High-dimensional Inference for Sparse Vector Autoregression Processes

Music City Center 

The rapid growth of big data has increased focus on high-dimensional data analysis across various fields. Vector Auto-Regression (VAR) models are widely used in econometrics for capturing dynamic relationships between variables. However, high-dimensional VAR models often exhibit sparsity, where many coefficients are zero. Exploiting this sparsity improves model efficiency, interpretability, and prediction accuracy.

In this study, we propose two algorithms for sparse VAR model identification, designed for situations where the number of parameters (m) is comparable to the sample size (n). Both methods use p-values for sparsification. The thresholding method (TLSE) removes coefficients with p-values above a cutoff determined by n, and the model is re-estimated. The information criterion-based method (BLSE) uses p-value rankings to fit increasingly larger models, selecting the one with the smallest Bayesian Information Criterion (BIC).

Simulation results show that the proposed algorithms outperform lasso and BigVAR methods in recovering sparsity patterns, demonstrating their effectiveness for high-dimensional data analysis.

threshold estimation

information criteria

oracle property

Granger-causality

Sparse VAR 

Section on Statistical Computing