Model selection for vector autoregressive processes using broken adaptive ridge

ABSTRACT We consider a sparse vector autoregressive model with divergent lag order. As a linear model, all its explanatory variables are lagged responses such that there may be high correlation between them. Hence, the broken adaptive ridge procedure is employed for its iterative algorithm, which starts with a ridge estimator as the initial one. We obtained parameter estimation and model selection simultaneously by the procedure named VBAR in this paper. Theoretically, we established that the VBAR procedure is consistent for model selection and an oracle for parameter estimation. Simulations demonstrate the superiority of the VBAR procedure over Lasso, Adaptive Lasso, and SCAD procedures. Additionally, the Google Flu Trends data are analyzed by the VBAR procedure, which gives a more sparse model and more accurate predictions compared with other procedures.