VARshrink {VARshrink}

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 + ... + 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, ..., 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")