snh.test {trend} | R Documentation |
Standard Normal Homogeinity Test (SNHT) for Change-Point Detection
Description
Performes the Standard Normal Homogeinity Test (SNHT) for change-point detection of a normal variate.
Usage
snh.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 |
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
.
The test statistic for the SNHT test is calculated as follows:
T_k = k z_1^2 + \left(n - k\right) z_2^2 \qquad (1 \le k < n)
where
\begin{array}{l l}
z_1 = \frac{1}{k} \sum_{i=1}^k \frac{x_i - \bar{x}}{\sigma} &
z_2 = \frac{1}{n-k} \sum_{i=k+1}^n \frac{x_i - \bar{x}}{\sigma}. \\
\end{array}
The critical value is:
T = \max T_k.
The p.value
is estimated with a Monte Carlo simulation
using m
replicates.
Critical values based on m = 1,000,000
Monte Carlo simulations
are tabulated for T
by Khaliq and Ouarda (2007).
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 Tk for plotting |
Note
The current function is for complete observations only.
References
H. Alexandersson (1986), A homogeneity test applied to precipitation data, Journal of Climatology 6, 661–675.
M. N. Khaliq, T. B. M. J. Ouarda (2007), On the critical values of the standard normal homogeneity test (SNHT), International Journal of Climatology 27, 681–687.
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
Examples
data(Nile)
(out <- snh.test(Nile))
plot(out)
data(PagesData) ; snh.test(PagesData)