SNSeg_Multi {SNSeg}

Self-normalization (SN) based change points estimation for multivariate time series

Description

The function SNSeg_Multi is a SN-based change-points estimation procedure for a multivariate time series based on changes in the multivariate means or covariance matrix.

Usage

SNSeg_Multi(
  ts,
  paras_to_test = "mean",
  confidence = 0.9,
  grid_size_scale = 0.05,
  grid_size = NULL,
  plot_SN = FALSE,
  est_cp_loc = TRUE
)

Arguments

ts

A multivariate 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 2.

paras_to_test

Type of the parameter as a string for which SN algorithms test. Available choices include mean and covariance.

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

Value

SNSeg_Multi returns an S3 object of class "SNSeg_Multi" including the time series, the type of parameter to be tested, 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.

paras_to_test

the parameter used for the SN test as character.

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_Multi.

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

Examples

# Please run this function before simulation
exchange_cor_matrix <- function(d, rho){
  tmp <- matrix(rho, d, d)
  diag(tmp) <- 1
  return(tmp)
}

# simulation of multivariate time series
library(mvtnorm)
set.seed(10)
d <- 5
n <- 600
nocp <- 5
cp_sets <- round(seq(0, nocp+1 ,1)/(nocp+1)*n)
mean_shift <- rep(c(0,2),100)[1:(length(cp_sets)-1)]/sqrt(d)
rho_sets <- 0.2
sigma_cross <- list(exchange_cor_matrix(d,0))
ts <- MAR_MTS_Covariance(n, 2, rho_sets, cp_sets = c(0,n), sigma_cross)
ts <- ts[1][[1]]

# Test for the change in multivariate means
# grid_size defined
result <- SNSeg_Multi(ts, paras_to_test = "mean", confidence = 0.99,
                      grid_size_scale = 0.05, grid_size = 45)
# Estimated change-point locations
result$est_cp

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