Regularized estimation in GINAR(p) process

This article is concerned with the regularized estimation methodology for generalized pth-order integer-valued autoregressive (GINAR(p)) process, especially when the regression coefficients are sparse. Under some mild regularity conditions, we show that the regularized estimators perform as well as if the correct submodel was known. The oracle properties of the estimators are established. Extensive Monte Carlo simulation studies demonstrate that the proposed procedure works well. To illustrate its usefulness, an application to a real data about epileptic patient is also provided.