Most of the time series analysis methods applied today rely heavily on the key assumptions of linearity, Gaussianity and stationarity. Natural time series, including hydrologic, climatic and environmental time series, which satisfy these assumptions seem to be the exception rather than the rule. Nevertheless, most time series analysis is performed using standard methods after relaxing the required conditions one way or another, in the hope that the departure from these assumptions is not large enough to affect the result of the analysis. A large amount of data is available today after almost a century of intensive data collection of various natural time series. In addition to a few older data series such as sunspot numbers, sea surface temperatures, and so on, data obtained through dating techniques (tree-ring data, ice core data, geological and marine deposits) are available. With the advent of powerful computers, the use of simplified methods can no longer be justified, especially with the limited success of those methods in explaining the inherent variability in natural time series.
This study presents a number of techniques that have been discussed in the literature during the 1980s and 1990s concerning the investigation of stationarity, linearity and Gaussianity of hydrologic and environmental times series. These techniques cover different approaches for assessing nonstationarity, ranging from time domain analysis, to frequency domain analysis, to the combined time-frequency and time-scale analyses, to segmentation analysis, in addition to formal statistical tests of linearity and Gaussianity.