Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 148

series of Kharagpur. The Link-Wallace test could not be applied to the second
fragmentation of annual rainfall time series and to both the fragmentations
(i.e., first and second) of maximum rainfall time series because of their unequal
sample sizes. The results of the Bartlett test (Table 7.3) indicate that the
homogeneity is associated with the annual rainfall time series for both the
fragmentations and with the second fragmentation of all maximum rainfall
time series (i.e., 1-, 2-, 3-, 4-, 5- and 6-day). However, the first fragmentation
of one-day, consecutive 3-, 4-, 5- and 6-day maximum rainfall time series are
found non-homogeneous based on the Bartlett test. Table 7.3 also reveals that
the results of the Hartley test are exactly similar to that of the Bartlett test for
the first fragmentation of all the rainfall time series under study. However, the
second fragmentation of consecutive 3-, 4- and 5-day maximum rainfall can
be declared non-homogeneous based on the Hartley test. Furthermore, based
on the historical information of the raingauge station, the Tukey test is found
to be more powerful in identifying the homogeneity than the Bartlett and
Hartley tests.
Based on the above results of three homogeneity tests and available
historical information for the raingauge station, it can be concluded that the
Cumulative Deviations and Bayesian tests are superior to the von Neumann
test. Similarly, Tukey test is better than Bartlett, Hartley and Link-Wallace
tests for multiple comparisons. All these superior tests indicated that annual
and maximum rainfall time series of Kharagpur are homogeneous. Here, it is
emphasized that adequate number of tests should be applied and the results of
all the applied tests should be critically analyzed to arrive at a reliable decision
about the characteristics of a hydrologic time series.
7.6 Checking Stationarity
The entire time series of annual and maximum rainfalls were divided into five
subseries according to the first-half, second-half, first one-third, second one-
third, and last one-third of the entire period of rainfall records, and then the
stationary tests were applied to examine whether the means of the five subseries
are significantly different from that of the entire series. The salient statistical
parameters of the entire and subseries, i.e., annual and maximum rainfalls, are
summarized in Table 7.4. It is obvious from Table 7.4 that the annual and
maximum rainfall series have been derived from positively skewed distributions
with wide variations from the mean (standard deviation 18% for annual
rainfall and standard deviation 25% for all maximum rainfall series). It is
also evident that the skewness coefficients for the first one-third rainfall
subseries are comparatively high, which indicates that the subseries contains
more low values than high values. This finding supports the earlier made
inferences based on the box plots of time series.