lstsp function

Main function for the low rank plus sparse structure VAR model

Main function for the low-rank plus sparse structure VAR model

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

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")