September 2023 Variable selection for an improved INAR(1) model with explanatory variables using 2SPCLS
Ye Liu, Dehui Wang
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Braz. J. Probab. Stat. 37(3): 493-512 (September 2023). DOI: 10.1214/23-BJPS578


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.

Funding Statement

This work is supported by Social Science Planning Foundation of Liaoning Province (No. L22ZD065) and National Natural Science Foundation of China (No. 12271231, 12001229, 11901053).


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Ye Liu. Dehui Wang. "Variable selection for an improved INAR(1) model with explanatory variables using 2SPCLS." Braz. J. Probab. Stat. 37 (3) 493 - 512, September 2023.


Received: 1 August 2022; Accepted: 1 July 2023; Published: September 2023
First available in Project Euclid: 22 November 2023

Digital Object Identifier: 10.1214/23-BJPS578

Keywords: integer-valued autoregressive , time-series analysis , two-step conditional least squares , Variable selection

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 3 • September 2023
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