In response to increased desertification in Africa due to climate change, understanding the behavior of particulate matter with aerodynamic diameters less than or equal to 2.5 and 10 \(\mu m\) ( \(PM_{2.5}\) and \(PM_{10}\) ) in the Caribbean is crucial. Fine particles originating from the African dust belt significantly impact the health of the Caribbean population. This study employs a multifractal framework to analyze \(PM_{2.5}\) and \(PM_{10}\) time series data in Puerto Rico from 2000 to 2010, marking the first such investigation in the Caribbean islands. Multifractal Detrended Fluctuation Analysis (MF-DFA) reveals similar multifractal behavior in \(PM_{10}\) and \(PM_{2.5}\) fluctuations, suggesting a shared influence on these pollutants. Hurst exponents of 0.594 for \(PM_{10}\) and 0.642 for \(PM_{2.5}\) indicate long-term persistence in particulate matter behavior. African dust notably influences \(PM_{10}\) , displaying slightly greater intermittency. Shuffled and surrogate signal analyses confirm multifractality in PMs time series, representing long-range correlations in small and large fluctuations and broadness in probability density function. The primary contributor to multifractality in \(PM_{2.5}\) is identified as the broadness of the probability density function. Multifractal Detrended Cross-Correlation Analysis (MF-DXA) reveals anti-persistence in cross-correlated multifractal behavior of PMs. These insights enhance the understanding of \(PM_{2.5}\) and \(PM_{10}\) dynamics, aiding predictions of natural occurrences like sand mist and improving health risk management in the Caribbean basin.
