mc.irf {MSBVAR} | R Documentation |
Simulates a posterior of impulse response functions (IRF) by
Monte Carlo integration. This can handle Bayesian and frequentist
VARs and Bayesian (structural) VARs estimated with the szbvar
,
szbsvar
or reduced.form.var
functions. The decomposition of the
contemporaneous innovations is handled by a Cholesky decomposition of
the error covariance matrix in reduced form (B)VAR object, or for the
contemporaneous structure in S-VAR models. Simulations of IRFs
from the Bayesian model utilize the posterior estimates for that model.
mc.irf(varobj, nsteps, draws=0, A0.posterior=NULL, sign.list=rep(1, ncol(varobj$Y))) mc.irf.VAR(varobj, nsteps, draws) mc.irf.BVAR(varobj, nsteps, draws) mc.irf.BSVAR(varobj, nsteps, A0.posterior, sign.list)
varobj |
VAR objects for a fitted VAR model from either
reduced.form.var , szbvar or szbsvar . |
nsteps |
Number of periods over which to compute the impulse responses |
draws |
Number of draws for the simulation of the posterior
distribution of the IRFs (if not a szbsvar object |
A0.posterior |
Posterior sample objects generated by
gibbs.A0() for B-SVAR models, based on the structural identification in
varobj$ident |
sign.list |
A list of signs (length = number of variables) for normalization given as either 1 or -1 |
VAR/BVAR:
Draws a set of posterior samples from the VAR coefficients and computes impulse responses for each sample. These samples can then be summarized to compute MCMC-based estimates of the responses using the error band methods described in Sims and Zha (1999).
B-SVAR:
Generates a set of N2 draws from the impulse responses for the
Bayesian SVAR model in varobj
. The function takes as its
arguments the posterior moments of the B-SVAR model in varobj
,
the draws of the contemporaneous structural coefficients
A(0) from gibbs.A0
, and a list of signs for
normalization. This function then computes a posterior sample of the
impulse responses based on the Schur product of the sign list and the
draws of A(0) and draws from the normal posterior pdf for
the other coefficients in the model.
The computations are done using compiled C++ code as of version 0.3.0. See the package source code for details about the implementation.
VAR/BVAR:
An mc.irf.VAR/mc.irf.BVAR class object object that is the array of
impulse response samples for the Monte Carlo samples
impulse |
draws X nsteps X (m*m) array of the impulse responses |
B-SVAR:
mc.irf.BSVAR object which is an (N2, nsteps, m^2) array of the impulse
responses for the associated B-SVAR model in varobj
and the posterior
A(0).
Users need to think carefully about the number of steps and the
size of the posterior sample in A(0), since enough memory
needs to be available to store and process the posterior of the
impulse responses. The number of bytes consumed by the impulse
responses will be approximately m^2 x nsteps x N2 x 16 where N2
is the number of
draws of A(0) from the gibbs.A0
. Be sure
you have enough memory available to store the object you create!
Patrick T. Brandt
Brandt, Patrick T. and John R. Freeman. 2006. "Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis" Political Analysis 14(1):1-36.
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.
Waggoner, Daniel F. and Tao A. Zha. 2003. "A Gibbs sampler for structural vector autoregressions" Journal of Economic Dynamics & Control. 28:349–366.
See also as plot.mc.irf
for plotting methods
and error band construction for the posterior of the impulse response
functions, szbsvar
for estimation of the
posterior moments of the B-SVAR model, gibbs.A0
for drawing posterior samples of A(0) for the B-SVAR model
before the IRF computations, and plot.mc.irf
for a
plotting method for the posterior of the impulse responses.
# Example 1 data(IsraelPalestineConflict) varnames <- colnames(IsraelPalestineConflict) fit.BVAR <- szbvar(Y=IsraelPalestineConflict, p=6, z=NULL, lambda0=0.6, lambda1=0.1, lambda3=2, lambda4=0.25, lambda5=0, mu5=0, mu6=0, nu=3, qm=4, prior=0, posterior.fit=FALSE) # Draw from the posterior pdf of the impulse responses. posterior.impulses <- mc.irf(fit.BVAR, nsteps=10, draws=5000) # Plot the responses plot(posterior.impulses, method=c("Sims-Zha2"), component=1, probs=c(0.16,0.84), varnames=varnames) # Example 2 ident <- diag(2) varobj <- szbsvar(Y=IsraelPalestineConflict, p=6, z = NULL, lambda=0.6, lambda1=0.1, lambda3=2, lambda4=0.25, lambda5=0, mu5=0, mu6=0, ident, qm = 4) A0.posterior <- gibbs.A0(varobj, N1=1000, N2=1000) # Note you need to explcitly reference the sampled A0.posterior object # in the following call for R to find it in the namespace! impulse.sample <- mc.irf(varobj, nsteps=12, A0.posterior=A0.posterior)