This study has demonstrated the value of inferring statistics of meteorological and climatological time series nonparametrically, thus avoiding time series analyses based on model assumptions. Nonlinearity undetected by basic diagnostic procedures was shown to invalidate the inference based on linear models, whereas the nonparametric (subsampling) method remains practical in complex dependent data situations typical for atmospheric and climatic events.

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.