MSBVAR (version 0.9-2)

irf: Impulse Response Function (IRF) Computation for a VAR

Description

Computes the impulse response function (IRF) or moving average representation (MAR) for an m-dimensional set of VAR/BVAR/B-SVAR coefficients.

Usage

irf(varobj, nsteps, A0=NULL)

Arguments

varobj

VAR, BVAR, or BSVAR objects for a fitted VAR, BVAR, or BSVAR model from szbvar, szbsvar or reduced.form.var

nsteps

Number or steps, or the horizon over which to compute the IRFs (typically 1.5 to 2 times the lag length used in estimation

A0

Decomposition contemporaneous error covariance of a VAR/BVAR/BSVAR, default is a Cholesky decomposition of the error covariance matrix for VAR and BVAR models, A0 = chol(varobj$mean.S), and the inverse of $A(0)$ for B-SVAR models, A0 = solve(varobj$A0.mode)

Value

A list of the AR coefficients used in computing the IRF and the impulse response matrices:

B

$ m x m x nstep$ Autoregressive coefficient matrices in lag order. Note that all AR coefficient matrices for $nstep > p$ are zero.

mhat

$m x m x nstep$ impulse response matrices. mhat[,,i] are the impulses for the i'th period for the $m$ variables.

Details

This function should rarely be called by the user. It is a working function to compute the IRFs for a VAR model. Users will typically want to used one of the simulation functions that also compute error bands for the IRF, such as mc.irf which calls this function and simulates its multivariate posterior distribution.

References

Sims, C.A. and Tao Zha. 1999. "Error Bands for Impulse Responses." Econometrica 67(5): 1113-1156.

Hamilton, James. 1994. Time Series Analysis. Chapter 11.

See Also

See also dfev for the related decompositions of the forecast error variance, mc.irf for Bayesian and frequentist computations of IRFs and their variances (which is what you probably really want).

Examples

data(IsraelPalestineConflict)
rf.var <- reduced.form.var(IsraelPalestineConflict, p=6)
plot(irf(rf.var, nsteps = 12))