Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 138

Natural time series, including hydrologic, climatic and environmental
time series, which satisfy the assumptions of normality, 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 (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 result of the
analysis (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 to date have considered all the aspects of time series analysis. Major
work is reported dealing with only linear trend analysis. However, other equally
important characteristics of the hydrologic time series, i.e., normality,
homogeneity, stationarity, periodicity and persistence, have been ignored.
Further, most past studies report only Regression and/or Kendall's Rank
Correlation tests for trend detection. Two of the past studies (Esterby, 1996;
Hess et al., 2001) report an overview of some selected trend tests. Thus, no
studies are reported to date, which deal with a complete and extensive analysis
of normality, homogeneity, stationarity, periodicity, persistence and stochastic
component in the hydrologic time series (Machiwal and Jha, 2006).
As mentioned in Chapter 4, several statistical tests are available for
determining a particular time series characteristic. Some of the available time
series tests are more powerful than others. However, the use of a specific
statistical test is still dependent on the user's familiarity with the test rather
than on the strength of the test. It has been found that the results of two
different tests may be dissimilar in characterizing the same characteristic of a
hydrologic time series (Machiwal and Jha, 2008). Therefore, the goal of this
chapter is to demonstrate the efficacy of various time series tests for detecting
particular characteristics through a case study on the annual and salient
consecutive days' maximum rainfall series of Kharagpur, West Bengal, eastern
India. This chapter draws significantly from Machiwal and Jha (2008).
7.2 Methodology
In this case study, annual rainfall series of 46 years (1957-2002) and the six
consecutive days' maximum rainfall series of 47 years (1956-2002) in
Kharagpur, West Bengal, India have been analyzed. Annual rainfall for a year
is the total rainfall occurring in that year. The consecutive days' maximum
rainfall denotes the maximum rainfall, which occurs during given consecutive
days in a particular year. For instance, consecutive 2-day maximum rainfall
denotes the amount of maximum rainfall that occurs in any of the two
consecutive days in a particular year. Needless to mention that the maximum