Scalable Regularized Vector Multiplicative Error Models for Positive-valued Financial Time Series

2026-10-06

AI Summary

This study addresses the computational bottleneck caused by parameter proliferation in modeling high-dimensional positive-valued financial time series by proposing a regularized log-vector multiplicative error model. Methodologically, it constructs a multivariate Gamma distribution framework incorporating a hierarchical lag structure and enforces sparsity through Group Lasso, MCP, and SCAD penalties. For optimization, a block coordinate descent algorithm based on Gauss-Seidel updates is designed, coupled with GPU-accelerated numerical integration to overcome high-dimensional computational constraints. Empirical results demonstrate that the proposed approach significantly enhances parameter recovery accuracy and computational scalability in high-dimensional settings, with its practical effectiveness further validated through intraday volatility forecasting for Microsoft stock.

Abstract

The logarithmic multiplicative error model (log-vMEM) has been useful in modeling and forecasting multivariate positive-valued financial time series. The number of parameters grow rapidly with the dimension of the system and the lag order, making estimation computationally demanding in high-dimensional settings. This paper describes regularized estimation via hierarchical lag structures (Nicholson et al., 2020) for log-vMEM models with multivariate gamma error distribution of Tsionas (2004). The parameter estimation is performed using a blockwise coordinate descent algorithm with a Gauss-Seidel-style update scheme (Wright, 2015). This enables an efficient computation strategy compared to traditional penalized maximum likelihood approaches. The competing models are juxtaposed against each other by combining three hierarchical lag structures (componentwise, elementwise, own-other) and four penalties(group-lasso, adaptive group-lasso, group-mcp, and group-scad). Extensive simulation runs have been performed to test the parameter recovery for both the unpenalized and the penalized models. We apply the proposed methods to model the joint dynamics of robust intraday realized volatility measures for Microsoft (NASDAQ: MSFT) for the competing models. The numerical integration step of the log-likelihood is identified to be the principal computational bottleneck. We address this issue by using GPU-accelerated quadrature integration thus improving computational scalability of the proposed models.

Problem

• log-vMEM
• high-dimensional estimation
• positive-valued financial time series
• computational scalability
• numerical integration bottleneck

Innovation

• Regularized log-vMEM
• Blockwise coordinate descent
• Hierarchical lag structures
• GPU-accelerated quadrature integration
• High-dimensional financial time series