changerob.cusum: Cumulative Sum Statistic

In robts: Robust Time Series Analysis

Description

Computes the test trajectory for the cusum change point test. See Dehling et al. (2013) for details.

Usage

changerob.cusum(x, var.method = c("window", "acf", "acfextra"),
                overlapping = TRUE, shiftcorrect = TRUE, borderN = 10, ...)

Arguments

x	numeric vector or univariate time series object.
var.method	character string defining the estimator of the long run variance, see Details.
overlapping	logical value indicating whether block sums should be distinct or overlapping. Only relevant if var.method = "window", see Details.
shiftcorrect	logical value. If TRUE, the estimation of the long run variance considers a change in location by first estimating the change point and then subtracting the estimated jump height from the second part of the time series. This should considerably improve the power of the test.
borderN	integer value. If shiftcorrect = TRUE, the change point for the estimation of the log run variance is not searched below the first and last borderN observations.
...	further arguments passed to the respective internal function for calculation of the asymptotical long run variance.

Details

The cusum change point test is a nonparametric test against a change in location under short range dependence. The test has high power under Gaussian processes and is able to detect even small changes. The test may suffer under outliers and in case of heavy tailed time series. In this case the Hodges-Lehmann change point test changerob.HL or the Wilcoxon change point test changerob.wilcox are preferable. See Dehling et al. (2013) for details. This function computes only the test trajectory, the actual test is executed by the function changerob.

More details on the different options for calculating the long run variance are given on the help page of the function changerob.

Value

Numeric vector which contains the whole path of the test statistic.

Author(s)

Roland Fried and Alexander Dürre

References

Carlstein, E. (1986): The use of subseries values for estimating the variance of a general statistic from a stationary sequence, The Annals of Statistics, vol. 14, 1171–1179, doi: 10.1214/aos/1176350057.

Dehling, H., Fried, R., Garcia, I., Wendler, M. (2013): Change-point detection under dependence based on two-sample U-statistics, preprint. arXiv 1304.2479

Peligrad, M., Shao, Q. (1995): Estimation of the Variance of Partial Sums for rho-Mixing Random Variables, Journal of Multivariate Analysis, vol. 152, 140–157, doi: 10.1006/jmva.1995.1008.

See Also

The wrapper function changerob.

The long run variance is calculated by asymvar.window, asymvar.acf or asymvar.acfextra.

Examples

set.seed(1066)
tss <- arima.sim(model = list(ar = 0.3, ma = 0.5), n = 100)
trajectory <- changerob.cusum(tss)
plot(trajectory)

robts documentation built on May 2, 2019, 4:55 p.m.