sim_Vn_stat {CPAT}

CUSUM Statistic Simulation

Description

Simulates multiple realizations of the CUSUM statistic.

Usage

sim_Vn_stat(size, kn = function(n) {     1 }, tau = 0,
  use_kernel_var = FALSE, kernel = "ba", bandwidth = "and",
  n = 500, gen_func = rnorm, args = NULL, parallel = FALSE)

Arguments

size

Number of realizations to simulate

kn

A function returning a positive integer that is used in the definition of the trimmed CUSUSM statistic effectively setting the bounds over which the maximum is taken

tau

The weighting parameter for the weighted CUSUM statistic (defaults to zero for no weighting)

use_kernel_var

Set to TRUE to use kernel-based long-run variance estimation (FALSE means this is not employed)

kernel

If character, the identifier of the kernel function as used in the cointReg (see documentation for cointReg::getLongRunVar); if function, the kernel function to be used for long-run variance estimation (default is the Bartlett kernel in cointReg); this parameter has no effect if use_kernel_var is FALSE

bandwidth

If character, the identifier of how to compute the bandwidth as defined in the cointReg package (see documentation for cointReg::getLongRunVar); if function, a function to use for computing the bandwidth; if numeric, the bandwidth to use (the default behavior is to use the method described in (Andrews 1991), as used in cointReg); this parameter has no effect if use_kernel_var is FALSE

n

The sample size for each realization

gen_func

The function generating the random sample from which the statistic is computed

args

A list of arguments to be passed to gen_func

parallel

Whether to use the foreach and doParallel packages to parallelize simulation (which needs to be initialized in the global namespace before use)

Details

This differs from sim_Vn() in that the long-run variance is estimated with this function, while sim_Vn() assumes the long-run variance is known. Estimation can be done in a variety of ways. If use_kernel_var is set to TRUE, long-run variance estimation using kernel-based techniques will be employed; otherwise, a technique resembling standard variance estimation will be employed. Any technique employed, though, will account for the potential break points, as described in Rice et al. (). See the documentation for stat_Vn for more details.

The parameters kernel and bandwidth control parameters for long-run variance estimation using kernel methods. These parameters will be passed directly to stat_Vn.

Versions of the CUSUM statistic, such as the weighted or trimmed statistics, can be simulated with the function by passing values to kn and tau; again, see the documentation for stat_Vn.

Value

A vector of simulated realizations of the CUSUM statistic

References

Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica, 59(3), 817-858.

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

Examples

CPAT:::sim_Vn_stat(100)
CPAT:::sim_Vn_stat(100, kn = function(n) {floor(0.1 * n)}, tau = 1/3,
                   use_kernel_var = TRUE, gen_func = CPAT:::rchangepoint,
                   args = list(changepoint = 250, mean2 = 1))