Methods for Time Series Analysis - Hydrologic Time Series Analysis: Theory and Practice - page 51

does not exist where detailed and easy-to-understand scientific information
about all the available statistical methods can be found. This chapter fulfils
this gap by presenting in-depth information about various statistical tests
available for the time series analysis. A total of 28 statistical tests/methods are
presented in this chapter, of which eight tests are for checking homogeneity,
three tests for checking stationarity, fifteen tests for detecting presence or
absence of trend, one test for checking periodicity, and one test for checking
persistence in the hydrologic time series.

4.1 Methods for Checking Homogeneity

Homogeneity or consistency implies that all the collected hydrologic time
series data belong to the same statistical population having a time invariant
mean. Therefore, the tests to check the homogeneity or consistency of data
series are based on evaluating the significance of changes in the mean value.
The features of three homogeneity tests namely, the von Neumann test,
Cumulative Deviations, and the Bayesian test are discussed in Buishand (1982)
and Jayawardena and Lau (1990).
Buishand (1982, 1984) presents a detailed methodology for the above-
mentioned three homogeneity tests, which can serve as major guidelines about
these tests. Kanji (2001) in his excellent collection of 100 statistical tests, has
reported various homogeneity tests for multiple comparisons (e.g., Tukey,
Link-Wallace, Dunnett, Bartlett, and Hartley tests). However, it has drawbacks
that the objectives of the tests are not clear and that original references are
lacking. On the other hand, some researchers (e.g., Radziejewski et al., 2002)
have considered a few homogeneity tests for trend detection. Such studies
may create confusion about the general perceptions of homogeneity and trend
for the researchers with no access to good literature in this line. It should be
noted here that the homogeneity tests for multiple comparisons (e.g., Bartlett,
Dunnett, Link-Wallace, Hartley, and Tukey tests) have not gained a wide
popularity in hydrology and climatology. In the hydrologic time series analysis,
multiple comparison tests are still contemporary , while these tests are
considered as classical in geotechnical studies (e.g., Phoon et al., 2003).
Detailed procedures for applying the homogeneity tests are described ahead.

4.1.1 The von Neumann Test

The von Neumann ratio ( N ) is the most widely used test for testing a time
series for the absence or presence of homogeneity. It is closely related to the
first-order serial correlation coefficient (WMO, 1966) and can be defined as
follows:

n 1 n

Ç Ç

2 2

xx xx

N = (1) t t 1 t

t1 t1