Methods for Time Series Analysis - Hydrologic Time Series Analysis: Theory and Practice - page 50

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Methods for Time Series Analysis
Natural time series, including hydrologic, climatic and environmental time
series, which satisfy the assumptions of homogeneity, randomness, non-
periodic, non-persistence and stationarity, seem to be the exception rather
than the rule (Rao et al., 2003). In fact, for all water resources studies involving
the use of hydrologic time series data, preliminary statistical analyses must
always be carried out to confirm whether the hydrologic time series possess
all the required assumptions/characteristics (Adeloye and Montaseri, 2002).
Nevertheless, most time series analysis is performed using standard methods
after relaxing the required conditions one way or another in the hope that the
departure from these assumptions is not large enough to affect the analysis
results (Rao et al., 2003). A comprehensive survey of the past studies on the
hydrologic time series analysis (Machiwal and Jha, 2006) revealed that no
studies considered all the aspects of time series analysis. Major work is reported
dealing with only linear trend analysis, and the homogeneity, stationarity,
periodicity, and persistence, which are equally important characteristics of the
hydrologic time series, have been ignored. In most past studies on time series
analysis, only regression and/or Kendall's rank correlation tests are applied
for trend detection. Esterby (1996) and Hess et al. (2001) presented an overview
of selected trend tests. Thus, very limited studies are reported to date concerning
a detailed analysis of homogeneity, stationarity, periodicity and persistence in
the hydrologic time series.
In the literature, several statistical tests/methods are available to determine
a particular characteristic of the time series. It has been seen that choosing a
specific statistical test for a particular characteristic of the time series is
dependent on the knowledge of data analyst or researcher rather than on the
assumptions/requirements of the test. Use of one or two statistical tests for
time series analysis is quite common for easy decision making. However,
Machiwal and Jha (2008) recommended that an adequate number of statistical
tests must be applied for detecting a particular time series characteristic and
the results should be analyzed critically to arrive at a reliable decision. Based
on the extensive literature search, it was found that a single reference/source