Advances in Time Series Methods and Applications pp 215-229 | Cite as

# Improved Seasonal Mann–Kendall Tests for Trend Analysis in Water Resources Time Series

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## Abstract

Nonparametric statistical procedures are commonly used in analyzing for trend in water resources time series (Chapter 23, Hipel and McLeod in Time series modelling of water resources and environmental systems. Elsevier, New York, 2005 [10]). One popular procedure is the seasonal Mann–Kendall tau test for detecting monotonic trend in seasonal time series data with serial dependence (Hirsch and Slack in Water Resour Res 20(6):727–732, 1984 [12]). However there is little rigorous discussion in the literature about its validity and alternatives. In this paper, the asymptotic normality of a seasonal Mann–Kendall test is determined for a large family of absolutely regular processes, a bootstrap sampling version of this test is proposed and its performance is studied through simulation. These simulations compare the performance of the traditional test, the bootstrapped version referred to above, as well as a bootstrapped version of Spearman’s rho partial correlation. The simulation results indicate that both bootstrap tests perform comparably to the traditional test when the seasonal effect is deterministic, but the traditional test can fail to converge to the nominal levels when the seasonal effect is stochastic. Both bootstrapped tests perform similarly to each other in terms of accuracy and power.

## Keywords

Kendall correlation Spearman partial correlation Weakly dependent observations Stationary ARMA process Bootstrap Hydrology## Mathematical Subject Classification (2000)

Primary 62G10 Secondary 62M10## Notes

### Acknowledgments

This research was supported in part by discovery grants from the Natural Sciences and Engineering Council of Canada and Acadia University Article 25.55. The authors wish to thank the Referees for their constructive comments and suggestions, and the program committee for organizing the event, *Time Series Methods and Applications: the A. Ian McLeod Festschrift*.

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