csmk.test: Correlated Seasonal Mann-Kendall Test
In trend: Non-Parametric Trend Tests and Change-Point Detection

csmk.test

R Documentation

Correlated Seasonal Mann-Kendall Test

Description

Performs a Seasonal Mann-Kendall test under the presence of correlated seasons.

Usage

csmk.test(x, alternative = c("two.sided", "greater", "less"))

Arguments

`x`	a time series object with class `ts` comprising >= 2 seasons; `NA` values are not allowed
`alternative`	the alternative hypothesis, defaults to `two.sided`

Details

The Mann-Kendall scores are first computed for each season seperately. The variance - covariance matrix is computed according to Libiseller and Grimvall (2002). Finally the corrected Z-statistics for the entire series is calculated as follows, whereas a continuity correction is employed for n \le 10:

z = \frac{\mathbf{1}^T \mathbf{S}} {\sqrt{\mathbf{1}^T \mathbf{\Gamma}~\mathbf{1}}}

where

z denotes the quantile of the normal distribution, 1 indicates a vector with all elements equal to one, \mathbf{S} is the vector of Mann-Kendall scores for each season and \mathbf{\Gamma} denotes the variance - covariance matrix.

Value

An object with class "htest"

`data.name`	character string that denotes the input data
`p.value`	the p-value for the entire series
`statistic`	the z quantile of the standard normal distribution for the entire series
`null.value`	the null hypothesis
`estimates`	the estimates S and varS for the entire series
`alternative`	the alternative hypothesis
`method`	character string that denotes the test
`cov`	the variance - covariance matrix

Note

Ties are not corrected. Current Version is for complete observations only.

References

Hipel, K.W. and McLeod, A.I. (1994), Time Series Modelling of Water Resources and Environmental Systems. New York: Elsevier Science.

Libiseller, C. and Grimvall, A., (2002), Performance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71–84, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/env.507")}.