This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. Specifically, we impose an autoregressive dynamic structure on MVP processes, which helps capture the MVP dynamics directly. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained $\ell_1$-minimization for inverse matrix estimation (CLIME) and calculate daily realized non-normalized MVP weights. Based on the realized non-normalized MVP weight estimator, we propose the dynamic MVP model, which we call the dynamic realized minimum variance portfolio (DR-MVP) model. To estimate a large number of parameters, we employ the least absolute shrinkage and selection operator (LASSO) and predict the future MVP and establish its asymptotic properties. Using high-frequency trading data, we apply the proposed method to MVP prediction.

翻译：本文提出一种基于高频金融数据的非线性波动率动态模型的最小方差投资组合（MVP）模型。具体而言，我们在MVP过程中引入自回归动态结构，从而直接捕捉MVP的动态特征。为评估动态MVP模型，我们采用约束ℓ₁-最小化逆矩阵估计（CLIME）方法估计逆波动率矩阵，并计算每日实现非归一化MVP权重。基于实现非归一化MVP权重估计量，我们提出动态MVP模型，即动态实现最小方差投资组合（DR-MVP）模型。为估计大量参数，我们采用最小绝对收缩与选择算子（LASSO），预测未来MVP并建立其渐近性质。利用高频交易数据，我们将所提方法应用于MVP预测。