A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal distribution, heavy tails, and dynamic changes over time. Hence, they cannot generate highly accurate information. To overcome this issue, this study proposes a combination of the Generalized Autoregressive Conditional Heteroskedasticity model, Generalized Pareto distribution, and stochastic copulas as a tool to investigate the dependence structure between the PM₁₀ variable and other pollutant variables, including CO, NO₂, O₃, and SO₂. Results indicate that the dynamic dependence structure between PM₁₀ and other pollutant variables can be described with a ranking of PM₁₀–CO > PM₁₀–SO₂ > PM₁₀–NO₂ > PM₁₀–O₃ for the overall time paths (δ) and the upper tail (τ^U) or lower tail (τ^L) dependency measures. This study reveals an evident correlation among pollutant variables that changes over time; such correlation reflects dynamic dependency.

Modeling time series data of particulate matter (PM) will provide a good understanding about the dynamic behavior of this pollution variable. In fact, a suitable model can be used as a practical tool for planning purposes and controlling adverse effects of air pollution. This article utilized an autoregressive integrated moving average (ARMA) with the combination of generalized autoregressive conditional heteroscedastic (ARCH/GARCH) to provide a suitable model that can overcome the problematic volatility effect that exists in the PM₁₀ data. Hourly PM₁₀ data for the city of Kuala Lumpur have been analyzed. Based on several statistical approaches, such as the autocorrelation function, R² coefficient, and Akaike's Information Criterion, an ARMA(1,0)-GARCH(1,1) has been determined to be the best model to describe the data. In fact, incorporation of GARCH(1,1) is able to improve forecasting performance of PM₁₀ data, instead of relying on only a single ARMA(1,0) model.