Clustering of financial time series in risky scenarios

A methodology is presented for clustering financial time series according to the association in the tail of their distribution. The procedure is based on the calculation of suitable pairwise conditional Spearman’s correlation coefficients extracted from the series. The performance of the method has been tested via a simulation study. As an illustration, an analysis of the components of the Italian FTSE–MIB is presented. The results could be applied to construct financial portfolios that can manage to reduce the risk in case of simultaneous large losses in several markets.

[1]  R. Engle.  Dynamic Conditional Correlation , 2002 .

[2]  Hans-Hermann Bock.  Special Issue on ‘Time series clustering’ , 2011, Adv. Data Anal. Classif..

[3]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[4]  Friedrich Schmid,et al.  Copula-Based Measures of Multivariate Association , 2010 .

[5]  Giovanni De Luca,et al.  Combining random forest and copula functions: A heuristic approach for selecting assets from a financial crisis perspective , 2010 .

[6]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[7]  Brendan Bradley,et al.  Framework for Analyzing Spatial Contagion between Financial Markets , 2004 .

[8]  Paul Embrechts,et al.  Quantitative Risk Management , 2011, International Encyclopedia of Statistical Science.

[9]  Eike Christian Brechmann,et al.  Hierarchical Kendall copulas: Properties and inference , 2012, 1202.1998.

[10]  Fabrizio Durante,et al.  Spatial contagion between financial markets: a copula-based approach , 2010 .

[11]  Eike Christian Brechmann,et al.  Handbook on Systemic Risk: Statistical Assessments of Systemic Risk Measures , 2013 .

[12]  Fabrizio Durante,et al.  A Spatial Contagion Test for Financial Markets , 2012, SMPS.

[13]  Fabrizio Durante,et al.  Copula Theory and Its Applications , 2010 .

[14]  Piotr Jaworski,et al.  On spatial contagion and multivariate GARCH models , 2014 .

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

[16]  Fabrizio Durante,et al.  An Analysis of the Dependence Among Financial Markets by Spatial Contagion , 2013, Int. J. Intell. Syst..

[17]  Marcella Corduas,et al.  Time series clustering and classification by the autoregressive metric , 2008, Comput. Stat. Data Anal..

[18]  D. Michele Cifarelli,et al.  Bruno de Finetti , 2007 .

[19]  Monica Billio,et al.  Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation , 2006 .

[20]  Umberto Cherubini,et al.  Dynamic Copula Methods in Finance: Cherubini/Dynamic , 2011 .

[21]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[22]  R. Rigobón,et al.  No Contagion, Only Interdependence: Measuring Stock Market Comovements , 2002 .

[23]  Edoardo Otranto.  Clustering heteroskedastic time series by model-based procedures , 2008, Comput. Stat. Data Anal..

[24]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[25]  C. Sempi,et al.  Copula Theory: An Introduction , 2010 .

[26]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[27]  Fabrizio Durante,et al.  Copulae in Mathematical and Quantitative Finance , 2013 .

[28]  Andrew J. Patton.  Copula Methods for Forecasting Multivariate Time Series , 2013 .

[29]  P. Embrechts.  CONCEPTS, TECHNIQUES AND TOOLS , 2004 .

[30]  Monica Billio,et al.  A Generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation , 2006, Math. Comput. Simul..

[31]  Luca De Angelis.  Latent class models for financial data analysis: some statistical developments , 2013, Stat. Methods Appl..

[32]  Xiaohong Chen,et al.  Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification , 2006 .

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

[34]  B. Everitt.  Unresolved Problems in Cluster Analysis , 1979 .

[35]  Claudia Czado,et al.  Pair-Copula Constructions of Multivariate Copulas , 2010 .

[36]  B. Rémillard.  Goodness-of-Fit Tests for Copulas of Multivariate Time Series , 2010 .

[37]  Andrew J. Patton.  A review of copula models for economic time series , 2012, J. Multivar. Anal..

[38]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[39]  Fabrizio Lillo,et al.  Cluster analysis for portfolio optimization , 2005, physics/0507006.

[40]  M. Rockinger,et al.  The Copula-GARCH model of conditional dependencies: An international stock market application , 2006 .

[41]  G. Caldarelli,et al.  Networks of equities in financial markets , 2004 .

[42]  Claudia Czado,et al.  Statistical Assessments of Systemic Risk Measures , 2012 .

[43]  Catherine Dehon,et al.  Influence functions of the Spearman and Kendall correlation measures , 2010, Stat. Methods Appl..

[44]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1990 .

[45]  Friedrich Schmid,et al.  Multivariate conditional versions of Spearman's rho and related measures of tail dependence , 2007 .

[46]  Juan Gabriel Brida,et al.  Hierarchical Structure of the German Stock Market , 2007, Expert Syst. Appl..

[47]  Umberto Cherubini,et al.  Dynamic Copula Methods in Finance , 2011 .

[48]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[49]  W. Härdle,et al.  Applied Multivariate Statistical Analysis , 2003 .

[50]  Charu C. Aggarwal.  An Introduction to Cluster Analysis , 2013, Data Clustering: Algorithms and Applications.

[51]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .

[52]  R. Nelsen.  An Introduction to Copulas (Springer Series in Statistics) , 2006 .

[53]  A Gordon,et al.  Classification, 2nd Edition , 1999 .

[54]  J. Fouque,et al.  Handbook on Systemic Risk: Contributors , 2013 .

[55]  Elizabeth Ann Maharaj,et al.  Time-Series Clustering , 2015 .

[56]  Friedrich Schmid,et al.  Dependence of Stock Returns in Bull and Bear Markets , 2010 .

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

[58]  Jorge Caiado,et al.  Identifying common dynamic features in stock returns , 2010 .

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

[60]  G. W. Milligan,et al.  An examination of procedures for determining the number of clusters in a data set , 1985 .

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