SNSeg_HD {SNSeg}

Self-normalization (SN) based change points estimation for high dimensional time series for changes in high-dimensional means (SNHD).

Description

The function SNSeg_HD is a SNHD change point estimation procedure.

Usage

SNSeg_HD(
  ts,
  confidence = 0.9,
  grid_size_scale = 0.05,
  grid_size = NULL,
  plot_SN = FALSE,
  est_cp_loc = TRUE,
  ts_index = c(1:5)
)

Arguments

ts

A high-dimensional time series represented as a matrix with p columns, where each column is a univariate time series. The dimension p for ts should be at least 10.

confidence

Confidence level of SN tests as a numeric value. Available choices of confidence levels contain 0.9, 0.95, 0.99, 0.995 and 0.999. The default is set to 0.9.

grid_size_scale

numeric value of the trimming parameter and only in use if grid_size = NULL. Users are allowed to choose any grid_size_scale between 0.05 and 0.5. A warning will be given if it is outside the range.

grid_size

Local window size h to compute the critical value for SN test. Since grid_size = n*grid_size_scale, where n is the length of time series, this function will compute the grid_size_scale by diving n from grid_size when it is not NULL.

plot_SN

Boolean value to plot the time series or not. The default setting is FALSE.

est_cp_loc

Boolean value to plot a red solid vertical line for estimated change-point locations if est_cp_loc = TRUE.

ts_index

The index number(s) of the univariate time series to be plotted. Users should enter a positive integer or a vector of positive integers that are no greater than the dimension of the input time series. The default is the first 5 time series, i.e., ts_index = c(1:5).

Value

SNSeg_HD returns an S3 object of class "SNSeg_HD" including the time series, the local window size to cover a change point, the estimated change-point locations, the confidence level and the critical value of the SN test. It also generates time series segmentation plot when plot_SN = TRUE.

ts

A numeric matrix of the input time series.

grid_size

A numeric value of the window size.

SN_sweep_result

A list of n matrices where each matrix consists of four columns: (1) SN-based test statistic for each change-point location (2) Change-point location (3) Lower bound of the window h and (4) Upper bound of the window h.

est_cp

A vector containing the locations of the estimated change-points.

confidence

Confidence level of SN test as a numeric value.

critical_value

Critical value of the SN-based test statistic.

Users can apply the functions summary.SN to compute the parameter estimate of each segment separated by the detected change-points. An additional function plot.SN can be used to plot the time series with estimated change-points. Users can set the option plot_SN = TRUE or use the function plot.SN to plot the time series.

It deserves to note that some change-points could be missing due to the constraint on grid_size_scale or related grid_size that grid_size_scale has a minimum value of 0.05. Therefore, SNCP claims no change-points within the first ngrid_size_scale or the last ngrid_size_scale time points. This is a limitation of the function SNSeg_HD.

For more examples of SNSeg_HD see the help vignette: vignette("SNSeg", package = "SNSeg")

Examples

n <- 500
p <- 50
nocp <- 5
cp_sets <- round(seq(0,nocp+1,1)/(nocp+1)*n)
num_entry <- 5
kappa <- sqrt(4/5)
mean_shift <- rep(c(0,kappa),100)[1:(length(cp_sets)-1)]
set.seed(1)
ts <- matrix(rnorm(n*p,0,1),n,p)
no_seg <- length(cp_sets)-1
for(index in 1:no_seg){
  tau1 <- cp_sets[index]+1
  tau2 <- cp_sets[index+1]
  ts[tau1:tau2,1:num_entry] <- ts[tau1:tau2,1:num_entry] +
    mean_shift[index]
}

# grid_size defined
result <- SNSeg_HD(ts, confidence = 0.9, grid_size_scale  = 0.05,
                   grid_size = 40)
# Estimated change-point locations
result$est_cp

# For more examples, please run the following command:
# vignette("SNSeg", package = "SNSeg")