Mann-Kendall for autocorrelated data

The Mann-Kendall test is a commonly-used nonparametric test for time trend. However, the standard P-values obtained from it are based on an assumption of independence between observations (since the theory is that of the Kendall correlation). However, observations in time series are often autocorrelated: knowing that one observation is larger than the mean may tell you that the next observation is larger than the mean also. Simulation studies reveal that a positive autocorrelation makes it too easy to claim a significant trend (ie. more than 5% of the time if there is actually no time trend), and a negative autocorrelation makes it too difficult to find a significant trend. Since most series in practice exhibit positive autocorrelation (if any), this makes it important to check the autocorrelation in a given series and to adjust the test if necessary.