A GARCH-based method for clustering of financial time series: International stock markets evidence

Caiado, Jorge and Crato, Nuno (2007): A GARCH-based method for clustering of financial time series: International stock markets evidence. Forthcoming in: Proceedings of the XIIth Applied Stochastic Models and Data Analysis International Conference

Abstract

In this paper, we introduce a volatility-based method for clustering analysis of financial time series. Using the generalized autoregressive conditional heteroskedasticity (GARCH) models we estimate the distances between the stock return volatilities. The proposed method uses the volatility behavior of the time series and solves the problem of different lengths. As an illustrative example, we investigate the similarities among major international stock markets using daily return series with different sample sizes from 1966 to 2006. From cluster analysis, most European markets countries, United States and Canada appear close together, and most Asian/Pacific markets and the South/Middle American markets appear in a distinct cluster. After the terrorist attack on September 11, 2001, the European stock markets have become more homogenous, and North American markets, Japan and Australia seem to come closer.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cluster analysis; GARCH; International stock markets; Volatility
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

References

Arshanapalli, B. and Doukas, J. (1993). "International stock market linkages: Evidence from the pre and post-October 1987 period", Journal of Banking & Finance, 17, 193-208. Ball, C. and Torous, W. (2000). "Stochastic correlation across international stock markets", Journal of Empirical Finance, 7, 373-388. Bessler, D. and Yang, J. (2003). "The structure of interdependence in international stock markets", Journal of International Money and Finance, 22, 261-287. Bollerslev, T. (1986). "Generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 31, 307-327. Bollerslev, T., Chou, R. and Kroner, K. (1992). "ARCH modeling in Finance", Journal of Econometrics, 52, 5-59. Bonanno G., Lillo F., and Mantegna, R. N. (2001). "High-frequency cross-correlation in a set of stocks", Quantitative Finance, 1, 96-104. Caiado, J., Crato, N. and Peña, D. (2007). "Comparison of time series with unequal lengths", manuscript. Engle, R. (1982). "Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation", Econometrica, 50, 987-1008. Engle, R. and Bollerslev, T. (1986). "Modelling the persistence of conditional variances", Econometric Reviews, 5, 1-50. Hui, T. (2005). "Portfolio diversification: a factor analysis approach", Applied Financial Economics, 15, 821-834. Johnson, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. 3rd Ed., Englewood Cliffs, Prentice-Hall. Karolyi, G. and Stulz, R. (1996). "Why do markets move together? An investigation of U.S.-Japan return comovements", The Journal of Finance, 51, 951-986. Longin, F. and Solnik, B. (1995). "Is the correlation in international equity returns constant: 1960-1990?", Journal of International Money and Finance, 14, 3-26. Mantegna, R. N. (1999). "Hierarchical structure in financial markets", The European Physical Journal B 11, 193-197. Mei, J. and Ammer, J. (1996). "Measuring international economic linkages with stock market data", The Journal of Finance, 51, 1743-1763. Morana, C. and Beltratti, A. (2006). "Comovements in international stock markets", Journal of International Financial Markets, Institutions and Money, in press. Ramchmand, L. and Susmel, R. (1998). "Volatility and cross correlation across major stock markets", Journal of Empirical Finance, 5, 397-416. Syriopoulos, T. (2004). "International portfolio diversification to Central European stock markets", Applied Financial Economics, 14, 1253-1268. Tahai, A., Rutledge, R. and Karim, K. (2004). "An examination of financial integration for the group of seven (G7) industrialized countries using an I(2) cointegration model", Applied Financial Economics, 14, 327-335.