Air quality data collected at 8 monitoring stations located in the central Taiwan Air Quality Total Quantity Control District were analyzed using multivariate statistical factor analyses. Based on the results thus obtained, 2 major factors, i.e. photochemical pollution factor and fuel factors, were selected for the purpose of evaluating their variations and the pattern of mutual influences for the various air pollution species with respect to time series. The evaluation was conducted using a vector time series coordinated with the ARCH (Autoregressive Conditional Heteroscedacity) and GARCH (Generalized Autoregressive Conditional Heteroscedacity) models in addition to being combined with dynamic impact response analyses using a multiple time series model. The results reveal that the current O3 value is affected by the PM10 values of both a one time lag and a two times lag, as well as the NO2 value of one time lag. When the current SO2 is produced, its concentration can be used to estimate the current CO concentration, and the one time lag SO2 concentration also influences the CO concentration. Additionally, results of impact response analyses show that current CO concentration responds to variations in current SO2; this indicates that the existence of SO2 due to incomplete combustion at the pollution source is immediately reflected by the current production of CO without lagging. In this paper, the vector time series is coupled with the (G)ARCH model to convert simple data series into valuable information so that raw data are better and more completely presented for the purpose of revealing future variation trends. Additionally, the results can be referenced by authorities for planning air quality total quantity control, applying and examining various air quality models, simulating the allowable increase of air quality limits, and evaluating the benefit of air quality improvement.