# Main function for the low rank plus sparse structure VAR model Main function for the low-rank plus sparse structure VAR model ```r lstsp( data, lambda.1 = NULL, mu.1 = NULL, lambda.1.seq = NULL, mu.1.seq = NULL, lambda.2 = NULL, mu.2 = NULL, lambda.3 = NULL, mu.3 = NULL, alpha_L = 0.25, omega = NULL, h = NULL, step.size = NULL, tol = 1e-04, niter = 100, backtracking = TRUE, skip = 5, cv = FALSE, nfold = NULL, verbose = FALSE ) ``` ## Arguments - `data`: A n by p dataset matrix - `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 - `alpha_L`: a positive numeric value, indicating the restricted space of low rank component, default is 0.25 - `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 - `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 list object including - **data**: the original dataset - **q**: the time lag for the time series, in this case, it is 1 - **cp**: Final estimated change points - **sparse_mats**: Final estimated sparse components - **lowrank_mats**: Final estimated low rank components - **est_phi**: Final estimated model parameter, equals to sum of low rank and sparse components - **time**: Running time for the LSTSP algorithm ## 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) try <- simu_var(method = "LS", nob = nob, k = p, lags = 1, brk = brk, sigma = as.matrix(diag(p)), signals = signals, rank = rank, singular_vals = singular_vals, info_ratio = info_ratio, sp_pattern = "off-diagonal", spectral_radius = 0.9) data <- try$series lambda1 = lambda2 = lambda3 <- c(2.5, 2.5) mu1 = mu2 = mu3 <- c(15, 15) fit <- lstsp(data, lambda.1 = lambda1, mu.1 = mu1, lambda.2 = lambda2, mu.2 = mu2, lambda.3 = lambda3, mu.3 = mu3, alpha_L = 0.25, step.size = 5, niter = 20, skip = 5, cv = FALSE, verbose = FALSE) summary(fit) plot(fit, data, display = "cp") plot(fit, data, display = "param") ```

lstsp function