simu_lstsp {VARDetect}

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)