Removing the Influence of the Serial Correlation on the Mann-kendall Test

The Pre-Whitening (PW), the Trend-Free Pre-Whitening (TFPW) and the Modified Trend-Free PreWhitening (MTFPW) were developed to remove the influence of serial correlations on the MannKendall trend test. The main purpose of this study was to compare the performance of these algorithms for evaluating trends in auto-correlated series. The PW, TFPW and MTFPW were also applied to the monthly values of the rainfall (Pre), minimum (Tmin) and maximum (Tmax) air temperature data obtained from the weather station of Ribeirão Preto, State of São Paulo, Brazil. Sets of Monte Carlo simulations were carried out to evaluate the occurrence of the type I and the type II errors obtained from these three algorithms. The TFPW has the highest power. However, it also presented the highest occurrence of type I errors. The PW clearly limits the influence of serial correlation on the occurrence of type I errors. Nevertheless, this feature is accomplished at a cost of a great reduction of its ability to detect trends. The MTFPW leads to a better balance between the probabilities of both statistical errors. It was also concluded that the hypothesis of the presence of no climate change in the location of Ribeirão Pareto cannot be accepted.