Estimating asymmetric dynamic distributions in high dimensions.

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.

Link to work
2018 chapters