Climatic variability and statistics. A simulation approach for estimating power and robustness of tests of stationarity
Statistical analysis of hydrometeorological time series is often used to identify climatic variations. Most often this analysis consists of applying and interpreting statistical tests of time series homogeneity. Hydrological time series (rainfall and runoff data) are often short and do not always comply with the hypotheses of the statistical methods. Through simulation we have investigated the power and the robustness of some tests which are widely used in the studies dealing with climatic variability. In each case studied, one hundred samples of fifty elements have been generated based on the main characteristics of natural rainfall series. A shift in the mean has been used to represent a possible climatic variation. The procedures used are the rank correlation test, Pettitt's test, Buishand's test, Lee and Heghinian's bayesian procedure, and Hubert and Carbonnel's segmentation procedure for hydrometeorological series. Each simulation of one hundred samples is used to assess the performances of the methods considering a specific characteristic of the series: normality or non-normality, autocorrelation, trend, shift in the variance. First of all, stationary series have been simulated to evaluate the type I error of the tests. Then the series have been simulated with a break in the mean with different levels of amplitude, from 25% to 100% of the standard deviation value. The rank correlation test, Pettitt's test, Buishand's test and the segmentation procedure with a significance level of 1% (significance level of Scheffé's test) reject as heterogeneous less than ten series over one hundred homogeneous simulated series. This result is consistent with the type I error of a statistical test. On the other hand, Lee and Heghinian's bayesian method rejects about 40% of the series. This result means that this latter procedure must only be applied under the hypothesis of heterogeneity. The estimated power of the methods exceeds 40% to 50% when the break in the mean is more than 75% of the standard deviation value. Independent series have been simulated from normal, log-normal and Pearson distributions to compare the performances of the methods requiring normality. The results show that normality has no significant impact on the performances of these methods. However, the simulations do show that the condition of independence of the successive elements of the series is essential to keep performances constant. Otherwise a trend in the series makes the tests inefficient, except for the rank correlation test for which the alternative is a trend. No method seems to be robust against both negative and positive autoregressive dependencies. The procedures requiring a constant variance are robust when the series keep a constant mean, but seem more or less slightly influenced by a break both in the mean and in the standard deviation.