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A note on the absolute moments of the bivariate normal distribution

Author

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  • Markus Haas

    (Institute for Quantitative Business and Economics Research (QBER), University of Kiel)

Abstract

A short and simple calculation of the expected absolute value of the product of two correlated zero-mean normal variables is provided.

Suggested Citation

  • Markus Haas, 2018. "A note on the absolute moments of the bivariate normal distribution," Economics Bulletin, AccessEcon, vol. 38(1), pages 650-656.
  • Handle: RePEc:ebl:ecbull:eb-17-00492
    as

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    References listed on IDEAS

    as
    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Charlot, Philippe & Darné, Olivier & Moussa, Zakaria, 2016. "Commodity returns co-movements: Fundamentals or “style” effect?," Journal of International Money and Finance, Elsevier, vol. 68(C), pages 130-160.
    3. Giamouridis, Daniel & Vrontos, Ioannis D., 2007. "Hedge fund portfolio construction: A comparison of static and dynamic approaches," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 199-217, January.
    4. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, vol. 7(2), pages 86-97, June.
    5. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    6. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    7. He, Changli & Teräsvirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(5), pages 904-926, October.
    8. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    9. Lejeune, Bernard, 2009. "A diagnostic m-test for distributional specification of parametric conditional heteroscedasticity models for financial data," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 507-523, June.
    10. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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    More about this item

    Keywords

    multivariate GARCH; moments; multivariate normal distribution;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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