2.3.1 Mann-Kendall Trend Test
The MK trend test is a nonparametric test for monotonicity of trends in
time series data (Mann, 1945; Kendall, 1975). By ranking the time series
observations and measuring the later observations (j ) against
earlier observations (i ), MK testing allows us to understand the
monotonicity of an upward or downward trend in a time series. A
perfectly monotonic trend consistently increases or decreases. For
example, a perfectly increasing monotonic function is never decreasing
at any point along the function. Using pairwise comparison of ranked
values from all data points, the test statistic (S ) is calculated
through either adding or subtracting 1 for every value that is larger or
smaller than the later value (Equation 1). This results in a test
statistic (S ) that characterizes the directionality and
monotonicity of a trend in a given time series. S is then used to
calculate the τ test statistic (Equation 2), which is a measure of
correlation that ranges from -1 to +1 with the sign indicating the
direction of the value’s change over time. This test determines whether
there is a significant, monotonic trend in a value over time in either a
positive or negative direction.