We analyzed the vapor phase atmospheric concentrations of representative persistent chemicals (i.e., α- and γ-hexachlorocyclohexane, phenanthrene, PCB-18 and PCB-52) in samples collected at a remote site near Eagle Harbor, Michigan, and at an urban site in Chicago, Illinois, using four time series models: a modified Clausius-Clapeyron equation, a multiple linear regression that includes both a linear and an harmonic dependence on time, digital filtration (DF), and dynamic harmonic regression (DHR). The results of these different models were evaluated in terms of goodness-of-fit, long-term trends, and halving times. The four approaches all provided highly significant descriptions of the data, with coefficients of determination (R(2)) ranging from 0.33 to 0.96. In general, the DF and DHR methods fit the data better, capturing not only the seasonal variations of the atmospheric concentrations but also smaller scale interannual variations in the long term trends. The halving times calculated using the four methods were generally similar to one another, and they ranged from about 4 years for γ-HCH at Chicago to about 60 years for PCB-52 at Chicago. This analysis showed that each of these four statistical methods for evaluating long-term time series has advantages and disadvantages. The choice of the appropriate method should depend on the output needed, the type of audience, and the availability and usability of the necessary software.