modifiedmk (version 1.1.0)

mmkh: Modified Mann-Kendall Test For Serially Correlated Data Using Hamed and Rao (1998) Variance Correction Approach.

Description

Time series data is often influenced by sub-sequent observations. When data is not random and influenced by auto-correlation, Modified Mann-Kendall tests are to be used in trend detction studies. Hamed and Rao (1998) have proposed variance correction approach to address the issue of serial correlation in Trend analysis. Trend is removed from the series and effective sample size is calulated using significant serial correlation coefficients.

Usage

mmkh(x,ci=0.95)

Arguments

x

- Time series data vector

ci

- Confidence Interval

Value

Corrected Zc - Z-Statistic after variance Correction

new P.value - P-Value after variance correction

N/N* - Effective sample size

Original Z - Original Mann-Kendall Z-Statistic

Old P-value - Original Mann-Kendall P-Value

Tau - Mann-Kendall's Tau

Sen's Slope - Sen's slope

old.variance - Old variance before variance Correction

new.variance - Variance after correction

Details

Trend free time series is constructed by calculating Sen's slope and Auto Correlation coefficient AR(1). Variance correction approach proposed by Hamed and Rao (1998) uses only significant values from all the available values of Auto-Correlation Coefficients.

References

Mann, H. B. (1945). Nonparametric Tests Against Trend. Econometrica, 13(3), 245<U+2013>259. http://doi.org/10.1017/CBO9781107415324.004

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

Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall<U+2019>s Tau. Journal of the American Statistical Association, 63(324), 1379. http://doi.org/10.2307/2285891

Hamed, K. H., & Ramachandra Rao, A. (1998). A modified Mann-Kendall trend test for autocorrelated data. Journal of Hydrology, 204(1<U+2013>4), 182<U+2013>196. http://doi.org/10.1016/S0022-1694(97)00125-X

Rao, A. R., Hamed, K. H., & Chen, H.-L. (2003). Nonstationarities in hydrologic and environmental time series. http://doi.org/10.1007/978-94-010-0117-5

Salas, J.D., 1980. Applied modeling of hydrologic times series. Water Resources Publication.

Examples

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

# }