Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 152

Moreover, two parametric tests (i.e., Student's t -test and Simple t -test)
and one non-parametric Mann-Whitney test were used for testing stationarity
in the rainfall series. The values of the Student's t -statistics for annual and
maximum (one-day, consecutive 2-, 3-, 4-, 5- and 6-day) rainfall series are
less than their critical values (Table 7.4), and hence the null hypothesis cannot
be rejected at 5% significance level. Here, the choice of 5% significance level
(or 95% confidence level) is arbitrary, but it seems to be a reasonable limit for
the type of data under study (Jayawardena and Lai, 1989). Critical values for
the t -statistic were taken from standard statistical texts (e.g., Shahin et al.,
1993). Further, the parametric Simple t -test was applied to the entire rainfall
series after dividing them into two half-subseries viz., annual rainfall series of
46 years into two 23-year series and the maximum rainfall series of 47 years
into two series (i.e., 23-year series and 24-year series). A comparison between
the calculated and the critical values of the test-statistics is shown in Table 7.5.
It is clear from this table that the stationarity exists in the annual series as well
as one-day, 2-, 3-, 4-, 5- and 6-day maximum rainfall time series of Kharagpur.
Also, the calculated values of the Mann-Whitney test-statistic are less than
their critical values (±1.96) for all the seven rainfall time series, which indicates
stationarity in the rainfall time series of Kharagpur. Thus, based on the results
of three stationarity tests, the annual and maximum rainfall time series under
study are undoubtedly stationary.
7.7 Checking Trend
7.7.1 Application of Trend Tests
The annual and the maximum rainfall time series of Kharagpur were examined
for the presence of a linear trend by applying the trend detection tests mentioned
in methodology. It can be seen that most of the available trend tests are of
parametric character, which necessitates that series should follow a normal
statistical distribution. Hence, the normality of the Kharagpur rainfall time
series data was tested using normal probability plots, and it was found that
they can be considered to follow a normal distribution as discussed earlier in
Section on Graphical Interpretation . The results of the twelve trend detection
tests are presented in Tables 7.5 and 7.6, together with the critical values of
the test-statistics. Critical values for the test-statistics of Regression test,
Spearman Rank Order Correlation test, Wald-Wolfowitz Total Number of
Runs test, Sum of Squares Lengths test, Adjacency test, Difference Sign test
and Runs test on Successive Differences were taken from Shahin et al. (1993).
Similarly, the critical values for the Mann-Kendall test were obtained from
Salas (1993). In the Kendall's Phase Lengths test, the phase length and observed
number of each phase length was counted in annual and maximum rainfall
(i.e., one-day, 2-, 3-, 4-, 5- and 6-day) time series, and then the expected
number of phase lengths was computed. For the one-day and consecutive