trend (version 0.2.0)

smk.test: Seasonal Mann-Kendall Test

Description

Performs a Seasonal Mann-Kendall test

Usage

smk.test(x)

Arguments

x

A time series object comprising >= 2 seasons

Value

method

The chosen method (i.e. SMK)

Sg

Vector of Mann-Kendall scores for each season

varSg

Vector of the variance of Mann-Kendall scores for each season

Zg

Vector of Z-values for each season

pvalg

Vector of p-values for each season

Covar

Variance - Covariance matrix for the seasonal Mann-Kendall statistics

Correl

Correlation matrix for the seasonal Mann-Kendall statistics

Stot

Mann-Kendall score for the entire series

Z

Z-value for the entire series

Varianz

variance for the entire series

pvalue

p-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. However, in the case of "method==smk" the covariance between the seasons is set to zero. Finally the 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 (which is zero between the seasons).

References

Hipel, K.W. and McLeod, A.I., (2005). Time Series Modelling of Water Resources and Environmental Systems. http://www.stats.uwo.ca/faculty/aim/1994Book/.

Hirsch, R., J. Slack and R. Smith, (1982): Techniques of Trend Analysis for Monthly Water Quality Data. Water Resour. Res., 18, 107-121.

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.

See Also

csmk.test, mk.test, SeasonalMannKendall, summary.trend.test

Examples

# NOT RUN {
data(co2)
plot(co2)
res <- smk.test(co2)
summary.trend.test(res)

data(nottem)
plot(nottem)
res <- smk.test(nottem)
summary.trend.test(res)
# }