Performs a Seasonal Mann-Kendall test under the presence of correlated
seasons.
Usage
csmk.test(x)
Arguments
x
A time series object that comprises $>= 2$ seasons
Value
methodThe chosen method (i.e. CSMK)
SgVector of Mann-Kendall scores for each season
varSgVector of the variance of Mann-Kendall scores for each season
ZgVector of Z-values for each season
pvalgVector of p-values for each season
CovarVariance - Covariance matrix for the seasonal Mann-Kendall statistics
CorrelCorrelation matrix for the seasonal Mann-Kendall statistics
StotMann-Kendall score for the entire series
ZZ-value for the entire series
Varianzvariance for the entire series
pvaluep-value for the entire series
Generic function summary.trend.test is provided.
Warning
Current Version is for complete observations only.
Details
The Mann-Kendall statistics are first computed for each season seperately.
The variance - covariance matrix is computed
according to Libiseller and Grimvall (2002) and ties are taken into
account. Finally the corrected Z-statistics for the entire series
is calculated as follows:
$$Z = \mathbf{1}^T \mathbf{S} / \mathbf{1}^T \mathbf{X}~\mathbf{1}$$
Z denotes the quantile of the normal distribution, 1 indicates a vector
with all elements equal to one, S is the vector of Mann-Kendall scores
for each season and X denotes the variance - covariance matrix.
References
Hipel, K.W. and McLeod, A.I., (2005).
Time Series Modelling of Water Resources and Environmental Systems.
Electronic reprint of our book orginally published in 1994.
http://www.stats.uwo.ca/faculty/aim/1994Book/.
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.