trend (version 1.1.2)

br.test: Buishand Range Test for Change-Point Detection

Description

Performes the Buishand range test for change-point detection of a normal variate.

Usage

br.test(x, m = 20000)

Arguments

x

a vector of class "numeric" or a time series object of class "ts"

m

numeric, number of Monte-Carlo replicates, defaults to 20000

Value

A list with class "htest" and "cptest"

data.name

character string that denotes the input data

p.value

the p-value

statistic

the test statistic

null.value

the null hypothesis

estimates

the time of the probable change point

alternative

the alternative hypothesis

method

character string that denotes the test

data

numeric vector of Sk for plotting

Details

Let \(X\) denote a normal random variate, then the following model with a single shift (change-point) can be proposed:

$$ x_i = \left\{ \begin{array}{lcl} \mu + \epsilon_i, & \qquad & i = 1, \ldots, m \\ \mu + \Delta + \epsilon_i & \qquad & i = m + 1, \ldots, n \\ \end{array} \right.$$

with \(\epsilon \approx N(0,\sigma)\). The null hypothesis \(\Delta = 0\) is tested against the alternative \(\Delta \ne 0\).

In the Buishand range test, the rescaled adjusted partial sums are calculated as

$$S_k = \sum_{i=1}^k \left(x_i - \hat{x}\right) \qquad (1 \le i \le n)$$

The test statistic is calculated as: $$Rb = \left(\max S_k - \min S_k\right) / \sigma$$.

The p.value is estimated with a Monte Carlo simulation using m replicates.

Critical values based on \(m = 19999\) Monte Carlo simulations are tabulated for \(Rb / \sqrt{n}\) by Buishand (1982).

References

T. A. Buishand (1982), Some Methods for Testing the Homogeneity of Rainfall Records, Journal of Hydrology 58, 11--27.

G. Verstraeten, J. Poesen, G. Demaree, C. Salles (2006), Long-term (105 years) variability in rain erosivity as derived from 10-min rainfall depth data for Ukkel (Brussels, Belgium): Implications for assessing soil erosion rates. Journal of Geophysical Research 111, D22109.

See Also

efp sctest.efp

Examples

# NOT RUN {
data(Nile)
(out <- br.test(Nile))
plot(out)


data(PagesData) ; br.test(PagesData)
 
# }