Confidence intervals for parameters in high-dimensional sparse vector autoregression

Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference of the transition matrices of VAR models are crucial for practitioners to make decisions in fields such as economics and finance. However, when the number of variables is larger than the sample size, it remains a challenge to perform inference of the model parameters. The de-biased Lasso and two bootstrap de-biased Lasso methods are proposed to construct confidence intervals for the elements of the transition matrices of high-dimensional VAR models. The proposed methods are asymptotically valid under appropriate sparsity and other regularity conditions. Moreover, feasible and parallelizable algorithms are developed to implement the proposed methods, which save a large amount of computational cost required by the nodewise Lasso and bootstrap. Simulation studies illustrate that the proposed methods perform well in finite-samples. Finally, the proposed methods are applied to analyze the price data of stocks in the S&P 500 index. Some stocks, such as the largest producer of gold in the world, Newmont Corporation, are found to have significant predictive power over most stocks.