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Return Interval, Dependence Structure and Multivariate Normality


  • Thierry Ané
  • Chiraz Labidi


We focus on changes in the multivariate distribution of index returns stemming purely from varying the return interval, assuming daily to quarterly returns. Whereas longtailedness is present in daily returns, we find that, in agreement with a well-established idea, univariate return distributions converge to normality as the return interval is lengthened. Such convergence does not occur, however, for multivariate distributions. Using a new method to parametrically model the dependence structure implying negative asymptotic dependence in return series is the reason for the rejection of multivariate normality for low return frequencies.

Suggested Citation

  • Thierry Ané & Chiraz Labidi, 2001. "Return Interval, Dependence Structure and Multivariate Normality," Research Paper Series 64, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:64

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    References listed on IDEAS

    1. Ramsey James B. & Lampart Camille, 1998. "The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-22, April.
    2. Shinn-Juh Lin & Max Stevenson, 1999. "Wavelet Analysis of Index Prices in Futures and Cash Markets: Implication for the Cost-Of-Carry Model," Research Paper Series 11, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Wiggins, James B, 1992. "Betas in Up and Down Markets," The Financial Review, Eastern Finance Association, vol. 27(1), pages 107-123, February.
    4. Domian, Dale L. & Louton, David A., 1995. "Business cycle asymmetry and the stock market," The Quarterly Review of Economics and Finance, Elsevier, vol. 35(4), pages 451-466.
    5. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    6. Bhardwaj, Ravinder K & Brooks, LeRoy D, 1993. "Dual Betas from Bull and Bear Markets: Reversal of the Size Effect," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 16(4), pages 269-283, Winter.
    7. Domian, Dale L. & Louton, David A., 1997. "A threshold autoregressive analysis of stock returns and real economic activity," International Review of Economics & Finance, Elsevier, vol. 6(2), pages 167-179.
    8. L. C. G. Rogers & S. E. Satchell, 2000. "Does the behaviour of the asset tell us anything about the option price formula? A cautionary tale," Applied Financial Economics, Taylor & Francis Journals, vol. 10(1), pages 37-39.
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    More about this item


    multivatiave normality; return interval; dependence structure; copula;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets


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