R: Mann-Kendall trend test

MannKendall {Kendall} | R Documentation

## Mann-Kendall trend test

### Description

This is a test for monotonic trend in a time series z[t] based on the Kendall rank correlation of z[t] and t.

### Usage

    MannKendall(x)

### Arguments

`x` | a vector of data, often a time series

### Details

The test was suggested by Mann (1945) and has been extensively used with environmental time series (Hipel and McLeod, 2005). For autocorrelated time series, the block bootstrap may be used to obtain an improved signficance test.

### Value

A list with class Kendall.

`tau` | Kendall's tau statistic
`sl` | two-sided p-value
`S` | Kendall Score
`D` | denominator, tau=S/D
`varS` | variance of S

Generic function print.Kendall and summary.Kendall are provided to print the output.

### Note

If you want to use the output from MannKendall, save the result as in res<-MannKendall(x,y) and then select from the list res the value(s) needed.

### Author(s)

A.I. McLeod, aimcleod@uwo.ca

### References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

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/.

Mann, H.B. (1945), Nonparametric tests against trend, Econometrica, 13, 245-259.

### See Also

`Kendall`, `SeasonalMannKendall` `tsboot`

### Examples

    # Annual precipitation entire Great Lakes
    # The time series plot with lowess smooth suggests an upward trend
    # The autocorrelation in this data does not appear significant.
    # The Mann-Kendall trend test confirms the upward trend.
    data(PrecipGL)
    plot(PrecipGL)
    lines(lowess(time(PrecipGL),PrecipGL),lwd=3, col=2)
    acf(PrecipGL)
    MannKendall(PrecipGL)
    #
    #Use block bootstrap
    library(boot)
    data(PrecipGL)
    MKtau<-function(z) MannKendall(z)$tau
    tsboot(PrecipGL, MKtau, R=500, l=5, sim="fixed")
    #
    # Deseasonalize a monthly time series and use the block bootstrap
    library(boot)
    data(manaus)
    z<-matrix(manaus, ncol=12, byrow=12)
    zm<-apply(z, MARGIN=2, FUN=mean)
    zs<-apply(z, MARGIN=2, FUN=sd)
    z2<-sweep(z, MARGIN=2, STATS=zm) #subtract monthly means
    z3<-sweep(z2, MARGIN=2, STATS=zs, FUN="/") #divide by monthly sd
    zds<-c(t(z3))
    attributes(zds)<-attributes(manaus)
    plot(zds)
    #do Mann-Kendall trend test
    MannKendall(zds)
    #check robustness by applying block bootstrap
    MKtau<-function(z) MannKendall(z)$tau
    tsboot(zds, MKtau, R=500, l=12, sim="fixed")
    #the significance level has dropped!
    #it is significant now at about 2 sd

[Package Kendall version 2.2 Index]