returns and volatility clustering in financial time series , 2010, 1002.0284.

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

[36]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

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

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