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On the Univariate Representation of BEKK Models with Common Factors

  • Hecq Alain
  • Laurent Sébastien
  • Palm Franz C.

    (METEOR)

First, we investigate the minimal order univariate representation of some well known n-dimensionalconditional volatility models. Even simple low order systems (e.g. a multivariate GARCH(0,1)) forthe joint behavior of several variables imply individual processes with a lot of persistence inthe form of high order lags. However, we show that in the presence of common GARCH factors,parsimonious univariate representations (e.g. GARCH(1,1)) can result from large multivariatemodels generating the conditional variances and conditional covariances/correlations. The trivialdiagonal model without any contagion effects in conditional volatilities gives rise to the sameconclusions though.Consequently, we then propose an approach to detect the presence of these commonalities inmultivariate GARCH process. The factor we extract is the volatility of a portfolio made up by theoriginal assets whose weights are determined by the reduced rank analysis.We compare the small sample performances of two strategies. First, extending Engle and Marcucci(2006), we use reduced rank regressions in a multivariate system for squared returns andcross-returns. Second we investigate a likelihood ratio approach, where under the null the matrixparameters of the BEKK have a reduced rank structure (Lin, 1992). It emerged that the latterapproach has quite good properties enabling us to discriminate between a system with seeminglyunrelated assets (e.g. a diagonal model) and a model with few common sources of volatility.

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Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 018.

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Date of creation: 2012
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Handle: RePEc:unm:umamet:2012018
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  1. Nijman, T. & Sentana, E., 1994. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Proceses," Papers 9419, Centro de Estudios Monetarios Y Financieros-.
  2. Isabel Ruiz, 2009. "Common volatility across Latin American foreign exchange markets," Applied Financial Economics, Taylor & Francis Journals, vol. 19(15), pages 1197-1211.
  3. Gianluca Cubadda & Alain Hecq, 2009. "Testing for Common Autocorrelation in Data Rich Environments," CEIS Research Paper 153, Tor Vergata University, CEIS, revised 04 Dec 2009.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  5. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
  6. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, 09.
  7. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, vol. 25(02), pages 336-363, April.
  8. Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 114-144, January.
  9. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
  10. B. Ravikumar & Surajit Ray & N. Eugene Savin, 2000. "Robust Wald Tests in SUR Systems with Adding-up Restrictions," Econometrica, Econometric Society, vol. 68(3), pages 715-720, May.
  11. Hafner, C.M. & Herwartz, H., 2004. "Testing for causality in variance using multivariate GARCH models," Econometric Institute Research Papers EI 2004-20, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  12. Engle, Robert F & Susmel, Raul, 1993. "Common Volatility in International Equity Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 167-76, April.
  13. Arshanapalli, Bala & Doukas, John & Lang, Larry H. P., 1997. "Common volatility in the industrial structure of global capital markets," Journal of International Money and Finance, Elsevier, vol. 16(2), pages 189-209, April.
  14. Anderson, Heather M. & Vahid, Farshid, 2007. "Forecasting the Volatility of Australian Stock Returns: Do Common Factors Help?," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 76-90, January.
  15. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  16. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2008. "Macro-panels and reality," Economics Letters, Elsevier, vol. 99(3), pages 537-540, June.
  17. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
  18. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
  19. Hecq, Alain & Issler, João Victor, 2012. "A Common-Feature Approach for Testing Present-Value Restrictions with Financial Data," Economics Working Papers (Ensaios Economicos da EPGE) 728, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  20. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  21. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
  22. Lin, Wen-Ling, 1992. "Alternative Estimators for Factor GARCH Models--A Monte Carlo Comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 259-79, July-Sept.
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