Estimation of banded time-varying precision matrix based on SCAD and group lasso

Abstract

A new banded time-varying precision matrix estimator is proposed for high-dimensional time series. The estimator utilizes the modified Cholesky decomposition, and the two factors in the decomposition are dynamically estimated by applying the GARCH model to the innovation variance and the Kalman filter on the Cholesky factor. The SCAD penalty and group lasso penalty are imposed on the Cholesky factor to estimate the banded structure. An efficient algorithm based on the alternating direction method of multipliers (ADMM), local linear approximation (LLA), and blockwise coordinate descent (BCD) algorithms is developed. The convergence of the algorithm is proven theoretically, and the estimator is guaranteed to be banded. Simulation and real-data analysis demonstrate the favorable performance of the proposed algorithm compared to other methods.