A modified Mann-Kendall trend test for autocorrelated data

One of the commonly used tools for detecting changes in climatic and hydrologic time series is trend analysis. A number of statistical tests exist to assess the significance of trends in time series. One of the commonly used non-parametric trend tests is the Mann-Kendall trend test. The null hypothesis in the Mann-Kendall test is that the data are independent and randomly ordered. However, the existence of positive autocorrelation in the data increases the probability of detecting trends when actually none exist, and vice versa. Although this is a well-known fact, few studies have addressed this issue, and autocorrelation in the data is often ignored. In this study, the effect of autocorrelation on the variance of the Mann-Kendall trend test statistic is discussed. A theoretical relationship is derived to calculate the variance of the Mann-Kendall test statistic for autocorrelated data. The special cases of AR(1) and MA(1) dependence are discussed as examples. An approximation to the theoretical relationship is also presented in order to reduce computation time for long time series. Based on the modified value of the variance of the Mann-Kendall trend test statistic, a modified non-parametric trend test which is suitable for autocorrelated data is proposed. The accuracy of the modified test in terms of its empirical significance level was found to be superior to that of the original Mann-Kendall trend test without any loss of power. The modified test is applied to rainfall as well as streamflow data to demonstrate its performance as compared to the original Mann-Kendall trend test.