Correlated Seasonal Mann-Kendall Test
Performs a Seasonal Mann-Kendall test under the presence of correlated seasons.
csmk.test(x, alternative = c("two.sided", "greater", "less"))x |
a time series object with class |
alternative |
the alternative hypothesis, defaults to |
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 <= 10:
z = 1^T S / sqrt(1^T Γ 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{Γ} denotes the variance - covariance matrix.
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 |
Ties are not corrected. Current Version is for complete observations only.
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, http://dx.doi.org/10.1002/env.507.
csmk.test(nottem)
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