Modeling the transition behaviors of PM₁₀ pollution index

Modeling and evaluating the behavior of particulate matter (PM₁₀) is an important step in obtaining valuable information that can serve as a basis for environmental risk management, planning, and controlling the adverse effects of air pollution. This study proposes the use of a Markov chain model as an alternative approach for deriving relevant insights and understanding of PM₁₀ data. Using first- and higher-order Markov chains, we analyzed daily PM₁₀ index data for the city of Klang, Malaysia and found the Markov chain model to fit the PM₁₀ data well. Based on the fitted model, we comprehensively describe the stochastic behaviors in the PM₁₀ index based on the properties of the Markov chain, including its states classification, ergodic properties, long-term behaviors, and mean return times. Overall, this study concludes that the Markov chain model provides a good alternative technique for obtaining valuable information from different perspectives for the analysis of PM₁₀ data.