Time series data is often influenced by serial correlation. When data are not random and influenced by autocorrelation, modified Mann-Kendall tests may be used for trend detction. Hamed and Rao (1998) have proposed variance correction approach to address the issue of serial correlation in Trend analysis. Data are initially detrended and the effective sample size is calulated using the ranks of significant serial correlation coefficients which are then used to correct the inflated (or deflated) variance of the test statistic.
mmkh3lag(x,ci=0.95)- Time series data vector
- Confidence interval
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
A detrended time series is constructed using Sen's slope and the lag-1 autocorreltation coefficient of the ranks of the data. The variance correction approach proposed by Hamed and Rao (1998) uses only significant lags of autocorrelation coefficients. As suggested by Rao et al. (2003), only the first three autocorrelation coefficients are used in this function.
Hamed, K. H. and Rao, A. R. (1998). A modified Mann-Kendall trend test for autocorrelated data. Journal of Hydrology, 204(1<U+2013>4): 182<U+2013>196. <doi:10.1016/S0022-1694(97)00125-X>.
Kendall, M. (1975). Rank Correlation Methods. Griffin, London, 202 pp.
Mann, H. B. (1945). Nonparametric Tests Against Trend. Econometrica, 13(3): 245-259.
Rao, A. R., Hamed, K. H., & Chen, H.-L. (2003). Nonstationarities in hydrologic and environmental time series. Ringgold Inc., Portland, Oregon, 362 pp. <doi:10.1007/978-94-010-0117-5>
Salas, J.D. (1980). Applied modeling of hydrologic times series. Water Resources Publication, 484 pp.
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. <doi:10.2307/2285891>
# NOT RUN {
x<-c(Nile)
mmkh3lag(x)
# }
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