Although multivariate stochastic volatility models usually produce more accurate forecasts compared with the MGARCH models, their estimation techniques such as Bayesian MCMC typically suffer from the curse of dimensionality. We propose a fast and efficient estimation approach for MSV based on a penalized OLS framework. Specifying the MSV model as a multivariate state-space model, we carry out a two-step penalized procedure. We provide the asymptotic properties of the two-step estimator and the oracle property of the first-step estimator when the number of parameters diverges. The performances of our method are illustrated through simulations and financial data. Supplementary Material presenting technical proofs is available online.

中文翻译：

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高维稀疏多元随机波动率模型

尽管与 MGARCH 模型相比，多变量随机波动率模型通常会产生更准确的预测，但它们的估计技术（例如贝叶斯 MCMC）通常会遭受维数灾难。我们基于惩罚性 OLS 框架提出了一种快速有效的 MSV 估计方法。将 MSV 模型指定为多元状态空间模型，我们执行两步惩罚程序。当参数数量发散时，我们提供了两步估计器的渐近特性和第一步估计器的 oracle 特性。我们的方法的性能通过模拟和财务数据来说明。提供技术证明的补充材料可在线获取。