Title: Simultaneous prediction intervals for high-dimensional vector autoregression
Authors: Mengyu Xu - University of Central Florida (United States)
Sayar Karmakar - University of Florida (United States) [presenting]
Abstract: Simultaneous prediction intervals for high-dimensional vector autoregressive processes are studied. Motivated from an online change-point problem, we wish to construct prediction intervals for one-step-ahead predictions in a high-dimensional VAR process. A de-biased calibration is used to post-regularize the lasso estimation, and a novel Gaussian-multiplier bootstrap-based method is developed for one-step-ahead prediction. The asymptotic coverage consistency of the prediction interval is obtained. We also substantiate the theoretical result by some simulations for evaluating finite sample performance and show some real data analysis. Our simulated results show considerably good performance even in situations where $p$ is much larger than $n$ where most of the previous literature only focused on situations where $p$ grows but remains less than $n$.