modifiedmk (version 1.1.0)

bbsmK: Block bootstrapped Mann-Kendall Trend Test

Description

Block lengths are automatically calculated using the lag of the smallest signigicant auto-correlation coefficient. And eta value of 1 is used as a default value following the results of Khaliq et al. (2009), 2000 bootstrapped replicates are recommended following the results of Svensson et al. (2005).

Usage

bbsmK(x, ci = 0.95, nsim = 2000, eta = 1, bl.len = NULL)

Arguments

x

- Time series data vector

ci

- Confidence Interval

nsim

- Number of simulations

eta

- Added to the block length

bl.len

- Block length

Value

Z - Mann- Kendall Z-statistic

slp - sen's slope

S - Mann-Kendall 's'- statistic

Tau - Mann-Kendall's Tau

lb- Lower bound of confidence interval value

ub- Upper bound of confidence interval value

Details

Block lengths are automatically selected using the lag of the least significance serial correlation, to which the 'eta' term is added. A value of eta = 1 is used as the default as per Khaliq et al. (2009). Alternatively, the user may define the block length. 2000 bootstrap replicates are recommended as per Svensson et al. (2005) and <U+00D6>n<U+00F6>z, B. and Bayazit (2012).

References

Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis Forecasting and Control. Holden-Day, San Fransisco, California, 712 pp.

Kendall, M. (1975). Multivariate analysis. Charles Griffin. Londres. 0-85264-234-2.

Khaliq, M. N., Ouarda, T. B. M. J., Gachon, P., Sushama, L., and St-Hilaire, A. (2009). Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers. Journal of Hydrology, 368: 117-130.

Kundzewicz, Z. W. and Robson, A. J. (2000). Detecting Trend and Other Changes in Meteorological Data. World Climate Program ? Data and Monitoring. World Meteorological Organization, Geneva (WMO/TD-No. 1013).

Kundzewicz, Z. W. and Robson, A. J. (2004). Change detection in hydrological records ? a review of the methodology. Hydrological Sciences Journal, 49(1): 7-19.

Mann, H. B. (1945). Nonparametric Tests Against Trend. Econometrica, 13(3), 245?259. <doi:10.1017/CBO9781107415324.004>

<U+00D6>n<U+00F6>z , B. and Bayazit M. (2012). Block bootstrap for Mann-Kendall trend test of serially dependent data. Hydrological Processes, 26: 3552-3560.

Svensson, C., Kundzewicz, Z. W., and Maurer, T. (2005). Trend detection in river flow series: 2. Floods and low-flow index series. Hydrological Sciences Journal, 50(5): 811-823.

Examples

# NOT RUN {
x<-c(Nile)
bbsmK(x)

# }