| Title: | Self-Normalization(SN) Based Change-Point Estimation for Time Series |
|---|---|
| Description: | Implementations self-normalization (SN) based algorithms for change-points estimation in time series data. This comprises nested local-window algorithms for detecting changes in both univariate and multivariate time series developed in Zhao, Jiang and Shao (2022) <doi:10.1111/rssb.12552>. |
| Authors: | Shubo Sun [aut], Zifeng Zhao [aut, cre], Feiyu Jiang [aut], Xiaofeng Shao [aut] |
| Maintainer: | Zifeng Zhao <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.0.3 |
| Built: | 2024-10-31 06:23:58 UTC |
| Source: | CRAN |
A dataset containing the critical value of SN-based change point estimates based on changes in high-dimensional means.
critical_values_HDcritical_values_HD
A data frame with 6 variables:
epsilonvalue used to compute grid_size_scale and SN-based test statistic
0.9critical value at confidence level 0.9
0.95critical value at confidence level 0.95
0.99critical value at confidence level 0.99
0.995critical value at confidence level 0.995
0.999critical value at confidence level 0.999
A dataset containing the critical value of SN-based change point estimates based on simultaneous changes in multiple parameters.
critical_values_multicritical_values_multi
A data frame with 7 variables:
epsilonvalue used to compute grid_size_scale and SN-based test statistic
pdimension of the multi-parameters
0.9critical value at confidence level 0.9
0.95critical value at confidence level 0.95
0.99critical value at confidence level 0.99
0.995critical value at confidence level 0.995
0.999critical value at confidence level 0.999
A dataset containing the critical value for SN-based change point estimates based on the change in a single parameter.
critical_values_singlecritical_values_single
A data frame with 6 variables:
epsilonvalue used to compute grid_size_scale and SN-based test statistic
0.9critical value at confidence level 0.9
0.95critical value at confidence level 0.95
0.99critical value at confidence level 0.99
0.995critical value at confidence level 0.995
0.999critical value at confidence level 0.999
The function MAR is used for generating MAR model(s) for examples
of the functions SNSeg_Uni, SNSeg_Multi, and SNSeg_HD.
MAR(n, reptime, rho)MAR(n, reptime, rho)
n |
the size (length) of time series to be generated |
reptime |
the number of time series to be generated |
rho |
value of autocorrelation |
Returns a matrix of the simulated MAR processes. The number of columns
of this matrix is equivalent to the value of input argument reptime, and
the number of rows is the value of input argument n.
MAR(n = 1000, reptime = 2, rho = -0.7)MAR(n = 1000, reptime = 2, rho = -0.7)
The function MAR_MTS_Covariance is used to generate MAR model(s) for
examples of the functions SNSeg_Uni, SNSeg_Multi, and SNSeg_HD.
MAR_MTS_Covariance(n, reptime, rho_sets, cp_sets, sigma_cross)MAR_MTS_Covariance(n, reptime, rho_sets, cp_sets, sigma_cross)
n |
the size of time series to be generated. |
reptime |
the number of time series to be generated. |
rho_sets |
autocorrelations for each univariate time series. |
cp_sets |
numeric values of the true change-point locations (0, change-point locations and the end point). |
sigma_cross |
a list of matrices to generate the multivariate covariance matrices. |
Returns a list of matrices where each matrix is a MAR process. The
number of columns for each sub-matrix is equivalent to the value of input
argument reptime.
n <- 1000 reptime <- 2 sigma_cross <- list(4*matrix(c(1,0.8,0.8,1), nrow=2), matrix(c(1,0.2,0.2,1), nrow=2), matrix(c(1,0.8,0.8,1), nrow=2)) cp_sets <- round(c(0,n/3,2*n/3,n)) noCP <- length(cp_sets)-2 rho_sets <- rep(0.5, noCP+1) MAR_MTS_Covariance(n, reptime, rho_sets, cp_sets, sigma_cross)n <- 1000 reptime <- 2 sigma_cross <- list(4*matrix(c(1,0.8,0.8,1), nrow=2), matrix(c(1,0.2,0.2,1), nrow=2), matrix(c(1,0.8,0.8,1), nrow=2)) cp_sets <- round(c(0,n/3,2*n/3,n)) noCP <- length(cp_sets)-2 rho_sets <- rep(0.5, noCP+1) MAR_MTS_Covariance(n, reptime, rho_sets, cp_sets, sigma_cross)
The function MAR_Variance is used for generating MAR model(s) for
examples of the functions SNSeg_Uni, SNSeg_Multi, and SNSeg_HD.
MAR_Variance(reptime, type = "V3")MAR_Variance(reptime, type = "V3")
reptime |
The number of time series to be generated |
type |
The type of time series for simulation, which includes V1, V2, V3
, A1, A2 and A3. The V-beginnings are for testing the variance, and the
A-beginnings are for testing the autocorrelation. The simulated time series
come from supplement of Zhao et al. (2022) doi:10.1111/rssb.12552.
Default The time length and "true change-points locations" (cps) for each |
Returns a matrix of the simulated MAR processes. The number of columns
of this matrix is equivalent to the value of input argument reptime.
MAR_Variance(reptime = 2, type = "V1")MAR_Variance(reptime = 2, type = "V1")
The function max_SNsweep allows users to compute and plot the SN-based
test statistics along with the identified change-points from functions
SNSeg_Uni, SNSeg_Multi, or SNSeg_HD.
max_SNsweep(SN_result, plot_SN = TRUE, est_cp_loc = TRUE, critical_loc = TRUE)max_SNsweep(SN_result, plot_SN = TRUE, est_cp_loc = TRUE, critical_loc = TRUE)
SN_result |
The output of functions SNSeg_Uni, SNSeg_Multi or SNSeg_HD. |
plot_SN |
A boolean value to return an SN-based segmentation plot if plot_SN = TRUE. |
est_cp_loc |
A boolean value to plot a red solid vertical line for estimated change-point locations if est_cp_loc = TRUE. |
critical_loc |
A boolean value to plot a blue dashed horizontal line for the critical value if critical_loc = TRUE |
Returns a vector of numeric values of calculated SN-based statistics for each time point. It also generates a SN-based test statistics segmentation plot with the estimated change-points.
For more examples of max_SNsweep please see the SNSeg vignette:
vignette("SNSeg", package = "SNSeg")
set.seed(7) n <- 2000 reptime <- 2 cp_sets <- round(n*c(0,cumsum(c(0.5,0.25)),1)) mean_shift <- c(0.4,0,0.4) rho <- -0.7 ts <- MAR(n, reptime, rho) 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,] <- ts[tau1:tau2,] + mean_shift[index] } ts <- ts[,2] result <- SNSeg_Uni(ts, paras_to_test = "mean", confidence = 0.9, grid_size_scale = 0.05, grid_size = 116, plot_SN = FALSE, est_cp_loc = FALSE) # Generate SN-based test statistic segmentation plot # To get the computed SN-based statistics, please run the command "test_stat" test_stat <- max_SNsweep(result, plot_SN = TRUE, est_cp_loc = TRUE, critical_loc = TRUE) # For more examples of \code{max_SNsweep} see the help vignette: # \code{vignette("SNSeg", package = "SNSeg")}set.seed(7) n <- 2000 reptime <- 2 cp_sets <- round(n*c(0,cumsum(c(0.5,0.25)),1)) mean_shift <- c(0.4,0,0.4) rho <- -0.7 ts <- MAR(n, reptime, rho) 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,] <- ts[tau1:tau2,] + mean_shift[index] } ts <- ts[,2] result <- SNSeg_Uni(ts, paras_to_test = "mean", confidence = 0.9, grid_size_scale = 0.05, grid_size = 116, plot_SN = FALSE, est_cp_loc = FALSE) # Generate SN-based test statistic segmentation plot # To get the computed SN-based statistics, please run the command "test_stat" test_stat <- max_SNsweep(result, plot_SN = TRUE, est_cp_loc = TRUE, critical_loc = TRUE) # For more examples of \code{max_SNsweep} see the help vignette: # \code{vignette("SNSeg", package = "SNSeg")}
Plotting method for S3 objects of class SNSeg_HD
## S3 method for class 'SNSeg_HD' plot(x, cpts.col = "red", ts_index = c(1:5), ...)## S3 method for class 'SNSeg_HD' plot(x, cpts.col = "red", ts_index = c(1:5), ...)
x |
a |
cpts.col |
a specification for the color of the vertical lines at the change point estimators, see par |
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., |
... |
The location of each change point estimator is plotted as a vertical line against the input time series.
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) # plot the 1st, 3rd and 5th time series plot(result, cpts.col = 'red', ts_index = c(1,3,5))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) # plot the 1st, 3rd and 5th time series plot(result, cpts.col = 'red', ts_index = c(1,3,5))
Plotting method for S3 objects of class SNSeg_Multi
## S3 method for class 'SNSeg_Multi' plot(x, cpts.col = "red", ...)## S3 method for class 'SNSeg_Multi' plot(x, cpts.col = "red", ...)
x |
a |
cpts.col |
a specification for the color of the vertical lines at the change point estimators, see par |
... |
The location of each change point estimator is plotted as a vertical line against the input time series.
# 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) # plot method plot(result)# 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) # plot method plot(result)
Plotting method for S3 objects of class SNSeg_Uni
## S3 method for class 'SNSeg_Uni' plot(x, cpts.col = "red", ...)## S3 method for class 'SNSeg_Uni' plot(x, cpts.col = "red", ...)
x |
a |
cpts.col |
a specification for the color of the vertical lines at the change point estimators, see par |
... |
additional graphical arguments, see plot and abline. Users are allowed to enter their own title for the univariate time series plot. The bivariate time series does not contain this option. |
The location of each change point estimator is plotted as a vertical line against the input time series.
set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) plot(result, cpts.col='red')set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) plot(result, cpts.col='red')
Print method for objects of class SNSeg_HD
## S3 method for class 'SNSeg_HD' print(x, ...)## S3 method for class 'SNSeg_HD' print(x, ...)
x |
a |
... |
not in use |
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) # print method print(result)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) # print method print(result)
Print method for objects of class SNSeg_Multi
## S3 method for class 'SNSeg_Multi' print(x, ...)## S3 method for class 'SNSeg_Multi' print(x, ...)
x |
a |
... |
not in use |
# 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) # print method print(result)# 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) # print method print(result)
Print method for objects of class SNSeg_Uni
## S3 method for class 'SNSeg_Uni' print(x, ...)## S3 method for class 'SNSeg_Uni' print(x, ...)
x |
a |
... |
not in use |
set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) print(result)set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) print(result)
The SNSeg package provides three functions for multiple change point
estimation using SN-based algorithms: SNSeg_Uni, SNSeg_Multi and SNSeg_HD.
Three critical value tables (critical_values_single,
critical_values_multi and critical_values_HD) were attached.
Functions MAR, MAR_Variance and MAR_MTS_Covariance can be utilized
to generate time series data that are used for the functions SNSeg_Uni, SNSeg_Multi and SNSeg_HD.
S3 methods plot(), print() and summary() are available for class "SNSeg_Uni",
"SNSeg_Multi" and "SNSeh_HD" objects. The function max_SNsweep enables users
to compute the SN test statistic and make the segmentation plot for these
statistics. The function SNSeh_estimate allows users to compute parameter
estimates of each segment that is separated by estimated change-points.
SNSeg_Uni provides SN-based change point estimates for a univariate
time series based on changes in a single parameter or multiple parameters.
For the parameters of the SN test, the function
SNSeg_Uni offers mean, variance, acf, bivariate
correlation and numeric quantiles as available options. It also allows users
to enter their own defined function as the input parameter. Besides, users can
use a composite set of parameters including one or more from the mean, variance,
acf or numeric quantiles quantile. To visualize the estimated change points,
users can set "plot_SN = TRUE" and "est_cp_loc = TRUE"
to generate the time series segmentation plot. The output comprises of the
parameter(s), the window size, and the estimated change point locations. The
function returns an S3 object of class "SNSeg_Uni", which can be applied to
S3 methods plot(), print() and summary().
SNSeg_Multi provides SN-based change point estimates for multivariate
time series based on changes in multivariate means or covariance matrix. The
"plot_SN = TRUE" option allows users to plot each individual time series and
the estimated change=points. The function returns an S3 object of class
"SNSeg_Multi", which can be applied to S3 methods plot(), print() and summary().
SNSeg_HD provides SN-based change point estimates for a
high-dimensional time series based on changes in high-dimensional means. The
"plot_SN = TRUE" option allows users to plot each individual time series and
the estimated change=points. The input argument "n_plot" enables users to plot
the first "n_plot" number of time series. The function returns an S3 object of
class "SNSeg_HD", which can be applied to S3 methods plot(), print() and
summary().
max_SNsweep provides SN based test statistic of each time point and
generates a plot for these statistics and the estimated change-points.
SNSeg_estimate computes the parameter estimates of each segment separated
by the estimated change-points.
The package SNSeg provides three critical values table.
Table critical_values_single tabulates critical values of SN-based
change point estimates based on the change in a single parameter.
Table critical_values_multi tabulates critical values of SN-based
change point estimates based on changes in multiple parameters.
Table critical_values_HD tabulates critical values of of SN-based
change point estimates based on changes in high-dimensional means.
The function SNSeg_estimate computes parameter estimates of each segment
that are separated by the SN-based change-point estimates.
SNSeg_estimate(SN_result)SNSeg_estimate(SN_result)
SN_result |
An S3 object served as the output of the functions |
SNSeg_estimate returns an S3 object of class "SNSeg_estimate" including
the parameter estimates of each segment separated by the SN-based change-point
estimates.
If the time series is univariate, for a single parameter change, the output
contains parameter estimates for one of the followings: mean, variance,
acf, quantile, or general, which can be referred to the change
in a single mean, variance, autocorrelation, a given quantile level, or a general
functional. For multi-parameter changes, the output can be a combination of
mean, variance, acf, and a dataframe with each quantile level
depending on the type of parameters (argument paras_to_test of SNSeg_Uni,
SNSeg_Multi, or SNSeg_HD) that users select.
If the time series is multivariate with a dimension no greater than 10, the output
contains parameter estimates for one of the followings: bivcor, multi_mean,
or covariance, which can be referred to the change in correlation between
bivariate time series and the change in multivariate means or covariance between
multivariate time series.
If the time series is high-dimensional with a dimension greater than 10, the output
contains the parameter estimate HD_mean to represent the change in high-dimensional
means.
For more examples of SNSeg_estimate see the help vignette:
vignette("SNSeg", package = "SNSeg")
# code to simulate a univariate time series set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = TRUE, est_cp_loc = TRUE) # estimated change-point locations result$est_cp # variance estimates of the separated segments SNSeg_estimate(SN_result = result) # For more examples of SNSeg_estimate, please run # the command: vignette("SNSeg", package = "SNSeg")# code to simulate a univariate time series set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = TRUE, est_cp_loc = TRUE) # estimated change-point locations result$est_cp # variance estimates of the separated segments SNSeg_estimate(SN_result = result) # For more examples of SNSeg_estimate, please run # the command: vignette("SNSeg", package = "SNSeg")
The function SNSeg_HD is a SNHD change point
estimation procedure.
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) )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) )
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., |
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.
tsA numeric matrix of the input time series.
grid_sizeA numeric value of the window size.
SN_sweep_resultA 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_cpA vector containing the locations of the estimated change-points.
confidenceConfidence level of SN test as a numeric value.
critical_valueCritical 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")
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$est_cp # For more examples, please run the following command: # vignette("SNSeg", package = "SNSeg")n <- 500 p <- 50 nocp <- 5 cp_sets <- round(seq(0,nocp+1,1)/(nocp+1)*n) num_entry <- 5 kappa <- sqrt(4/5) mean_shift <- rep(c(0,kappa),100)[1:(length(cp_sets)-1)] set.seed(1) ts <- matrix(rnorm(n*p,0,1),n,p) no_seg <- length(cp_sets)-1 for(index in 1:no_seg){ tau1 <- cp_sets[index]+1 tau2 <- cp_sets[index+1] ts[tau1:tau2,1:num_entry] <- ts[tau1:tau2,1:num_entry] + mean_shift[index] } # grid_size defined result <- SNSeg_HD(ts, confidence = 0.9, grid_size_scale = 0.05, grid_size = 40) # Estimated change-point locations result$est_cp # For more examples, please run the following command: # vignette("SNSeg", package = "SNSeg")
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.
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 )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 )
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 |
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 |
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.
tsA numeric matrix of the input time series.
paras_to_testthe parameter used for the SN test as character.
grid_sizeA numeric value of the window size.
SN_sweep_resultA 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_cpA vector containing the locations of the estimated change-points.
confidenceConfidence level of SN test as a numeric value.
critical_valueCritical 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")
# 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$est_cp # For more examples, please run the following command: # vignette("SNSeg", package = "SNSeg")# Please run this function before simulation exchange_cor_matrix <- function(d, rho){ tmp <- matrix(rho, d, d) diag(tmp) <- 1 return(tmp) } # simulation of multivariate time series library(mvtnorm) set.seed(10) d <- 5 n <- 600 nocp <- 5 cp_sets <- round(seq(0, nocp+1 ,1)/(nocp+1)*n) mean_shift <- rep(c(0,2),100)[1:(length(cp_sets)-1)]/sqrt(d) rho_sets <- 0.2 sigma_cross <- list(exchange_cor_matrix(d,0)) ts <- MAR_MTS_Covariance(n, 2, rho_sets, cp_sets = c(0,n), sigma_cross) ts <- ts[1][[1]] # Test for the change in multivariate means # grid_size defined result <- SNSeg_Multi(ts, paras_to_test = "mean", confidence = 0.99, grid_size_scale = 0.05, grid_size = 45) # Estimated change-point locations result$est_cp # For more examples, please run the following command: # vignette("SNSeg", package = "SNSeg")
The function SNSeg_Uni is a SN change point estimation procedure for a
univariate time series based on the change in a single or multiple parameters
. It also detect changes in correlation between two univariate time series.
SNSeg_Uni( ts, paras_to_test, confidence = 0.9, grid_size_scale = 0.05, grid_size = NULL, plot_SN = TRUE, est_cp_loc = TRUE )SNSeg_Uni( ts, paras_to_test, confidence = 0.9, grid_size_scale = 0.05, grid_size = NULL, plot_SN = TRUE, est_cp_loc = TRUE )
ts |
A univariate time series expressed as a numeric vector. when the argument paras_to_test is specified as "bivcor", the correlation between bivariate time series, the input ts must be an n by 2 matrix |
paras_to_test |
The parameters that SN algorithm aim to examine, which are presented as a string, a number, or a combination of both. Available choices of paras_to_test include "mean", "variance", "acf", "bivcor" and a numeric value of quantile between 0 and 1. In the scenario where the input ts is a univariate time series, users are allowed to enter a combination of parameters for paras_to_test except "bivcor". Users can also set up their own function as the input of "paras_to_test". If so,
the user-fined function should use the univariate time series as the input and
return a numeric value as the output. Please see the help vignette for more details
by running |
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 |
A 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 dividing 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 |
SNSeg_Uni returns an S3 object of class "SNSeg_Uni" 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 a time series segmentation
plot when plot_SN = TRUE.
tsA numeric vector or two-dimensional matrix of the input time series.
paras_to_testA character, numeric value, a function or vector of the parameter(s) used for the SN test. If it is a function defined by the user, please refer to the section "test in a general functional" in the help vignette for more details on how to write the function correctly.
grid_sizeA numeric value of the window size.
SN_sweep_resultA list of 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 local window and (4) Upper bound of the local window.
est_cpA vector containing the locations of the estimated change-points.
confidenceConfidence level of SN test as a numeric value.
critical_valueCritical 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_Uni.
For more examples of SNSeg_Uni see the help vignette:
vignette("SNSeg", package = "SNSeg")
# code to simulate a univariate time series set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = TRUE, est_cp_loc = TRUE) # estimated change-point locations result$est_cp # For more examples of change in a single or multiple parameters, please run # the command: vignette("SNSeg", package = "SNSeg")# code to simulate a univariate time series set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = TRUE, est_cp_loc = TRUE) # estimated change-point locations result$est_cp # For more examples of change in a single or multiple parameters, please run # the command: vignette("SNSeg", package = "SNSeg")
Summary method for objects of class SNSeg_HD
## S3 method for class 'SNSeg_HD' summary(object, ...)## S3 method for class 'SNSeg_HD' summary(object, ...)
object |
a |
... |
not in use |
Provide information about estimated change-point locations, the
parameter tested by SN-based procedures, the confidence level, the grid_size,
and the critical value of the SN-based test.
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) # summary method summary(result)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) # summary method summary(result)
Summary method for objects of class SNSeg_Multi
## S3 method for class 'SNSeg_Multi' summary(object, ...)## S3 method for class 'SNSeg_Multi' summary(object, ...)
object |
a |
... |
not in use |
Provide information about estimated change-point locations, the
parameter tested by SN-based procedures, the confidence level, the grid_size,
and the critical value of the SN-based test.
# 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) # summary method summary(result)# 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) # summary method summary(result)
Summary method for objects of class SNSeg_Uni
## S3 method for class 'SNSeg_Uni' summary(object, ...)## S3 method for class 'SNSeg_Uni' summary(object, ...)
object |
a |
... |
not in use |
Provide information about estimated change-point locations, the
parameter tested by SN-based procedures, the confidence level, the grid_size,
and the critical value of the SN-based test.
set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) summary(result)set.seed(7) ts <- MAR_Variance(2, "V1") ts <- ts[,2] # test the change in a single parameter (variance) # grid_size defined result <- SNSeg_Uni(ts, paras_to_test = "variance", confidence = 0.9, grid_size_scale = 0.05, grid_size = 67, plot_SN = FALSE, est_cp_loc = TRUE) summary(result)