createVARCoefs_ltriangular: Create coefficients of a VAR model

In VARshrink: Shrinkage Estimation Methods for Vector Autoregressive Models

Create coefficients of a VAR model

Description

Randomly create sparse lower-triangular matrices for VAR coefficients of lagged endogenous variables, and set a constant vector.

Usage

createVARCoefs_ltriangular(
  p = 1,
  K = 5,
  diag_val = 1/p,
  num_nonzero = 0,
  const_vector = NULL,
  range_min = 0.2,
  range_max = 1/p
)

Arguments

p	lag order
K	Number of time series variables.
diag_val	diagonal values of A_1, \ldots, A_p.
num_nonzero	Number of nonzero entries on the lower-triangular parts of A1, ..., Ap
const_vector	constant vector c of the VAR model
range_min, range_max	Each nonzero off-diagonal entry of coefficient matrices is drawn uniformly from the interval [-range_max, -range_min] U [range_min, range_max]

Details

Consider VAR(p) model:

y_t = A_1 y_{t-1} + \cdots + A_p y_{t-p} + c + e_t,

with the constant deterministic variable (d_t = 1). The function creates the coefficient matrices A_1, \ldots, A_p and constant vector c.

Diagonal elements of each K-by-K matrix A_i are all equal to diag_val, and off-diagonal elements are all zero except for a few randomly selected nonzero elements. Nonzero off-diagonal elements are selected from lower-triangular parts of A_i and the values are drawn from a uniform distribution over [-range_max, -range_min] U [range_min, range_max].

Value

A list object with components $A and $c. $A is a list of K-by-K matrices A_1, \ldots, A_p, and $c is a constant vector of length K.

Examples

p <- 1; K <- 20;
const_vector <- c(rep(0.2, 5), rep(0.7, 15))
createVARCoefs_ltriangular(p = p, K = K, diag_val = 0.6,
num_nonzero = K, const_vector = const_vector, range_max = 1)

VARshrink documentation built on Jan. 10, 2026, 1:06 a.m.