Performs a Seasonal Mann-Kendall test under the presence of correlated seasons.
csmk.test(x, alternative = c("two.sided", "greater", "less"))An object with class "htest"
character string that denotes the input data
the p-value for the entire series
the z quantile of the standard normal distribution for the entire series
the null hypothesis
the estimates S and varS for the entire series
the alternative hypothesis
character string that denotes the test
the variance - covariance matrix
a time series object with class ts comprising >= 2 seasons;
NA values are not allowed
the alternative hypothesis, defaults to two.sided
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.
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, tools:::Rd_expr_doi("10.1002/env.507").