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On the Univariate Representation of BEKK Models with Common Factors

Author

Listed:
  • Hecq Alain
  • Palm Franz C.

    () (Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands)

  • Laurent Sébastien

    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS, Aix-Marseille Graduate School of Management – IAE, France)

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.

Suggested Citation

  • Hecq Alain & Palm Franz C. & Laurent Sébastien, 2016. "On the Univariate Representation of BEKK Models with Common Factors," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 91-113, July.
  • Handle: RePEc:bpj:jtsmet:v:8:y:2016:i:2:p:91-113:n:4
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    Cited by:

    1. 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.
    2. Dovonon, Prosper & Renault, Eric, 2011. "Testing for Common GARCH Factors," MPRA Paper 40224, University Library of Munich, Germany.
    3. repec:eee:intfor:v:34:y:2018:i:1:p:45-63 is not listed on IDEAS
    4. Chevillon G. & Hecq A.W. & Laurent S.F.J.A., 2015. "Long memory through marginalization of large systems and hidden cross-section dependence," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. 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.
    6. 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.

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