simVAR function

Simulates a VAR(p) with various sparsity patterns

Simulates a VAR(p) with various sparsity patterns

simVAR(
  periods,
  k,
  p,
  coef_mat = NULL,
  const = rep(0, k),
  e_dist = rnorm,
  init_y = rep(0, k * p),
  max_abs_eigval = 0.8,
  burnin = periods,
  sparsity_pattern = c("none", "lasso", "L1", "hvar", "HLag"),
  sparsity_options = NULL,
  decay = 1/p,
  seed = NULL,
  ...
)

Arguments

  • periods: Scalar indicating the desired time series length

  • k: Number of time series

  • p: Maximum lag number. In case of sparsity_patter="none" this will be the actual number of lags for all variables

  • coef_mat: Coefficient matrix in companion form. If not provided, one will be simulated

  • const: Constant term of VAR. Default is zero. Must be either a scalar, in which case it will be broadcasted to a k-vector, or a k-vector

  • e_dist: Either a function taking argument n indicating the number of variables in the system, or a matrix of dimensions k x (periods+burnin)

  • init_y: Initial values. Defaults to zero. Expects either a scalar or a vector of length (k*p)

  • max_abs_eigval: Maximum allowed eigenvalue of companion matrix. Only applicable if coefficient matrix is being simulated

  • burnin: Number of time points to be used for burnin

  • sparsity_pattern: The sparsity pattern that should be simulated. Options are: "none" for a dense VAR, "lasso" (or "L1") for a VAR with random zeroes, and "hvar" (or "HLag") for an elementwise hierarchical sparsity pattern

  • sparsity_options: Named list of additional options for when sparsity pattern is lasso (L1) or hvar (HLag). For lasso (L1) the option num_zero

    determines the number of zeros. For hvar (HLag), the options zero_min (zero_max) give the minimum (maximum) of zeroes for each variable in each equation, and the option zeroes_in_self (boolean) determines if any of the coefficients of a variable on itself should be zero.

  • decay: How much smaller should parameters for later lags be. The smaller, the larger will early parameters be w.r.t. later ones.

  • seed: Seed to be used for the simulation

  • ...: Additional arguments passed to e_dist

Returns

Returns an object of S3 class bigtime.simVAR containing the following - Y: Simulated Data

  • periods: Time series length

  • k: Number of endogenous variables

  • p: Maximum lag length; effective lag length might be shorter due to sparsity patterns

  • coef_mat: Companion form of the coefficient matrix. Will be of dimensions (k``p)x(k``p). First k rows correspond to the actual coefficient matrix.

  • is_coef_mat_simulated: TRUE if the coef_mat was simulated, FALSE if it was user provided

  • const: Constant term

  • e_dist: Errors used in the construction of the data

  • init_y: Initial conditions

  • max_abs_eigval: Maximum eigenvalue to which the companion matrix was constraint

  • burnin: Burnin period used

  • sparsity_pattern: Sparsity pattern used

  • sparsity_options: Extra options for the sparsity patterns used

  • seed: Seed used for the simulation

Examples

periods <- 200 # time series length
k <- 5 # number of variables
p <- 10 # maximum lag
sparsity_pattern <- "HLag" # HLag sparsity structure
sparsity_options <- list(zero_min = 0, # variables can be included with all lags
                         zero_max = 10, # but some could also include no lags
                         zeroes_in_self = TRUE)
sim <- simVAR(periods=periods, k=k, p=p, sparsity_pattern=sparsity_pattern,
              sparsity_options=sparsity_options, seed = 12345)
summary(sim)
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