Current Status of Time Series Analysis in Hydrological Sciences - Hydrologic Time Series Analysis: Theory and Practice - page 97

groundwater flow and water quality are the variables, which have employed
application of the time series methods. This chapter discusses the current
status of time series analysis in hydrological sciences; it has been largely
drawn from Machiwal and Jha (2006) with updates. Although the reviewed
literature is extensive, only major relevant reviews in the context of this topic
are included in this chapter.
6.1 Theoretical Research on Hydrologic Time Series
Sen (1968) studied a simple and robust estimator (point as well as interval) of
BETA based on the Kendall's rank correlation tau. Various properties of these
estimators were studied and compared with those of the least squares and
some other nonparametric estimators. Statistical tests for monotonic trend in
seasonal hydrologic time series are commonly confounded by some of the
following problems: non-normal data, missing values, seasonality, censoring
(detection limits), and serial dependence. Hirsch and Slack (1984) presented
an extension of the Mann-Kendall trend test for such data. Because the
suggested test is based entirely on ranks, it is robust against non-normality
and censoring. Seasonality and missing values present no theoretical or
computational obstacles to its application. Monte Carlo experiments indicated
that, in terms of Type I error, it is robust against serial correlation except when
the data have strong long-term persistence [e.g., ARMA (1,1) monthly processes
with phi greater than 0.6] or short records (approximately five years). When
there is no serial correlation, it is less powerful than a related simpler test not
robust against serial correlation.
Anh et al. (1997) developed a new class of stochastic models to represent
the properties of time series (i.e., long-range dependence and small-scale
behaviour) from various fields, such as geophysics, meteorology, hydrology,
and air pollution. An efficient estimation procedure is described, which was
tested on two concentration time series collected in an environmental wind
tunnel. These time series simulated two different types of odour sources and
possessed quite different statistical properties that were well described by the
new model.
Hamed and Rao (1998) studied the effects of autocorrelation on the
variance of the Mann-Kendall trend test-statistic. A theoretical relationship
was derived to calculate the variance of the Mann-Kendall test statistic for
autocorrelated data. The special cases of AR(1) and MA(1) dependence were
discussed as examples. Based on the modified value of the variance of the
Mann-Kendall trend test statistic, a modified nonparametric trend test suitable
for the autocorrelated data is proposed. The modified test was applied to
rainfall and streamflow data to demonstrate its performance compared to the
original Mann-Kendall trend test. The accuracy of the modified test was
found to be superior to that of the original Mann-Kendall trend test without
any loss of power.