Spillovers and Co-movements in Multivariate Volatility: A Vector Multiplicative Error Model
Edoardo Otranto, Luca Scaffidi Domianello
TL;DR
The paper tackles the challenge of modeling volatility spillovers and global comovement in high-dimensional financial panels. It proposes a vector MEM with a diagonal log-vMEM structure augmented by a latent common component $\xi_t$, driven by $p_{t-1}$, the first principal component of demeaned log-volatilities, to capture co-movement and spillovers. A novel clustering-based parameterization reduces the parameter space from hundreds to a small, interpretable set $p = 2(k_1+1) + (k_2-1)$, enabling scalable estimation for large $n$. Empirically, the approach applied to 29 DJIA components shows that vMEM-SeC models outperform standard vMEMs in both in-sample and out-of-sample evaluations, with c-vMEM-SeC achieving best BIC and substantial parameter reduction (13 vs 523) while preserving strong predictive accuracy. Overall, the framework provides a scalable, interpretable tool for detecting spillover directionality and shared market dynamics in high-dimensional volatility data, with practical uses in forecasting and risk management; the authors also supply replication code.
Abstract
Recent developments in financial time series focus on modeling volatility across multiple assets or indices in a multivariate framework, accounting for potential interactions such as spillover effects. Furthermore, the increasing integration of global financial markets provides a similar dynamics (referred to as comovement). In this context, we introduce a novel model for volatility vectors within the Multiplicative Error Model (MEM) class. This framework accommodates both spillover and co-movement effects through a distinct latent component. By adopting a specific parameterization, the model remains computationally feasible even for high-dimensional volatility vectors. To reduce the number of unknown coefficients, we propose a simple model-based clustering procedure. We illustrate the effectiveness of the proposed approach through an empirical application to 29 assets of the Dow Jones Industrial Average index, providing insight into volatility spillovers and shared market dynamics. Comparative analysis against alternative vector MEMs, including a fully parameterized version of the proposed model, demonstrates its superior or at least comparable performance across multiple evaluation criteria.