dcbs.alg {hdbinseg}

Double CUSUM Binary Segmentation

Description

Perform the Double CUSUM Binary Segmentation algorithm detecting change points in the mean or second-order structure of the data.

Usage

dcbs.alg(
  x,
  cp.type = c(1, 2)[1],
  phi = 0.5,
  thr = NULL,
  trim = NULL,
  height = NULL,
  tau = NULL,
  temporal = TRUE,
  scales = NULL,
  diag = FALSE,
  B = 1000,
  q = 0.01,
  do.parallel = 4
)

Arguments

x

input data matrix, with each row representing the component time series

cp.type

cp.type = 1 specifies change points in the mean, cp.type = 2 specifies change points in the second-order structure

phi

choice of parameter for weights in Double CUSUM statistic; 0 <= phi <= 1 or phi = -1 allowed with the latter leading to the DC statistic combining phi = 0 and phi = 1/2, see Section 4.1 of Cho (2016) for further details

thr

pre-defined threshold values; when thr = NULL, bootstrap procedure is employed for the threshold selection; when thr != NULL and cp.type = 1, length(thr) should be one, if cp.type = 2, length(thr) should match length(scales)

trim

length of the intervals trimmed off around the change point candidates; trim = NULL activates the default choice (trim = round(log(dim(x)[2])))

height

maximum height of the binary tree; height = NULL activates the default choice (height = floor(log(dim(x)[2], 2)/2))

tau

a vector containing the scaling constant for each row of x; if tau = NULL, a data-driven choice is made which takes into account the presence of possibly multiple mean shifts and temporal dependence when temporal = TRUE

temporal

used when cp.type = 1; if temporal = FALSE, rows of x are scaled by mad estimates, if temporal = TRUE, their long-run variance estimates are used

scales

used when cp.type = 2; negative integers representing Haar wavelet scales to be used for computing nrow(x)*(nrow(x) + 1)/2 dimensional wavelet transformation of x; a small negative integer represents a fine scale

diag

used when cp.type = 2; if diag = TRUE, only changes in the diagonal elements of the autocovariance matrices are searched for

B

used when is.null(thr); number of bootstrap samples for threshold selection

q

used when is.null(thr); indicates the quantile of bootstrap test statistics to be used for threshold selection

do.parallel

used when is.null(thr); number of copies of R running in parallel, if do.parallel = 0, %do% operator is used, see also foreach

Value

S3 bin.tree object, which contains the following fields:

tree

a list object containing information about the nodes at which change points are detected

mat

matrix concatenation of the nodes of tree

ecp

estimated change points

thr

threshold used to construct the tree

References

H. Cho (2016) change point detection in panel data via double CUSUM statistic. Electronic Journal of Statistics, vol. 10, pp. 2000–2038.

Examples

x <- matrix(rnorm(10*100), nrow = 10)
dcbs.alg(x, cp.type = 1, phi=.5, temporal = FALSE, do.parallel = 0)$ecp

x <- matrix(rnorm(100*300), nrow = 100)
x[1:10, 151:300] <- x[1:10, 151:300] + 1
dcbs.alg(x, cp.type = 1, phi=-1, temporal = FALSE, do.parallel = 0)$ecp