This study adopted the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to examine the 10 ozone precursors of the highest concentrations among the 54 that were assessed over a number of years at the four photochemical assessment monitoring stations (PAMSs) in the Kaohsiung–Pingtung Area in Taiwan. First, the 10 ozone precursors, which were all volatile organic compounds (VOCs), were analyzed using the factor analyses in multiple statistical analyses that had the most significant impact on the area’s ozone formation: mobile pollution factor, which included 1,2,4-Trimethylbenzene (C9H12), toluene (C7H8), and Isopropyl benzene (C9H12). Then, taking into consideration that the number sequences might be affected by standardized residuals, this study applied the vector autoregressive moving average-EGARCH (VARMA-EGARCH) model to analyze the correlation between the three VOCs under different polluting activities. The VARMA-EGARCH model in this research included dummy variables representing changing points of variance structures in the variance formula to predict the conditional variance. This process proved able to effectively estimate the relevant coefficients of the three VOCs’ dynamic conditions that changed with time. The model also helped to prevent errors from occurring when estimating the conditional variance. Based on the testing results, this study determined the VARMA(2,1)-EGARCH(1,0) as the most suitable model for exploring the correlation between the three VOCs and meteorological phenomena, as well as the interplay between them in regard to interaction and formation. With the most representative of the three, toluene (TU), as the dependent variable and 1,2,4-Trimethylbenzene (TB) and Isopropyl benzene (IB) as the independent variables, this study found it impossible to calculate the TU concentration with TB and IB concentrations in the same period; estimations of TB and IB concentrations with a period of lag time were required because TU was mainly contributed by automobiles and motorcycles in Kaohsiung. TB and IB resulted from other stationary pollution sources in the region besides cars and motorbikes. When TU was evenly distributed and stayed longer in the atmosphere, the TB and IB concentrations were lower, so distribution conditions and concentrations could not be used to effectively estimate the concentration of toluene. This study had to wait until the next period, or when stationary pollution sources started producing TB and IB of higher concentrations during the daytime, in order to estimate the TU concentrations in a better photochemical situation.