# Function to deploy simulation with LSTSP algorithm A function to generate simulation with LSTSP algorithm ```r simu_lstsp( nreps, simu_method = c("LS"), nob, k, lags = 1, lags_vector = NULL, brk, sigma, skip = 50, group_mats = NULL, group_type = c("columnwise", "rowwise"), group_index = NULL, sparse_mats = NULL, sp_density = NULL, signals = NULL, rank = NULL, info_ratio = NULL, sp_pattern = c("off-diagonal", "diagoanl", "random"), singular_vals = NULL, spectral_radius = 0.9, alpha_L = 0.25, lambda.1 = NULL, mu.1 = NULL, lambda.1.seq = NULL, mu.1.seq = NULL, lambda.2, mu.2, lambda.3, mu.3, omega = NULL, h = NULL, step.size = NULL, tol = 1e-04, niter = 100, backtracking = TRUE, rolling.skip = 5, cv = FALSE, nfold = NULL, verbose = FALSE ) ``` ## Arguments - `nreps`: A positive integer, indicating the number of simulation replications - `simu_method`: the structure of time series: only available for "LS" - `nob`: sample size - `k`: dimension of transition matrix - `lags`: lags of VAR time series. Default is 1. - `lags_vector`: a vector of lags of VAR time series for each segment - `brk`: a vector of break points with (nob+1) as the last element - `sigma`: the variance matrix for error term - `skip`: an argument to control the leading data points to obtain a stationary time series - `group_mats`: transition matrix for group sparse case - `group_type`: type for group lasso: "columnwise", "rowwise". Default is "columnwise". - `group_index`: group index for group lasso. - `sparse_mats`: transition matrix for sparse case - `sp_density`: if we choose random pattern, we should provide the sparsity density for each segment - `signals`: manually setting signal for each segment (including sign) - `rank`: if we choose method is low rank plus sparse, we need to provide the ranks for each segment - `info_ratio`: the information ratio leverages the signal strength from low rank and sparse components - `sp_pattern`: a choice of the pattern of sparse component: diagonal, 1-off diagonal, random, custom - `singular_vals`: singular values for the low rank components - `spectral_radius`: to ensure the time series is piecewise stationary. - `alpha_L`: a positive numeric value, indicating the restricted space of low rank component, default is 0.25 - `lambda.1`: tuning parameter for sparse component for the first step - `mu.1`: tuning parameter for low rank component for the first step - `lambda.1.seq`: a sequence of lambda to the left segment for cross-validation, it's not mandatory to provide - `mu.1.seq`: a sequence of mu to the left segment, low rank component tuning parameter - `lambda.2`: tuning parameter for sparse for the second step - `mu.2`: tuning parameter for low rank for the second step - `lambda.3`: tuning parameter for estimating sparse components - `mu.3`: tuning parameter for estimating low rank components - `omega`: tuning parameter for information criterion, the larger of omega, the fewer final selected change points - `h`: window size of the first rolling window step - `step.size`: rolling step - `tol`: tolerance for the convergence in the second screening step, indicates when to stop - `niter`: the number of iterations required for FISTA algorithm - `backtracking`: A boolean argument to indicate use backtrack to FISTA model - `rolling.skip`: The number of observations need to skip near the boundaries - `cv`: A boolean argument, indicates whether the user will apply cross validation to select tuning parameter, default is FALSE - `nfold`: An positive integer, the number of folds for cross validation - `verbose`: If is TRUE, then it will print all information about current step. ## Returns A S3 object of class `VARDetect.simu.result`, containing the following entries: - **sizes**: A 2-d numeric vector, indicating the size of time series data - **true_lag**: True time lags for the process, here is fixed to be 1. - **true_lagvector**: A vector recording the time lags for different segments, not available under this model setting, here is fixed to be NULL - **true_cp**: True change points for simulation, a numeric vector - **true_sparse**: A list of numeric matrices, indicating the true sparse components for all segments - **true_lowrank**: A list of numeric matrices, indicating the true low rank components for all segments - **est_cps**: A list of estimated change points, including all replications - **est_lag**: A numeric value, estimated time lags, which is user specified - **est_lagvector**: A vector for estimated time lags, not available for this model, set as NULL. - **est_sparse_mats**: A list of estimated sparse components for all replications - **est_lowrank_mats**: A list of estimated low rank components for all replications - **est_phi_mats**: A list of estimated model parameters, transition matrices for VAR model - **running_times**: A numeric vector, containing all running times ## Examples ```r nob <- 100 p <- 15 brk <- c(50, nob+1) rank <- c(1, 3) signals <- c(-0.7, 0.8) singular_vals <- c(1, 0.75, 0.5) info_ratio <- rep(0.35, 2) lambda1 = lambda2 = lambda3 <- c(2.5, 2.5) mu1 = mu2 = mu3 <- c(15, 15) try_simu <- simu_lstsp(nreps = 3, simu_method = "LS", nob = nob, k = p, brk = brk, sigma = diag(p), signals = signals, rank = rank, singular_vals = singular_vals, info_ratio = info_ratio, sp_pattern = "off-diagonal", spectral_radius = 0.9, lambda.1 = lambda1, mu.1 = mu1, lambda.2 = lambda2, mu.2 = mu2, lambda.3 = lambda3, mu.3 = mu3, step.size = 5, niter = 20, rolling.skip = 5, cv = FALSE, verbose = TRUE) summary(try_simu, critical = 5) ```

simu_lstsp function