# Self-normalization (SN) based change points estimation for multivariate time series 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. ```r 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 ## Returns `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 n**`grid_size_scale` or the last n**`grid_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 ```r # 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") ```

SNSeg_Multi function