  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.
