可扩展正则化向量乘法误差模型用于正值金融时间序列
Scalable Regularized Vector Multiplicative Error Models for Positive-valued Financial Time Series
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中文总结 AI 辅助
本文提出针对正值金融时间序列的log-vMEM模型正则化估计方法，结合分层滞后结构与多种惩罚，采用块坐标下降算法，并利用GPU加速积分提升计算可扩展性。
中文摘要 AI 辅助
对数乘法误差模型（log-vMEM）在多元正值金融时间序列的建模和预测中一直很有用。参数数量随系统维度和滞后阶数快速增长，使得高维设置下的估计计算需求很高。本文描述了基于Tsionas（2004）多元伽马误差分布的log-vMEM模型，采用Nicholson等人（2020）的分层滞后结构的正则化估计。参数估计使用块坐标下降算法，并采用Gauss-Seidel式更新方案（Wright，2015）。与传统惩罚最大似然方法相比，这实现了高效的计算策略。通过结合三种分层滞后结构（分量式、元素式、自身-其他）和四种惩罚（组套索、自适应组套索、组MCP和组SCAD），将竞争模型相互对比。进行了大量模拟运行，以测试未惩罚和惩罚模型的参数恢复。我们将所提方法应用于对微软（NASDAQ: MSFT）的稳健日内已实现波动率度量的联合动态建模，以比较竞争模型。对数似然的数值积分步骤被确定为主要计算瓶颈。我们通过使用GPU加速求积积分来解决此问题，从而提高了所提模型的计算可扩展性。
英文摘要
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.
发表机构
- University of Connecticut（康涅狄格大学）
- Cornell University（康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。
