Modeling normalcy‐dominant ordinal time series: An application to air quality level

Abstract

Inspired by the study of air quality level data, this article proposes a new model for the normalcy‐dominant ordinal time series. The proposed model is based on a new zero‐one‐inflated bounded Poisson distribution with an autoregressive feedback mechanism in intensity. Under certain conditions, the stationarity and maximum likelihood estimation are established for the model. Moreover, a Lagrange multiplier test is constructed to detect the inflation phenomenon in the model. Applications find that the model can adequately capture the air quality level data in 30 major cities in China. More importantly, this article uses the fitted models to make the overall and dynamic air quality rankings for these cities, and finds that both rankings are rational and informative to the public.