simu_var function

Generate VAR(p) model data with break points

This function is used for generate simulated time series

simu_var(
  method = c("sparse", "group sparse", "fLS", "LS"),
  nob = 300,
  k = 20,
  lags = 1,
  lags_vector = NULL,
  brk,
  sigma = NULL,
  skip = 50,
  spectral_radius = 0.98,
  seed = NULL,
  sp_density = NULL,
  group_mats = NULL,
  group_index = NULL,
  group_type = c("columnwise", "rowwise"),
  sparse_mats = NULL,
  sp_pattern = c("off-diagonal", "diagonal", "random"),
  rank = NULL,
  info_ratio = NULL,
  signals = NULL,
  singular_vals = NULL
)

Arguments

• method: the structure of time series: "sparse","group sparse", "fLS", "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
• spectral_radius: to ensure the time series is piecewise stationary.
• seed: an argument to control the random seed. Default seed is 1.
• sp_density: if we choose random pattern, we should provide the sparsity density for each segment
• group_mats: transition matrix for group sparse case
• group_index: group index for group lasso.
• group_type: type for group lasso: "columnwise", "rowwise". Default is "columnwise".
• sparse_mats: transition matrix for sparse case
• sp_pattern: a choice of the pattern of sparse component: diagonal, 1-off diagonal, random, custom
• 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
• signals: manually setting signal for each segment (including sign)
• singular_vals: singular values for the low rank components

Returns

A list object, which contains the followings

• series: matrix of timeseries data
• noises: matrix of noise term data
• sparse_mats: list of sparse matrix in the transition matrix
• lowrank_mats: list of low-rank matrix in the transition matrix

Examples

nob <- (10^3 * 4) # number of time points
p <- 15 # number of time series components
brk <- c(floor(nob / 3), floor(2 * nob / 3), nob + 1)
m0 <- length(brk) - 1 # number of break points
q.t <- 2 # the true AR order
m <- m0 + 1 # number of segments
sp_density <- rep(0.05, m * q.t) # sparsity level (5%)
try <- simu_var("sparse", nob = nob, k = p, lags = q.t, brk = brk,
                sp_pattern = "random", sp_density = sp_density)
print(plot_matrix(do.call("cbind", try$model_param), m * q.t))