Methods for Time Series Analysis - Hydrologic Time Series Analysis: Theory and Practice - page 77

analysis as a whole are described, and thereafter the merits and demerits of
individual tests used for time series analysis are highlighted:
(i) The assumptions of the classical parametric tests viz., normality,
linearity, and independence are usually not met by the hydrological
time series data, especially in case of surface water quality data.
Therefore, recently some nonparametric tests have been proposed to
determine the trend in surface water quality time series (Kalayci and
Kahya, 1998). At the same time, the statistical tests for trend detection
in water quality are normally confounded by one or more of the
following problems: missing values, censored data, flow relatedness,
and seasonality.
(ii) In general, the parametric methods to assess significance of trend
employ pre-specified models and associated tests, whereas the
nonparametric methods generally apply rank tests to the data. Neither
approach is suitable for exploratory analysis (Ramesh and Davison,
2002).
(iii) Cumulative Deviations test is superior to the classical von Neumann
test for a model with only one change in the mean (Buishand, 1982).
(iv) The major limitation with all the multiple comparison tests of
homogeneity (i.e., Tukey, Link-Wallace, Dunnett, Bartlett and Hartley
tests) is the requirement that populations should be normally distributed
with equal variances, which makes the tests parametric in nature.
Although the Link-Wallace test, the Dunnett's test and the Hartley's
test can be employed for the same purpose as the Tukey's test, the
former three tests can be applied only when the sample size of all
populations is equal, though methodology of the Hartley's test can
still be followed in case sample size of all the populations are more
or less similar.
(v) Of the three stationarity tests, both the t -tests are parametric in nature,
which require normality assumption of the time series to be tested.
However, the Mann-Whitney test is nonparametric in nature and is
more robust as it can be applied to normal as well as normal non-
normal time series.
(vi) Although the linear model (i.e., Regression test) is most commonly
used for trend detection, it has a demerit that it does not distinguish
between trend and persistence. The linear model can also be misleading
if seasonal cycles are present, the data are not normally distributed,
and/or the data are serially correlated (Gilbert, 1987). The Spearman
Rank Order Correlation (SROC) test overcomes these demerits of the
linear model. The merit of this test is its nearly uniform power for
detecting linear as well as nonlinear trends (WMO, 1966; Dahmen
and Hall, 1990). Among the trend tests, the superiority of one over
other is mainly associated with the extent of adaptability of a chosen
test to the structure of the time series to be tested.