Dynamic Principal Component Analysis: Identifying the Relationship   between Multiple Air Pollutants
  The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurements of five pollutants (O3, CO, NO2, SO2, PM2.5) from January 1, 2009 through December 31, 2011 for each of the 24 hours in a day. The resulting dynamic components are examined by hour across days for the 3 year period. Diurnal and seasonal patterns are revealed underlining times when DPCA performs best and two principal components (PCs) explain most variability in the multivariate series. DPCA is shown to be superior to static principal component analysis (PCA) in discovery of linear relations among transformed pollutant measurements. DPCA captures the time-dependent correlation structure of the underlying pollutants recorded at up to 34 monitoring sites in the region. In winter mornings the first principal component (PC1) (mainly CO and NO2) explains up to 70% of variability. Augmenting with the second principal component (PC2) (mainly driven by SO2) the explained variability rises to 90%. In the afternoon, O3 gains prominence in the second principal component. The seasonal profile of PCs' contribution to variance loses its distinction in the afternoon, yet cumulatively PC1 and PC2 still explain up to 65% of variability in ambient air data. DPCA provides a strategy for identifying the changing air quality profile for the region studied. 
Oleg Melnikov, Loren H. Raun, Katherine B. Ensor
stat.AP stat.ML