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Bootstrap rank tests for trend in time series

The Mann–Kendall (MK) test is a popular test for monotonic trend when the observations are independent, but its null distribution properties under independence do not apply to the situation where the observations are dependent. We provide block and sieve bootstrap methods for approximating the null distribution of MK in such a situation. In the case of the block bootstrap, when the observations follow a weakly dependent β mixing process, such an approximation is based on the determination that MK and its block bootstrap counterpart are asymptotically normal. In addition, we note that sieve methods are applicable to a statistic that is asymptotically equivalent to MK. Simulations are conducted to compare the significance levels achieved by both block and sieve bootstrap methods for various models. An effective procedure is proposed for testing for trend when the form of the underlying process is unknown. Copyright © 2013 John Wiley & Sons, Ltd.