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<p>With the acceleration of urbanization, public concern regarding air pollution has been growing substantially. Air quality indicators, such as AQI and PM<sub>2.5</sub>, have been demonstrated to exhibit significant autocorrelation and cross-correlation characteristics. To better capture these features, we propose a full generalized bivariate first-order integer-valued autoregressive (FGBINAR(1)) model, and study the statistical properties and parameter estimation method of the model. Furthermore, the monitoring of these air quality indicators is equally crucial. Under the assumption of FGBINAR(1) model, we use several multivariate control charts to monitor the changes in the process mean and get effective simulation results. Finally, combined with the results of the empirical analysis, we provide practical suggestions for the selection of control charts. These findings can provide accurate and timely air quality assessment outcomes, offering support for decision-making and policy planning.</p>

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A generalized bivariate integer-valued process with applications in air quality monitoring

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Qiqi Shan,
  • Cong Li

摘要

With the acceleration of urbanization, public concern regarding air pollution has been growing substantially. Air quality indicators, such as AQI and PM2.5, have been demonstrated to exhibit significant autocorrelation and cross-correlation characteristics. To better capture these features, we propose a full generalized bivariate first-order integer-valued autoregressive (FGBINAR(1)) model, and study the statistical properties and parameter estimation method of the model. Furthermore, the monitoring of these air quality indicators is equally crucial. Under the assumption of FGBINAR(1) model, we use several multivariate control charts to monitor the changes in the process mean and get effective simulation results. Finally, combined with the results of the empirical analysis, we provide practical suggestions for the selection of control charts. These findings can provide accurate and timely air quality assessment outcomes, offering support for decision-making and policy planning.