VARDetect (version 0.1.8)

lstsp: Main function for the low rank plus sparse structure VAR model

Description

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

Usage

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
)

Value

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

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.

Examples

# \donttest{
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")
# }