Modeling air quality level with a flexible categorical autoregression

Abstract

To study urban air quality, this paper proposes a novel categorical time series model, which is based on a linear combination of bounded Poisson distribution and discrete distribution to describe the dynamic and systemic features of air quality, respectively. Daily air quality level data of three major cities in China, including Beijing, Shanghai and Guangzhou, are analyzed. It is concluded that the air quality in Beijing is the worst among the three cities but is gradually improving, and its dynamics is also the most pronounced. Theoretically, the design of our model increases the flexibility of the probabilistic structure while ensuring a dynamic feedback mechanism without high computational stress. We estimate the parameters through an adaptive Bayesian Markov chain Monte Carlo sampling scheme and show the satisfactory finite sample performance of the model through simulation studies.

A Systematic Review of INGARCH Models for Integer-Valued Time Series

“…Compared with the model in vector form, the ZOBPAR model is concise both in terms of estimation and its own form. The follow-up Liu et al [ 97 ] is also based on this and is an application-oriented study completed using Bayesian estimation methods.…”

Soft-clipping INGARCH models for time series of bounded counts

“…As our second application, let us consider the air quality data (Data provided as online supplementary material for Liu et al, 2022a.) discussed by Liu et al (2022a, 2022b). For 30 Chinese cities, they analyzed a time series of daily air quality levels (December 2013–July 2019, so length T=2 068).…”

“…But then, parameter values are more difficult to interpret, and closed formulae for the ACF and further moments are not available. Further recent articles on bounded INGARCH models are Liu et al (2022a, 2022b).…”