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Clustering heteroskedastic time series by model-based procedures

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  • Otranto, Edoardo

Abstract

Financial time series are often characterized by similar volatility structures. The detection of clusters of series displaying similar behavior could be important in understanding the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant when dealing with many series, as in financial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the Autoregressive metrics to measure the distance between GARCH processes, it is shown that it is possible to develop a clustering algorithm, which can provide three classifications (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 fixed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indices of the Italian market.

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  • Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4685-4698
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    Cited by:

    1. Edoardo Otranto & Massimo Mucciardi & Pietro Bertuccelli, 2016. "Spatial effects in dynamic conditional correlations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 604-626, March.
    2. Edoardo Otranto & Romana Gargano, 2015. "Financial clustering in presence of dominant markets," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 315-339, September.
    3. 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.
    4. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2015. "Clustering of time series via non-parametric tail dependence estimation," Statistical Papers, Springer, vol. 56(3), pages 701-721, August.
    5. M. Mucciardi & E. Otranto, 2016. "A Flexible Specification of Space–Time AutoRegressive Models," Working Paper CRENoS 201608, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    6. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    7. Francesca Di Iorio & Umberto Triacca, 2014. "Testing for A Set of Linear Restrictions in VARMA Models Using Autoregressive Metric: An Application to Granger Causality Test," Econometrics, MDPI, Open Access Journal, vol. 2(4), pages 1-14, December.
    8. De Gregorio, Alessandro & Maria Iacus, Stefano, 2010. "Clustering of discretely observed diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 598-606, February.
    9. Sonia Díaz & José Vilar, 2010. "Comparing Several Parametric and Nonparametric Approaches to Time Series Clustering: A Simulation Study," Journal of Classification, Springer;The Classification Society, vol. 27(3), pages 333-362, November.
    10. 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.
    11. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2014. "Clustering of financial time series in risky scenarios," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(4), pages 359-376, December.
    12. Aielli, Gian Piero & Caporin, Massimiliano, 2014. "Variance clustering improved dynamic conditional correlation MGARCH estimators," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 556-576.
    13. Argimiro Arratia & Alejandra Cabaña, 2013. "A Graphical Tool for Describing the Temporal Evolution of Clusters in Financial Stock Markets," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 213-231, February.
    14. 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.
    15. Borja Lafuente-Rego & José A. Vilar, 2016. "Clustering of time series using quantile autocovariances," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(3), pages 391-415, September.
    16. Argimiro Arratia & Alejandra Caba~na, 2011. "Tracing the temporal evolution of clusters in a financial stock market," Papers 1111.3127, arXiv.org.
    17. Liu, Shen & Maharaj, Elizabeth Ann, 2013. "A hypothesis test using bias-adjusted AR estimators for classifying time series in small samples," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 32-49.
    18. Luca De Angelis, 2013. "Latent class models for financial data analysis: some statistical developments," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 227-242, June.
    19. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 323-340, December.
    20. repec:bpj:strimo:v:34:y:2017:i:1-2:p:1-12:n:2 is not listed on IDEAS
    21. 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.
    22. Di Iorio, Francesca & Triacca, Umberto, 2013. "Testing for Granger non-causality using the autoregressive metric," Economic Modelling, Elsevier, vol. 33(C), pages 120-125.
    23. repec:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0718-7 is not listed on IDEAS
    24. 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.
    25. E. Otranto & M. Mucciardi, 2017. "Clustering Space-Time Series: A Flexible STAR Approach," Working Paper CRENoS 201707, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

    More about this item

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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