simu_tbss function

Simulation function for TBSS algorithm

Function for deploying simulation using TBSS algorithm

simu_tbss(
  nreps,
  simu_method = c("sparse", "group sparse", "fLS"),
  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,
  est_method = c("sparse", "group sparse", "fLS"),
  q = 1,
  tol = 0.01,
  lambda.1.cv = NULL,
  lambda.2.cv = NULL,
  mu = NULL,
  group.index = NULL,
  group.case = c("columnwise", "rowwise"),
  max.iteration = 100,
  refit = FALSE,
  block.size = NULL,
  blocks = NULL,
  use.BIC = TRUE,
  an.grid = NULL,
  verbose = FALSE
)

Arguments

• nreps: A numeric integer number, indicates the number of simulation replications
• simu_method: the structure of time series: "sparse","group sparse", and "fLS"
• 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.
• est_method: method: sparse, group sparse, and fixed low rank plus sparse. Default is sparse
• q: the AR order
• tol: tolerance for the fused lasso
• lambda.1.cv: tuning parameter lambda_1 for fused lasso
• lambda.2.cv: tuning parameter lambda_2 for fused lasso
• mu: tuning parameter for low rank component, only available when method is set to "fLS"
• group.index: group index for group sparse case
• group.case: group sparse pattern: column, row.
• max.iteration: max number of iteration for the fused lasso
• refit: logical; if TRUE, refit the VAR model for parameter estimation. Default is FALSE.
• block.size: the block size
• blocks: the blocks
• use.BIC: use BIC for k-means part
• an.grid: a vector of an for grid searching
• verbose: a Boolean argument; if TRUE, function provides detailed information. Default is FALSE

Returns

A S3 object of class, named VARDetect.simu.result

• est_cps: A list of estimated change points, including all replications
• 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

nob <- 4000; p <- 15
brk <- c(floor(nob / 3), floor(2 * nob / 3), nob + 1)
m <- length(brk); q.t <- 1
sp_density <- rep(0.05, m * q.t)
signals <- c(-0.6, 0.6, -0.6)
try_simu <- simu_tbss(nreps = 3, simu_method = "sparse", nob = nob,
                      k = p, lags = q.t, brk = brk, sigma = diag(p),
                      signals = signals, sp_density = sp_density,
                      sp_pattern = "random", est_method = "sparse", q = q.t,
                      refit = TRUE)