Buishand U Test for Change-Point Detection
Performes the Buishand U test for change-point detection of a normal variate.
bu.test(x, m = 20000)
x |
a vector of class "numeric" or a time series object of class "ts" |
m |
numeric, number of Monte-Carlo replicates, defaults to 20000 |
Let X denote a normal random variate, then the following model with a single shift (change-point) can be proposed:
x[i] = μ + ε[i] for i = 1, ..., m and x[i] = μ + δ + ε_i for i = m + 1, ..., n
with ε \approx N(0,σ). The null hypothesis Δ = 0 is tested against the alternative δ != 0.
In the Buishand U test, the rescaled adjusted partial sums are calculated as
S[k] = ∑ (x[i] - xmean) (1, <= i <= n)
The sample standard deviation is
Dx = sqrt(n^(-1) ∑(x - μ))
The test statistic is calculated as:
U = 1 / [n * (n + 1)] * ∑_{k=1}^{n-1} (S[k] - Dx)^2
.
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 U by Buishand (1982, 1984).
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 |
The current function is for complete observations only.
T. A. Buishand (1982), Some Methods for Testing the Homogeneity of Rainfall Records, Journal of Hydrology 58, 11–27.
T. A. Buishand (1984), Tests for Detecting a Shift in the Mean of Hydrological Time Series, Journal of Hydrology 73, 51–69.
data(Nile) (out <- bu.test(Nile)) plot(out) data(PagesData) bu.test(PagesData)
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