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On the Univariate Representation of BEKK Models with Common Factors

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Author Info

  • Hecq Alain
  • Laurent Sébastien
  • Palm Franz C.

    (METEOR)

Abstract

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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Bibliographic Info

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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Postal: P.O. Box 616, 6200 MD Maastricht
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Web page: http://www.maastrichtuniversity.nl/
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Keywords: econometrics;

References

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  1. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  3. HAFNER, Christian M. & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," CORE Discussion Papers 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Isabel Ruiz, 2009. "Common volatility across Latin American foreign exchange markets," Applied Financial Economics, Taylor & Francis Journals, vol. 19(15), pages 1197-1211.
  6. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2002. "Likelihood-based estimation of latent generalised ARCH structures," Economics Papers 2002-W19, Economics Group, Nuffield College, University of Oxford.
  7. 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.
  8. Gianluca Cubadda & Alain Hecq, 2011. "Testing for common autocorrelation in data‐rich environments," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(3), pages 325-335, April.
  9. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
  10. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers 9312, Tilburg - Center for Economic Research.
  11. Heather Anderson & Fashid Vahid, 2005. "Forecasting the Volatility of Australian Stock Returns: Do Common Factors Help?," ANU Working Papers in Economics and Econometrics 2005-451, Australian National University, College of Business and Economics, School of Economics.
  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. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2008. "Macro-panels and reality," Economics Letters, Elsevier, vol. 99(3), pages 537-540, June.
  14. 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.
  15. 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.
  16. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
  17. 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.
  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. 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.
  20. 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.
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Cited by:
  1. Prosper Dovonon & Éric Renault, 2012. "Testing for Common GARCH Factors," CIRANO Working Papers 2012s-34, CIRANO.

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