Methods for Time Series Analysis - Hydrologic Time Series Analysis: Theory and Practice - page 78

(vii) The Turning Point test is easy to apply, especially when the time
series is plotted graphically. It is an effective test for randomness
against systematic oscillation. However, if the turning points tend to
bunch together, the Kendall's Phase test is more relevant (Shahin et
al., 1993). The demerit of the Kendall's phase test is that a comparison
of observed and theoretical numbers of phases by the usual chi-
square test is invalidated due to the fact that the lengths of phases are
not independent. Also, the distribution of phase lengths does not tend
to be normal for large lengths of a series, but the number of phases
follows a normal distribution (Kendall, 1973). The Turning Point test
and Kendall's phase test are practically out-dated due to the availability
of much more powerful tests (Shahin et al., 1993).
(viii) The Wald-Wolfowitz test has demerit that it does not consider length
of runs and significant information about the time series is ignored.
Hence, this test is not very powerful nor efficient. The Sum of Squared
Lengths test is more powerful than the Wald-Wolfowitz test
(Himmelblau, 1969).
(ix) The Adjacency test for checking trends has demerit that it inherently
considers that the time series data points are independent and the data
are collected under uniform conditions (Kanji, 2001), which may not
be true for the real-world time series.
(x) The Difference Sign test for trend detection has a demerit almost
similar to the Adjacency test that the data points of the time series are
collected under uniform conditions and the number of data points is
large, which may not be true for short-term time series where data
were collected under dissimilar conditions.
(xi) The Run test on Successive Differences has a demerit very similar to
the Adjacency test that the time series data are collected under uniform
conditions, which may not be true for real-world time series.
(xii) The Wilcoxon-Mann-Whitney test has merit that it is a nonparametric
test (i.e., distribution-free) and hence, it may be applicable to normal
and non-normal time series. However, this test has demerit that it
considers that the time series data points are random and independent
of time, which may not be true for an autocorrelated or persistent
time series.
(xiii) The Kendall's Rank Correlation test is one of the most powerful tests
for trend checking in the hydrologic time series.
(xiv) The Mann-Kendall test is a nonparametric test for trend detection in
a time series without specifying whether the trend is linear or nonlinear.
Hence, this test has an advantage of being applicable for non-normal
as well as normal time series. The nonparametric nature of the test
avoids testing of normality in the time series. However, the existence
of serial correlation in a time series may affect the ability of the
Mann-Kendall test to assess the site significance of a trend, and the