Bayesian analysis for an improved mixture binomial autoregressive model with applications to rainy-days and air quality level data

Non-negative integer-valued time series with a finite range are sometimes suffered in environmental science, such as the weekly number of rainy-days in European cities (Góuveia et al. in Stoch Environ Res Risk Assess 32:2495–2514, 2018) and the air quality level in Chinese cities (Liu et al. in J Time Ser Anal 43:460–478, 2022) . To enhance the applicability of these environmental science data, this article employs a combination of Pegram and binomial thinning operators to develop a novel first-order mixture binomial autoregressive (BAR(1)) model. The proposed model represents an improved and generalized version of the mixture BAR(1) model introduced by Kang et al. (Stat Pap 62:745–767, 2021). The probabilistic and statistical properties, marginal distribution and some special cases of the proposed model are also studied. The conditional maximum likelihood estimation via EM algorithm and Bayesian estimation via Markov chain Monte Carlo sampling scheme are employed to estimate model parameters. Applications to the weekly number of rainy-days and air quality level counts are conducted to illustrate the usefulness of the new model in data analysis of the environmental studies.