Methods for Time Series Analysis - Hydrologic Time Series Analysis: Theory and Practice - page 60

examined prior to applying the Student's t -test to assess the statistical
significance of these two types of trends (Hoel, 1954). Unfortunately, some
researchers (e.g., Fanta et al., 2001) ignore this important check. If normality
is violated, the nonparametric test such as the Mann-Kendall test (Mann,
1945; Kendall, 1975) is commonly applied to assess the statistical significance
of trends. This test detects a monotonic trend in the mean or median of a time
series. As mentioned earlier, the nonparametric tests are more suitable for
non-normal data and censored data compared to the parametric t -test (Helsel
and Hirsch, 1988; Hirsch and Slack, 1984). The application of the nonparametric
Mann-Kendall test for detecting monotonic trends in hydrological time series
is reported by Hirsch et al. (1982), Hirsch and Slack (1984), Burn (1994),
Burn and Elnur (2002), Lettenmaier et al. (1994), Gan (1992, 1998), Lins and
Slack (1999), Douglas et al. (2000), Zhang et al. (2001), Yue et al. (2003), and
others. Another important trend test is the Spearman Rank Order Correlation
test, which has been applied by Khan (2001) and Adeloye and Montaseri
(2002). However, in some hydrologic studies, the Kendall's Rank Correlation
test has been preferred (Jayawardena and Lai, 1989; Zipper et al., 1998;
Kumar, 2003).
Various parametric and nonparametric statistical tests have been reported
in the literature for detecting trend in a hydrologic time series. The parametric
statistical tests are: turning point, Kendall's phase, Kendall's rank, regression,
Wald-Wolfowitz total number of runs, sum of squared lengths, and inversion
tests (Shahin et al., 1993). The nonparametric tests are: Mann-Kendall test for
a linear and/or nonlinear trend (Salas, 1993), Hotelling-Pabst test (Conover,
1971), and Sen test (Gilbert, 1987). Some more rank correlation tests have
been suggested by Kanji (2001). Dahmen and Hall (1990) present salient
established methods to detect the presence of a significant trend in the
hydrologic time series.
Most of the tests (i.e., Turning Point, Kendall's Phase, Wald-Wolfowitz
Total Number of Runs, Sum of Square Lengths, Adjacency, Difference Sign,
Run Test on Successive Differences, Wilcoxon-Mann-Whitney, and Inversions
tests) have not attracted the attention of hydrologists, which may be due to the
availability of some sound trend detection tests. Esterby (1996) and Hess et al.
(2001) present an excellent overview of the statistical methods for trend
detection and estimation in environmental time series (e.g., water quality and
atmospheric deposition monitoring data). Hess et al. (2001) evaluated six
methods of trend detection using real-world data and provided
recommendations based on a simulation study. It should be noted that the t -
test adjusted for seasonality and the Seasonal Kendall tests are more powerful
than the remaining four tests viz., the Spearman Partial Rank Correlation test,
Ordinary Least Square Regression, Generalized Least Square Regression, and
the Kolmogorov-Zurbenko test. However, all the trend detection tests, which
are currently available, sound and widely employed in the hydrologic time
series analysis, have not been reported by Hess et al. (2001). Some additional