tbss function

Block segmentation scheme (BSS).

Perform the block segmentation scheme (BSS) algorithm to detect the structural breaks in large scale high-dimensional non-stationary VAR models.

tbss(
  data,
  method = c("sparse", "group sparse", "fLS"),
  group.case = c("columnwise", "rowwise"),
  group.index = NULL,
  lambda.1.cv = NULL,
  lambda.2.cv = NULL,
  mu = NULL,
  q = 1,
  max.iteration = 50,
  tol = 10^(-2),
  block.size = NULL,
  blocks = NULL,
  refit = FALSE,
  use.BIC = TRUE,
  an.grid = NULL,
  verbose = FALSE
)

Arguments

• data: input data matrix, with each column representing the time series component
• method: method: sparse, group sparse, and fixed low rank plus sparse. Default is sparse
• group.case: group sparse pattern: column, row.
• group.index: group index for group sparse case
• 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"
• q: the VAR lag
• max.iteration: max number of iteration for the Fused lasso
• tol: tolerance for the fused lasso
• block.size: the block size
• blocks: the blocks
• refit: logical; if TRUE, refit the VAR model for parameter estimation. Default is FALSE.
• use.BIC: use BIC for k-means part
• an.grid: a vector of an for grid searching
• verbose: a Boolean argument to determine whether provide detailed outputs for each step. Default is FALSE

Returns

S3 object of class VARDetect.result, which contains the followings

• data: the original dataset
• q: the time lag user specified, a numeric value
• cp: final estimated change points, a numeric vector
• sparse_mats: estimated sparse components for each segment, a list of numeric matrices
• lowrank_mats: estimated low rank components for each segment, a list of numeric matrices
• est_phi: estimated final model parameters, the summation of the sparse and the low rank components
• time: computation time for each step

Examples

#### sparse VAR model
nob <- (10^3) # number of time points
p <- 15; # number of time series components
brk <- c(floor(nob/3),floor(2*nob/3),nob+1); # true break points with nob+1 as the last element
m0 <- length(brk) -1; # number of break points
q.t <- 1; # the true AR order
m <- m0+1 #number of segments
try<-simu_var('sparse',nob=nob,k=p,lags=q.t,brk = brk,sp_pattern="off-diagonal",seed=1)
data <- try$series
data <- as.matrix(data)
#run the bss method
fit <- tbss(data, method = "sparse", q = q.t)
print(fit)
summary(fit)
plot(fit, data, display = "cp")
plot(fit, data, display = "param")

###### Example for fixed low rank plus sparse structure VAR model
nob <- 300
p <- 15
brk <- c(floor(nob/3), floor(2*nob/3), nob+1)
m <- length(brk)
q.t <- 1
signals <- c(-0.7, 0.7, -0.7)
rank <- c(2, 2, 2)
singular_vals <- c(1, 0.75)
info_ratio <- rep(0.35, 3)
try <- simu_var(method = "fLS", nob = nob, k = p, lags = 1, brk = brk,
                sigma = as.matrix(diag(p)), signals = signals, seed=1,
                rank = rank, singular_vals = singular_vals, info_ratio = info_ratio,
                sp_pattern = "off-diagonal", spectral_radius = 0.9)
data <- try$series
data <- as.matrix(data)
fit <- tbss(data, method = "fLS", mu = 150)
print(fit)
summary(fit)
plot(fit, data, display = "cp")
plot(fit, data, display = "param")