Paper: arXiv 2406.06860
Authors: Chen Tong, Peter Reinhard Hansen, Ilya Archakov
Abstract
We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 8.5/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper makes a strong contribution by integrating convolution-t heavy-tailed distributions into a score-driven multivariate GARCH model using a tractable block correlation matrix. The empirical rigor is outstanding, featuring both in-sample and out-of-sample backtests up to 100 assets, backed by sound statistical derivations for the likelihood score and information matrices.
Research Flowchart
flowchart TD
A[Goal: High-dimensional multivariate GARCH model with flexible tail dependencies] --> B[Data: Daily returns of 100 equity assets]
B --> C[Method: Cluster GARCH with Convolution-t Distributions]
C --> D[Compute Tractable Log-Likelihood & Score Derivatives]
D --> E[Model Dynamic Correlations & Cluster Structures]
E --> F[Outperforms Existing Models & Multivariate t-Distribution In/Out-of-Sample]