simu_lstsp function

Function to deploy simulation with LSTSP algorithm

A function to generate simulation with LSTSP algorithm

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.

Returns

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)