Often, the Mann-Kendall (MK) test (Mann 1945, Kendall 1975) is used to test if the variable consistently increases (decreases) through time, but the trend may or may not be linear.
Why not using linear regression instead?
Regression analysis requires that the residuals from the fitted regression line be normally distributed. But the MK test is a non-parametric (distribution-free) test, which is based on the rank of the data. The measurements do not have to be normally distributed or that the trend, if present, is linear.
The MK test can be computed if there are missing values and values below the one or more limits of detection (LD), but the performance of the test will be affected. The time between samples should be sufficiently large so that there is no correlation between measurements collected at different times.
H0: No monotonic trend
A positive (negative) value of MK statistics indicates that the data tend to increase (decrease) with time.
MK test can be performed with R Package ‘Kendall’ and function MannKendall(x)
where x a vector of data, often a time series
For autocorrelated time series, the block bootstrap may be used to obtain an improved significance test.
Value of MannKendall(x)
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.
Good resources with more information on this:
- "Time Series Modelling of Water Resources and Environmental Systems" by Keith W. Hipel and A. Ian McLeod.
- http://cran.r-project.org/web/packages/Kendall/Kendall.pdf
- Trend analysis on climate and weather data
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