VARshrink: Shrinkage estimation of VAR parameters

In VARshrink: Shrinkage Estimation Methods for Vector Autoregressive Models

Shrinkage estimation of VAR parameters

Description

Shrinkage estimation methods for high-dimensional VAR models. Consider VAR(p) model:

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

where y_t is K-dimensional time series, d_t is deterministic regressors, e_t is a noise process, and A_1, \ldots, A_p, and C are coefficient matrices. Exogenous variables can be included additionally as regressors.

Usage

VARshrink(
  y,
  p = 1,
  type = c("const", "trend", "both", "none"),
  season = NULL,
  exogen = NULL,
  method = c("ridge", "ns", "fbayes", "sbayes", "kcv"),
  lambda = NULL,
  lambda_var = NULL,
  dof = Inf,
  ...
)

Arguments

y	A T-by-K matrix of endogenous variables
p	Integer for the lag order
type	Type of deterministic regressors to include. 1) const - the constant. 2) trend - the trend. 3) both - both the constant and the trend. 4) none - no deterministic regressors. ***Note: In the package version <= 0.3, method="ns" does not accept type="const" and type="both" to avoid constant term.
season	An integer value of frequency for inclusion of centered seasonal dummy variables. abs(season) >= 3.
exogen	A T-by-L matrix of exogenous variables. Default is NULL.
method	1) "ridge" - multivariate ridge regression. 2) "ns" - a Stein-type nonparametric shrinkage method. 3) "fbayes" - a full Bayesian shrinkage method using noninformative priors. 4) "sbayes" - a semiparametric Bayesian shrinkage method using parameterized cross validation. 5) "kcv" - a semiparametric Bayesian shrinkage method using K-fold cross validation
lambda, lambda_var	Shrinkage parameter value(s). Use of this parameter is slightly different for each method: the same value does not imply the same shrinkage estimates.
dof	Degree of freedom of multivariate t-distribution for noise. Valid only for method = "fbayes" and method = "sbayes". dof = Inf means multivariate normal distribution.
...	Extra arguments to pass to a specific function of the estimation method. For example, burnincycle and mcmccycle are for "fbayes".

Details

Shrinkage estimation methods can estimate the coefficients even when the dimensionality K is larger than the number of observations.

Value

An object of class "varshrinkest" with the components: varresult, datamat, y, type, p, K, obs, totobs, restrictions, method, lambda, call. The class "varshrinkest" inherits the class "varest" in the package vars.

Examples

data(Canada, package = "vars")
y <- diff(Canada)
VARshrink(y, p = 2, type = "const", method = "ridge")

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