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Clustering heteroskedastic time series by model-based procedures

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Otranto, Edoardo

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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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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 10 (June)
Pages: 4685-4698
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Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4685-4698

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  1. Gallo, Giampiero M. & Otranto, Edoardo, 2008. "Volatility spillovers, interdependence and comovements: A Markov Switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3011-3026, February. [Downloadable!] (restricted)
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  2. Tim Chenoweth & Robert Hubata & Robert D. St. Louis, 2004. "The power of tests for equivalent ARMA models: The implications for practitioners," Empirical Economics, Springer, vol. 29(2), pages 281-292, 05. [Downloadable!] (restricted)
  3. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June. [Downloadable!] (restricted)
  4. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  5. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series 2001-15, Department of Economics, UC San Diego. [Downloadable!]
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  6. Edoardo Otranto, 2004. "Classifying the Markets Volatility with ARMA Distance Measures," Econometrics 0402009, EconWPA, revised 05 Mar 2004. [Downloadable!]
  7. Corduas, Marcella & Piccolo, Domenico, 2008. "Time series clustering and classification by the autoregressive metric," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1860-1872, January. [Downloadable!] (restricted)
  8. Steece, Bert & Wood, Steven, 1985. "A Test for the Equivalence of k ARMA Models," Empirical Economics, Springer, vol. 1(1), pages 1-11.
  9. Edoardo Otrano & Umberto Triacca, 2007. "Testing for Equal Predictability of Stationary ARMA Processes," Journal of Applied Statistics, Taylor and Francis Journals, vol. 34(9), pages 1091-1108. [Downloadable!] (restricted)
  10. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  11. Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March. [Downloadable!] (restricted)
  12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  13. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  14. Giampiero Gallo & Edoardo Otranto, 2006. "Volatility Transmission Across Markets: A Multi-Chain Markov Switching Model," Econometrics Working Papers Archive wp2006_04, Universita' degli Studi di Firenze, Dipartimento di Statistica "G. Parenti". [Downloadable!]
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  1. M. Pitzalis & Isabella Sulis & Mariano 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. [Downloadable!]
  2. Isabella Sulis & Mariano 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. [Downloadable!]
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