# Self-normalization (SN) based change points estimation for high dimensional time series for changes in high-dimensional means (SNHD). The function `SNSeg_HD` is a SNHD change point estimation procedure. ```r 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)`. ## Returns 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 n**`grid_size_scale` or the last n**`grid_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 ```r 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") ```

SNSeg_HD function