A1837
Title: Estimation of large dynamic precision matrices with a latent semiparametric structure
Authors: Jia Chen - University of Macau (China) [presenting]
Yuning Li - University of York (United Kingdom)
Oliver Linton - University of Cambridge (United Kingdom)
Abstract: The estimation of dynamic precision matrices with multiple conditioning variables is studied for high-dimensional time series. The high-dimensional time series is assumed to have an approximate factor structure plus an idiosyncratic error term, which allows the time series to have a non-sparse dynamic precision matrix and enhances the applicability of the method. Exploiting the Sherman-Morrison-Woodbury formula, the estimation of the dynamic precision matrix for the time series reduces to the estimation of a low-rank factor structure and the precision matrix of the idiosyncratic error term. For the latter, a semiparametric method is introduced to estimate the entries of the corresponding dynamic covariance matrix via the Model Averaging MArginal Regression (MAMAR) before applying the constrained $l_1$ minimisation for inverse matrix estimation (CLIME) method to obtain the dynamic precision matrix. Under some regularity conditions, uniform consistency for the proposed estimators is derived. A simulation study illustrates the finite-sample performance of the developed methodology, and an application in the construction of minimum-variance portfolios using daily returns of S\&P 500 constituents from 2000 to 2024 is provided.
