Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 156

and Mann-Kendall tests have been used widely in recent hydrological studies
as well as in studies related to soil, plant and meteorology.
7.7.2 Assessment of Trend Tests
Based on the results of various trend detection tests (Tables 7.5 and 7.6), a
comparative evaluation could be done. The only test which indicates presence
of trend in all the seven rainfall time series under study (i.e., annual rainfall
and one-day, 2-, 3-, 4-, 5- and 6-day maximum rainfalls) is Wald-Wolfowitz
test. However, this test is reported to be neither very powerful nor efficient by
Himmelblau (1969) because this test does not take into account the phase
length for computing the test-statistic and thus some useful information is
ignored. The Kendall's Phase test indicates a trend in all the maximum rainfall
time series, whereas it indicated no trends in the annual rainfall time series.
On the contrary, the SROC test, which is recommended by the World Health
Organization for hydrologic time series analysis, suggests presence of trend
of the annual rainfall time series, but it suggests no trend in all the maximum
rainfall time series. It is worth mentioning that the Kendall's Phase test is
currently outdated due to the availability of sound and robust trend detection
tests (Shahin et al., 1993). Therefore, results of SROC test can be considered
superior to the Kendall's Phase test. A trend is also detected in the 4-day
maximum rainfall time series by the Difference Sign test. Apart from the
above-mentioned tests, the remaining nine trend tests did not reveal any trends
in the annual as well as the one-day, 2-, 3-, 4-, 5- and 6-day maximum rainfall
time series of Kharagpur. Thus, bearing in mind the fact that more the applied
tests, more is the chance to reject a true null hypothesis, it can be inferred that
the annual rainfall series (46 years) of Kharagpur does not have any trends
(i.e., series is stable) and similarly the one-day, consecutive 2-, 3-, 4-, 5- and
6-day maximum rainfall series (47 years) are free from any linear trends.
Based on the above results, it can be concluded that the SROC test, Kendall's
Rank Correlation test and Mann-Kendall test are more reliable or powerful
than the Wald-Wolfowitz test, Kendall's Phase test and Difference Sign test.
It is a usual practice to consider a hydrologic time series to be stationary
if it is homogeneous and trend-free. Therefore, all the rainfall time series of
Kharagpur can also be considered stationary. This finding is in agreement
with that based on the three specific stationary tests (mentioned in Section on
Checking Stationarity ). It is also well discernible from the results of different
trend tests that if more tests are applied for the same objective, it is usually
difficult to arrive at a common conclusion. This is due to the fact that on
increasing the number of tests for analyzing a time series, the probability that
at least one test rejects the null hypothesis of being true increases. Therefore,
it is strongly recommended that the null hypothesis should not be rejected on
the basis of only one or two test results (Brockwell and Davis, 1991).