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A Multivariate Generalized Orthogonal Factor GARCH Model

  • Lanne, Markku
  • Saikkonen, Pentti

The paper studies a factor GARCH model and develops test procedures which can be used to test the number of factors needed to model the conditional heteroskedasticity in the considered time series vector. Assuming normally distributed errors the parameters of the model can be straightforwardly estimated by the method of maximum likelihood. Inefficient but computationally simple preliminary estimates are first obtained and used as initial values to maximize the likelihood function. Maximum likelihood estimation with nonnormal errors is also straightforward. Motivated by the empirical application of the paper a mixture of normal distributions is considered. An interesting feature of the implied factor GARCH model is that some parameters of the conditional covariance matrix which are not identifiable in the case of normal errors become identifiable when the mixture distribution is used. As an empirical example we consider a system of four exchange rate return series.

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Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 25 (2007)
Issue (Month): (January)
Pages: 61-75

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Handle: RePEc:bes:jnlbes:v:25:y:2007:p:61-75
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  1. Donald W.K. Andrews, 1985. "Asymptotic Results for Generalized Wald Tests," Cowles Foundation Discussion Papers 761R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1986.
  2. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  3. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  4. Javier F. Mencia & Enrique Sentana, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
  5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  6. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
  7. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika, Springer, vol. 67(2), pages 219-239, March.
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