Estimation of Large Dynamic Precision Matrices with a Latent Semiparametric Structure

Abstract

This paper studies the estimation of dynamic precision matrices with multiple conditioning variables for high-dimensional time series. We assume that the high-dimensional time series has an approximate factor structure plus an idiosyncratic error term; this allows the time series to have a non-sparse dynamic precision matrix, which enhances the applicability of our method. Exploiting the Sherman-Morrison-Woodbury formula, the estimation of the dynamic precision matrix for the time series boils down to the estimation of a low-rank factor structure and the precision matrix of the idiosyncratic error term. For the latter, we introduce an easy-to-implement semiparametric method to estimate the entries of the corresponding dynamic covariance matrix via the Model Averaging MArginal Regression (MAMAR) before applying the constrained ℓ1 minimisation for inverse matrix estimation (CLIME) method to obtain the dynamic precision matrix. Under some regularity conditions, we derive the uniform consistency for the proposed estimators. We provide a simulation study that illustrates the finite-sample performance of the developed methodology and an application in construction of minimum-variance portfolios using daily returns of S&P 500 constituents from 2000 to 2024.