Pablo Pavón-Domínguez

Multi-fractal detrended fluctuation analysis (MF-DFA) describes long-range correlations across scales in time series in terms of the linear fittings of the fluctuation functions $$F_q(s)$$ F q ( s ) for every moment q considered. It is relatively common to find time scales, also called crossovers, where different linearities are found at each side of the $$F_q(s)$$ F q ( s ) , leading to different (multi-)fractal properties. Generally, crossovers are manually identified by experts, subject then to their skills and possible bias. In this work, a novel methodology based on the variances of the slope differences (CDV-A) is proposed to automatically detect crossovers. A set of synthetic fluctuation functions with different mono-fractal and multi-fractal features, different noise levels and known crossovers is generated to assess the CDV-A. Moreover, the proposed methodology is also applied to state of the art fluctuation functions in order to compare the proposed manual and automated locations of the crossovers. Results show the proposed methodology is highly accurate, specially in low noise synthetic fluctuation functions and in most of the real cases.

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.