We present a flexible method that employs a power series expansion and Fourier series analysis to characterize the average long-term change and seasonal cycle, respectively, from a time series of observations of a trace atmospheric species. This approach maximizes the statistically significant information derived, including non-linear aspects of the long-term trends, without over fitting the data. Generally, a small set of parameter values (e.g., 7 or 8) provides this characterization.