Estimation of Large Dynamic Precision Matrices with a Latent Semiparametric Structure

Abstract: This paper studies the estimation of dynamic precision matrices of high-dimensional time series satisfying an approximate factor model with multiple conditioning variables. We introduce an easy-to-implement semiparametric method to estimate each entry of the conditional covariance matrices of the common factors and the idiosyncratic components via Model Averaging MArginal Regression (MAMAR). We apply the CLIME method to obtain the estimate of the dynamic precision matrix for the idiosyncratic components and then we utilise the Sherman-Morrison-Woodbury formula to obtain the dynamic precision matrix for the time series. 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 then apply the proposed method in construction of the minimum variance portfolio from daily stock returns of S\&P 500 index constituents in 2022.

Mathematics

Audience: researchers in the topic

Applied Maths and Stats @ UEA