simu_lstsp: Function to deploy simulation with LSTSP algorithm

In VARDetect: Multiple Change Point Detection in Structural VAR Models

Function to deploy simulation with LSTSP algorithm

Description

A function to generate simulation with LSTSP algorithm

Usage

simu_lstsp(
  nreps,
  simu_method = c("LS"),
  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,
  alpha_L = 0.25,
  lambda.1 = NULL,
  mu.1 = NULL,
  lambda.1.seq = NULL,
  mu.1.seq = NULL,
  lambda.2,
  mu.2,
  lambda.3,
  mu.3,
  omega = NULL,
  h = NULL,
  step.size = NULL,
  tol = 1e-04,
  niter = 100,
  backtracking = TRUE,
  rolling.skip = 5,
  cv = FALSE,
  nfold = NULL,
  verbose = FALSE
)

Arguments

nreps	A positive integer, indicating the number of simulation replications
simu_method	the structure of time series: only available for "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
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.
alpha_L	a positive numeric value, indicating the restricted space of low rank component, default is 0.25
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
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
rolling.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.

Value

A S3 object of class VARDetect.simu.result, containing the following entries:

sizes

A 2-d numeric vector, indicating the size of time series data

true_lag

True time lags for the process, here is fixed to be 1.

true_lagvector

A vector recording the time lags for different segments, not available under this model setting, here is fixed to be NULL

true_cp

True change points for simulation, a numeric vector

true_sparse

A list of numeric matrices, indicating the true sparse components for all segments

true_lowrank

A list of numeric matrices, indicating the true low rank components for all segments

est_cps

A list of estimated change points, including all replications

est_lag

A numeric value, estimated time lags, which is user specified

est_lagvector

A vector for estimated time lags, not available for this model, set as NULL.

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 <- 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)
lambda1 = lambda2 = lambda3 <- c(2.5, 2.5)
mu1 = mu2 = mu3 <- c(15, 15)
try_simu <- simu_lstsp(nreps = 3, simu_method = "LS", nob = nob, k = p, 
                       brk = brk, sigma = diag(p), signals = signals, 
                       rank = rank, singular_vals = singular_vals, 
                       info_ratio = info_ratio, sp_pattern = "off-diagonal", 
                       spectral_radius = 0.9, lambda.1 = lambda1, mu.1 = mu1, 
                       lambda.2 = lambda2, mu.2 = mu2, lambda.3 = lambda3, 
                       mu.3 = mu3, step.size = 5, niter = 20, rolling.skip = 5,
                       cv = FALSE, verbose = TRUE)
summary(try_simu, critical = 5)

VARDetect documentation built on May 10, 2022, 9:07 a.m.