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Clustering Heteroskedastic Time Series by Model-Based Procedures

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  • E. Otranto

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Abstract

Financial time series are often characterized by similar volatility structures, often represented by GARCH processes. The detection of clusters of series displaying similar behavior could be important to understand the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant dealing with many series, as in ?nancial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the AR metrics to measure the distance between GARCH processes, it is possible to develop a clustering algorithm, which can provide three classi?cations (with increasing degree of deepness) based on the heteroskedastic patterns of the time series. The number of clusters is detected automatically and it is not ?xed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indexes of the Italian market.

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Bibliographic Info

Paper provided by Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia in its series Working Paper CRENoS with number 200801.

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Date of creation: 2008
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Handle: RePEc:cns:cnscwp:200801

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Keywords: agglomerative algorithm; ar metrics; cluster analysis; garch models; wald test;

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Citations

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Cited by:
  1. Sonia Díaz & José Vilar, 2010. "Comparing Several Parametric and Nonparametric Approaches to Time Series Clustering: A Simulation Study," Journal of Classification, Springer, vol. 27(3), pages 333-362, November.
  2. Argimiro Arratia & Alejandra Caba\~na, 2011. "Tracing the temporal evolution of clusters in a financial stock market," Papers 1111.3127, arXiv.org.
  3. F. Lisi & E. Otranto, 2008. "Clustering Mutual Funds by Return and Risk Levels," Working Paper CRENoS 200813, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  4. M. Pitzalis & I. Sulis & M. Porcu, 2008. "Differences of Cultural Capital among Students in Transition to University. Some First Survey Evidences," Working Paper CRENoS 200805, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  5. Di Iorio, Francesca & Triacca, Umberto, 2013. "Testing for Granger non-causality using the autoregressive metric," Economic Modelling, Elsevier, vol. 33(C), pages 120-125.
  6. Luca De Angelis, 2013. "Latent class models for financial data analysis: some statistical developments," Statistical Methods and Applications, Springer, vol. 22(2), pages 227-242, June.
  7. Vilar, J.A. & Alonso, A.M. & Vilar, J.M., 2010. "Non-linear time series clustering based on non-parametric forecast densities," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2850-2865, November.
  8. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer, vol. 5(4), pages 323-340, December.
  9. Alessandro De Gregorio & Stefano Maria Iacus, 2008. "Clustering of discretely observed diffusion processes," Papers 0809.3902, arXiv.org.
  10. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
  11. E. Otranto, 2011. "Classification of Volatility in Presence of Changes in Model Parameters," Working Paper CRENoS 201113, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  12. Argimiro Arratia & Alejandra Cabaña, 2013. "A Graphical Tool for Describing the Temporal Evolution of Clusters in Financial Stock Markets," Computational Economics, Society for Computational Economics, vol. 41(2), pages 213-231, February.
  13. R. Gargano & E. Otranto, 2013. "Financial Clustering in Presence of Dominant Markets," Working Paper CRENoS 201318, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  14. I. Sulis & M. Porcu, 2008. "Assessing the Effectiveness of a Stochastic Regression Imputation Method for Ordered Categorical Data," Working Paper CRENoS 200804, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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