Dynamic Realized Minimum Variance Portfolio Models

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.