mc.irf {MSBVAR}R Documentation

Monte Carlo Integration / Simulation of Impulse Response Functions

Description

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.

Usage

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)

Arguments

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

Details

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.

Value

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).

Note

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!

Author(s)

Patrick T. Brandt

References

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

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.

Examples

# 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)

[Package MSBVAR version 0.3.2 Index]