BVAR function

Bayesian Vector Autoregression

Estimate a VAR(p) model using Bayesian approach, including the use of Minnesota prior

BVAR(z,p=1,C,V0,n0=5,Phi0=NULL,include.mean=T)

Arguments

• z: A matrix of vector time series, each column represents a series.
• p: The AR order. Default is p=1.
• C: The precision matrix of the coefficient matrix. With constant, the dimension of C is (kp+1)-by-(kp+1). The covariance matrix of the prior for the parameter vec(Beta) is Kronecker(Sigma_a,C-inverse).
• V0: A k-by-k covariance matrix to be used as prior for the Sigma_a matrix
• n0: The degrees of freedom used for prior of the Sigma_a matrix, the covariance matrix of the innovations. Default is n0=5.
• Phi0: The prior mean for the parameters. Default is set to NULL, implying that the prior means are zero.
• include.mean: A logical switch controls the constant term in the VAR model. Default is to include the constant term.

Details

for a given prior, the program provide the posterior estimates of a VAR(p) model.

Returns

• est: Posterior means of the parameters

• Sigma: Residual covariance matrix

References

Tsay (2014, Chapter 2).

Author(s)

Ruey S. Tsay

Examples

data("mts-examples",package="MTS")
z=log(qgdp[,3:5])
zt=diffM(z)*100
C=0.1*diag(rep(1,7))
V0=diag(rep(1,3))
BVAR(zt,p=2,C,V0)