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On the univariate representation of BEKK models with common factors

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  • Hecq, A.W.

    (Quantitative Economics)

  • Palm, F.C.

    (Quantitative Economics)

  • Laurent, S.F.J.A.

    (Quantitative Economics)

Abstract

Simple low order multivariate GARCH models imply marginal processes with a lot of persistence in the form of high order lags. This is not what we find in many situations however, where parsimonious univariate GARCH(1,1) models for instance describe quite well the conditional volatility of some asset returns. In order to explain this paradox, we show that in the presence of common GARCH factors, parsimonious univariate representations can result from large multivariate models generating the conditional variances and conditional covariances/correlations. The diagonal model without any contagion effects in conditional volatilities gives rise to similar conclusions though. Consequently, after having extracted a block of assets representing some form of parsimony, remains the task of determining if we have a set of independent assets or instead a highly dependent system generated with a few factors. To investigate this issue, we first evaluate a reduced rank regressions approach for squared returns that we extend to cross-returns. Second we investigate a likelihood ratio approach, where under the null the matrix parameters have a reduced rank structure. It emerged that the latter approach has quite good properties enabling us to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) and a model with few common sources of volatility.
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  • Hecq, A.W. & Palm, F.C. & Laurent, S.F.J.A., 2012. "On the univariate representation of BEKK models with common factors," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2012018
    DOI: 10.26481/umamet.2012018
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    Cited by:

    1. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    2. Chevillon, Guillaume & Hecq, Alain & Laurent, Sébastien, 2018. "Generating univariate fractional integration within a large VAR(1)," Journal of Econometrics, Elsevier, vol. 204(1), pages 54-65.
    3. Dovonon, Prosper & Renault, Eric, 2011. "Testing for Common GARCH Factors," MPRA Paper 40224, University Library of Munich, Germany.
    4. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    5. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    6. Nguyen, Giang & Engle, Robert & Fleming, Michael & Ghysels, Eric, 2020. "Liquidity and volatility in the U.S. Treasury market," Journal of Econometrics, Elsevier, vol. 217(2), pages 207-229.
    7. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2019. "Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure," Papers 1902.10991, arXiv.org, revised Dec 2020.
    8. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Jun 2021.

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