Variable selection for an improved INAR(1) model with explanatory variables using 2SPCLS

Abstract

In the era of Big Data, a tremendous amount of usable data is produced every day. Count data is an essential component. The first-order integer-valued autoregressive (INAR(1)) model is one of the most effective tools for evaluating count data. In this study, we provide an improved INAR(1) model with explanatory variables. This model can well characterize the type of data where the variance of innovation is influenced by other time-varying factors. We introduce a two-step penalized conditional least squares (2SPCLS) method for unknown parameter estimation and variable selection. This method facilitates the selection of explanatory variables in the model, allowing us to more effectively address a modeling challenge. The asymptotical properties have been thoroughly investigated. This paper demonstrates, via a simulation study, that the 2SPCLS approach can accurately and effectively select the zero parameters. Finally, we perform a real-time series analysis, suggesting that this method can be used to solve problems in real life.