SAP HANA Predictive Analysis Library (PAL)

The difference-sign test counts the number S of times that x(t)−x(t−1) is positive, t=1,2,...,n. For an IID
(Independent and Identically Distributed) series, the theoretical expectation of S is
µ s =(n−1)/2,
and the corresponding standard deviation is
For a large n, S approximately behaves Gaussian distribution
. Hence, a large positive or negative
value of S−µ S indicates the presence of an increasing (or decreasing) trend. The data is considered to have a
trend if |S−µ S |>σ S , otherwise no trend exists. Nevertheless, the difference-sign test must be used with great
caution. In the case of large proportion of tie data, for example, it may give a result of negative trend, while in
fact it has no trend.
Rank Test
The second solution is the rank test, which is usually known as Mann-Kendall (MK) Test (Mann 1945, Kendall
1975, Gilbert 1987). It tests whether to reject the null hypothesis (H 0 ) and accept the alternative hypothesis
(H α ), where
H 0 : No monotonic trend,
H α : Monotonic trend is present,
α: the tolerance probability that falsely concludes a trend exists when there is none, 0