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Variable selection for first‐order Poisson integer‐valued autoregressive model with covariables

In recent years, modelling count data has become one of the most important and popular topics in time‐series analysis. At the same time, variable selection methods have become widely used in many fields as an effective statistical modelling tool. In this paper, we consider using a variable selection method to solve a modelling problem regarding the first‐order Poisson integer‐valued autoregressive (PINAR(1)) model with covariables. The PINAR(1) model with covariables is widely used in many areas because of its practicality. When using this model to deal with practical problems, multiple covariables are added to the model because it is impossible to know in advance which covariables will affect the results. But the inclusion of some insignificant covariables is almost impossible to avoid. Unfortunately, the usual estimation method is not adequate for the task of deleting the insignificant covariables that cause statistical inferences to become biased. To overcome this defect, we propose a penalised conditional least squares (PCLS) method, which can consistently select the true model. The PCLS estimator is also provided and its asymptotic properties are established. Simulation studies demonstrate that the PCLS method is effective for estimation and variable selection. One practical example is also presented to illustrate the practicability of the PCLS method.