Time Series Graphical Lasso and Sparse VAR Estimation

TL;DR

This paper introduces a modified two-stage sparse VAR estimation method using time series graphical lasso, which improves computational efficiency and structure learning in multivariate time series analysis.

Contribution

The paper proposes an alternative two-stage sparse VAR method that leverages graphical lasso for spectral density estimation, enhancing speed and structure inference.

Findings

Significant reduction in computational time.

Better structure learning of AR coefficients.

Comparable forecasting performance to existing methods.

Abstract

We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral density in the first stage, and the second stage refines non-zero entries of the AR coefficient matrices using a false discovery rate (FDR) procedure. Our method has the advantage of avoiding the inversion of the spectral density matrix but has to deal with optimization over Hermitian matrices with complex-valued entries. It significantly improves the computational time with a little loss in forecasting performance. We study the properties of our proposed method and compare the performance of the two methods using simulated and a real macro-economic dataset. Our simulation results show that the proposed modification or msVAR is a preferred choice when the goal is to learn the structure of the AR coefficient matrices while sVAR outperforms msVAR when the ultimate task is forecasting.