MannKendallLTP {HKprocess}

Mann-Kendall trend test under the scaling hypothesis.

Description

The function MannKendallLTP applies the Mann-Kendall test under the scaling hypothesis for the data (Hamed 2008).

Usage

MannKendallLTP(data)

Arguments

data

time series data

Value

A list with three components.

Mann_Kendall

Kendall's tau statistic, score, variance of score, Sen's slope, denominator D where tau=S/D and p-value for the Mann-Kendall test

Significance_of_H

H estimate (eq.21, Hamed 2008) of the modified variables and p-value

Mann_Kendall_LTP

Variance of score (p.356, Hamed 2008) and p-value for the Mann-Kendall test under the scaling hypothesis

Note

The functions score.c, score0.c and VstarSfunction.c are called from the C library of the package. The estimator of H for the stochastic process in eq(18) (Hamed 2008) is the ML estimator in Tyralis and Koutsoyiannis (2011). The denominator for the Mann-Kendall test is calculated according to eq(23.3.4) in Hipel and McLeod (1994). The Mann-Kendall and modified Mann-Kendall test's hypotheses are Ho: no trend vs H1: trend is present. The H test's hypotheses are H0: H is not significant vs H1: H is significant.

Author(s)

Hristos Tyralis

References

Hamed KH (2008) Trend detection in hydrologic data: The Mann-Kendall trend test under the scaling hypothesis. Journal of Hydrology 349(3–4):350–363. doi:10.1016/j.jhydrol.2007.11.009.

Hipel KW, McLeod AI (1994) Time series modelling of water resources and environmental systems. Amsterdam: Elsevier.

Tyralis H, Koutsoyiannis D (2011) Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process. Stochastic Environmental Research & Risk Assessment 25(1):21–33. doi:10.1007/s00477-010-0408-x.

Examples

# Modified Mann-Kendall test for the Nile time series.

MannKendallLTP(Nile)