VARDetect (version 0.1.8)

tbss: Block segmentation scheme (BSS).

Description

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

Usage

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
)

Value

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

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

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")