Comparative evaluation of statistical tests for time series analysis: application to hydrological time series / Evaluation comparative de tests statistiques pour l'analyse de séries temporelles: application à des séries temporelles hydrologiques

Abstract

Statistical analyses of hydrological time series play a vital role in water resources studies. Twenty-nine statistical tests for detecting time series characteristics were evaluated by applying them to analyse 46 years of annual rainfall, 47 years of 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfalls at Kharagpur, West Bengal, India. The performance of all the tests was evaluated. No severe outliers were found, and both the annual and maximum rainfall series were found to be normally distributed. Based on the known physical parameters affecting the homogeneity, the cumulative deviations and the Bayesian tests were found to be superior to the classical von Neumann test. Similarly, the Tukey test proved excellent among all the multiple comparison tests. These tests indicated that all the seven rainfall series are homogeneous. Two parametric t tests and the non-parametric Mann-Whitney test indicated stationarity in all the rainfall series. Of 12 trend detection tests, nine tests indicated no trends in the rainfall series. The Kendall's Rank Correlation test and the Mann-Kendall test were found equally powerful. Moreover, the Fourier series analysis revealed no apparent periodicities in all the seven rainfall series. The annual rainfall series was found persistent with a time lag of nine years. All the rainfall series were subjected to stochastic analysis by fitting 35 autoregressive moving-average (ARMA) models of different orders. The best-fit models for the original annual rainfall and 1-, 2- and 3-day maximum rainfall series were found to be ARMA(0,4), ARMA(0,2), ARMA(0,2) and ARMA(3,0), respectively. The best-fit model for the logarithmically transformed 4-day maximum rainfall was found to be ARMA(0,2). However, for the inversely transformed 4-, 5- and 6-day maximum rainfall series, ARMA(0,1) was obtained as the best-fit model. It is concluded that proper selection of time series tests and use of several tests is indispensable for making useful and reliable decisions.