Closed-Form Multi-Factor Copula Models with Observation-Driven Dynamic Factor Loadings

Abstract

We develop new multi-factor dynamic copula models with time-varying factor loadings and observation-driven dynamics. The new models are highly flexible, scalable to high dimensions, and ensure positivity of covariance and correlation matrices. A closed-form likelihood expression allows for straightforward parameter estimation and likelihood inference. We apply the new model to a large panel of 100 U.S. stocks over the period 2001-2014. The proposed multi-factor structure is much better than existing (singlefactor) models at describing stock return dependence dynamics in high-dimensions. The new factor models also improve one-step-ahead copula density forecasts and global minimum variance portfolio performance. Finally, we investigate different mechanisms to allocate firms into groups and find that a simple industry classification outperforms alternatives based on observable risk factors, such as size, value or momentum.

Intermittent Demand Forecasting in Retail: Applications of the Gas Framework

“…The possibility of using the GAS framework with dynamic copulas was first introduced and exemplified in the paper that proposed the score-driven dynamic [6]. Opschoor et al [16] model the dependence of 100 stocks through a factor dynamic copula model. GAS models can be set up using two possible structures: an ARMAlike structure and an unobserved components structure, akin to the structural models of Harvey [17].…”