Title: Seasonal and Periodic Patterns of PM2.5 in Manhattan using the Variable Bandpass Periodic Block Bootstrap

Abstract: Air quality is a critical component of environmental health. Monitoring and analysis of particulate matter with a diameter of 2.5 micrometers or smaller (PM2.5) plays a pivotal role in understanding air quality changes. This study focuses on the application of a new bandpass bootstrap approach, termed the Variable Bandpass Periodic Block Bootstrap (VBPBB), for analyzing time series data which provides modeled predictions of daily mean PM2.5 concentrations over 16 years in Manhattan, New York, the United States. The VBPBB can be used to explore periodically correlated (PC) principal components for this daily mean PM2.5 dataset. This method uses bandpass filters to isolate distinct PC components from datasets, removing unwanted interference including noise, and bootstraps the PC components. This preserves the PC structure and permits a better understanding of the periodic characteristics of time series data. The results of the VBPBB are compared against outcomes from alternative block bootstrapping techniques. The findings of this research indicate potential trends of elevated PM2.5 levels, providing evidence of significant semi-annual and weekly patterns missed by other methods.