Two data sets, one meteorological (vertical velocity, W) and one climatological (Palmer Drought Index, PDI), were chosen to demonstrate the need to depart from linear models. A first order autoregressive model, typically used as a default model for correlated time series in climate studies, was altered with a nonlinear component to provide insight to possible errors in estimation due to nonlinearities. The nonlinear model, W and PDI time series all three have comparable skewness, kurtosis and integral scales. Records of W and PDI are of sufficient lengths to make reliable statistical inference without questionable model assumptions. Meteorological observations are much more likely to have adequate record lengths for nonparametric inference, while the shortness of record lengths in the majority of climatological time series presents a formidable obstacle for most statistical methods.