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Reconstructing high dimensional dynamic distributions from distributions of lower dimension

Author

Listed:
  • Stanislav Anatolyev

    () (New Economic School)

  • Renat Khabibullin

    () (Barclays Capital)

  • Artem Prokhorov

    () (University of Sydney, CIREQ)

Abstract

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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    Keywords

    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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