Nonoverlapping Block Stratified Random Sampling Approach for Assessment of Stationarity

Abstract

Assessment of stationarity in any hydroclimatic time series is a vital task for hydrologic design and climate change assessments. Methods that rely on the presence of statistically significant trends or change points to derive inferences about stationarity may fail to check for all the time-invariant characteristics of time series. An approach that uses nonoverlapping stratified random sampling blocks of time series and nonparametric tests is proposed and evaluated in this study to assess stationarity. Chronologically continuous data from contiguous blocks are evaluated using two-sample and multisample nonparametric tests for the assessment of distributional, median and variance similarity, invariance of statistical moments, and autocorrelation at several lags. Explicit methods for the evaluation of different characteristics of time series are also developed to assess the two forms (viz., weak and strict) of stationarity. The multiple test evaluations are weighted using the analytical hierarchy process (AHP) to draw conclusions about stationarity. The proposed approach is tested using several real-world and synthetically generated hydroclimatic data sets through extensive simulations. Stationarity assessments derived from nonparametric trend and unit root tests have been compared to those from the approach developed. Results from this study point to the correct identification of weak and strict stationarity in real-world hydroclimatic time series compared to similar evaluations from unit root and trend tests. The robustness of the approach is also confirmed by an accurate assessment of the stationarity of several synthetic time series representing various hydroclimatic processes at different time scales. The proposed approach is a conceptually simple and superior alternative to trend and unit root tests since it provides a comprehensive assessment of stationarity using multiple nonparametric tests.