Citation:
Anatolyev, Stanislav, Renat Khabibullin and Artem Prokhorov (2018) "An algorithm for constructing high dimensional distributions from distributions of lower dimension", chapter 8 in: Alcock, Jamie and Satchell, Stephen (eds.), Asymmetric Dependence in Finance: Diversification, Correlation and Portfolio Management in Market Downturns, John Wiley & Sons, pp. 169-197
Abstract:
We consider estimation of dynamic joint distributions of large groups of assets. Conventional likelihood functions based on 'off-the-shelf' distributions quickly become inaccurate as the number of parameters grows. Alternatives based on a fixed number of parameters do not permit sufficient flexibility in modelling asymmetry and dependence. This chapter considers a sequential procedure, where the joint patterns of asymmetry and dependence are unrestricted, yet the method does not suffer from the curse of dimensionality encountered in non-parametric estimation. We construct a flexible multivariate distribution using tightly parameterized lower-dimensional distributions coupled by a bivariate copula. This effectively replaces a high-dimensional parameter space with many simple estimations with few parameters. We provide theoretical motivation for this estimator as a pseudo-MLE with known asymptotic properties. In an asymmetric GARCH-type application with regional stock indexes, the procedure provides excellent fit when dimensionality is moderate, and remains operational when the conventional method fails.
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