CUSUM.test {CPAT}

CUSUM Test

Description

Performs the (univariate) CUSUM test for change in mean, as described in (Rice et al. ). This is effectively an interface to stat_Vn; see its documentation for more details. p-values are computed using pkolmogorov, which represents the limiting distribution of the statistic under the null hypothesis.

Usage

CUSUM.test(x, use_kernel_var = FALSE, stat_plot = FALSE,
  kernel = "ba", bandwidth = "and")

Arguments

x

Data to test for change in mean

use_kernel_var

Set to TRUE to use kernel methods for long-run variance estimation (typically used when the data is believed to be correlated); if FALSE, then the long-run variance is estimated using \hat{\sigma}^2_{T,t} = T^{-1}\left( \sum_{s = 1}^t \left(X_s - \bar{X}_t\right)^2 + \sum_{s = t + 1}^{T}\left(X_s - \tilde{X}_{T - t}\right)^2\right), where \bar{X}_t = t^{-1}\sum_{s = 1}^t X_s and \tilde{X}_{T - t} = (T - t)^{-1} \sum_{s = t + 1}^{T} X_s

stat_plot

Whether to create a plot of the values of the statistic at all potential change points

kernel

If character, the identifier of the kernel function as used in cointReg (see getLongRunVar); if function, the kernel function to be used for long-run variance estimation (default is the Bartlett kernel in cointReg)

bandwidth

If character, the identifier for how to compute the bandwidth as defined in cointReg (see getBandwidth); if function, a function to use for computing the bandwidth; if numeric, the bandwidth value to use (the default is to use Andrews' method, as used in cointReg)

Value

A htest-class object containing the results of the test

References

Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.

Examples

CUSUM.test(rnorm(1000))
CUSUM.test(rnorm(1000), use_kernel_var = TRUE, kernel = "bo",
           bandwidth = "nw")