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Reconstructing high dimensional dynamic distributions from distributions of lower dimension


  • Stanislav Anatolyev

    () (New Economic School)

  • Renat Khabibullin

    () (Barclays Capital)

  • Artem Prokhorov

    () (University of Sydney, CIREQ)


We propose a new sequential procedure for estimating a dynamic joint distribution of a group of assets. The procedure is motivated by the theory of composite likelihood and by the theory of copula functions. It recovers m-variate distributions by coupling univariate distributions with distributions of dimension m - 1. This copula-based method produces pseudo-maximum-likelihood type estimators of the distribution of all pairs, triplets, quadruples, etc, of assets in the group. Eventually the joint distribution of unrestricted dimension can be recovered. We show that the resulting density can be viewed as a exible factorization of the underlying true distribution, subject to an approximation error. Therefore, it inherits the well known asymptotic properties of the conventional copula-based pseudo-MLE but offers important advantages. Specifically, the proposed procedure trades the dimensionality of the parameter space for numerous simpler estimations, making it feasible when conventional methods fail in finite samples. Even though there are more optimization problems to solve, each is of a much lower dimension. In addition, the parameterization tends to be much more exible. Using a GARCH-type application from stock returns, we demonstrate how the new procedure provides excellent fit when the dimension is moderate and how it remains operational when the conventional method fails due to high dimensionality.

Suggested Citation

  • Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2013. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers w0167, Center for Economic and Financial Research (CEFIR).
  • Handle: RePEc:cfr:cefirw:w0167

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    1. Eli Berman & Jacob N. Shapiro & Joseph H. Felter, 2011. "Can Hearts and Minds Be Bought? The Economics of Counterinsurgency in Iraq," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 766-819.
    2. Oeindrila Dube & Suresh Naidu, 2010. "Bases, Bullets, and Ballots: The Effect of U.S. Military Aid on Political Conflict in Colombia," Working Papers 197, Center for Global Development.
    3. Eli Berman & Michael Callen & Joseph H. Felter & Jacob N. Shapiro, 2009. "Do Working Men Rebel? Insurgency and Unemployment in Iraq and the Philippines," NBER Working Papers 15547, National Bureau of Economic Research, Inc.
    4. Radha Iyengar & Jonathan Monten, 2008. "Is There an "Emboldenment" Effect? Evidence from the Insurgency in Iraq," NBER Working Papers 13839, National Bureau of Economic Research, Inc.
    5. James D. Fearon, 2004. "Why Do Some Civil Wars Last So Much Longer than Others?," Journal of Peace Research, Peace Research Institute Oslo, vol. 41(3), pages 275-301, May.
    6. Luke N. Condra & Joseph H. Felter & Radha K. Iyengar & Jacob N. Shapiro, 2010. "The Effect of Civilian Casualties in Afghanistan and Iraq," NBER Working Papers 16152, National Bureau of Economic Research, Inc.
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    More about this item


    pseudo-likelihood; composite likelihood; multivariate distribution; copulas;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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