Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 139

rainfall series comprising one-day, consecutive two, three, four, five and six
days maximum rainfall are equally important for estimating the total annual
runoff and maximum runoff produced during a rainfall event. The daily rainfall
data of Kharagpur for the 1956-2002 period were obtained from the Physics
and Meteorology Department of Indian Institute of Technology Kharagpur,
West Bengal, India. These data were checked for the anomalies, and the
rainfall records were found free from anomalies, with no missing data in the
series. It is worth mentioning that the length of the daily rainfall records is
large enough to be used successfully for demonstrating the proper application
of various time series tests.
Three tests (i.e., Geary's test, Kolmogorov-Smirnov test and D'Agostino-
Pearson Omnibus test) have been applied for testing normality, seven tests
(i.e., The von Neumann test, Cumulative Deviations tests, Bayesian test, Tukey
test, Link-Wallace test, Bartlett test, and Hartley test) for testing homogeneity,
three tests (i.e., Student's t -test, Simple t -test and Mann-Whitney test) for
examining stationarity, and twelve tests (i.e., Regression test, Spearman Rank
Order Correlation test, Turning Point test, Kendall's Phase test, Wald-Wolfowitz
Total Number of Runs test, Sum of Squared Lengths test, Adjacency test,
Difference Sign test, Run test on Successive Differences, Inversions test,
Kendall's Rank Correlation test and Mann-Kendall test) for detecting trend.
Additionally, periodicity and persistence have been examined through harmonic
analysis and autocorrelation analysis, respectively. These time series tests are
described in Chapters 3 and 4.
7.3 Graphical Interpretation
It is always a good practice to present a time series in the form of a simple
x-y plot prior to the application of statistical techniques. Seven such plots
(i.e., total annual, one-day, 2-, 3-, 4-, 5- and 6-day maximum rainfall) showing
mean and range of the rainfall time series in this study were drawn and two
plots for annual and one-day maximum rainfall are shown in Figs 7.1(a-b) as
an example. It is apparent from Fig. 7.1(a) that the time series plot of annual
rainfall does not depict any temporal trend. Similarly, the plots of maximum
rainfalls have no overall trends [Fig. 7.1(b)]. One significant observation is
discernible from time plots of maximum rainfall series that the time pattern of
maximum rainfalls is similar for all the series regardless of the consecutive
days (i.e., one-day, 2-, 3-, 4-, 5- and 6-day). It is also obvious that the increment
in rainfall with an increase in the number of consecutive days is not considerable
compared to the amount of maximum rainfall, which is a major reason for the
similar time patterns in all the maximum rainfall series.
In addition to the time plots, box plots (Fig. 7.2) were drawn to compare
all the rainfall time series under investigation which provide an excellent
summary of five important aspects (lowest value, 25 th percentile, median, 75 th