MSBVAR (version 0.2.2)

mc.irf: Monte Carlo Integration / Simulation of Impulse Response Functions

Description

Simulates a posterior sample 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 mlevar() functions. The decomposition of the contemporaneous innovations is handled by a Cholesky decomposition of the error covariance matrix in each VAR object. Simulations of IRFs from the Bayesian model utilize the posterior estimates for that model.

Usage

mc.irf(varobj, nsteps, draws=0, A0.posterior=NULL)
mc.irf.VAR(varobj, nsteps, draws)
mc.irf.BVAR(varobj, nsteps, draws)
mc.irf.BSVAR(varobj, nsteps, A0.posterior)

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 samplesimpulse$draws \times nsteps \times m^2$ array of the impulse responsesB-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 $A_0$.

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 and the draws of the contemporaneous structural coefficients $A_0$ from gibbs.A0. This function then computes a posterior sample of the impulse responses based on the draws of $A_0$ and draws from the normal posterior pdf for the other coefficients in the model.

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(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
varobj <- szbsvar(Y, p, z = NULL,
                            lambda0, lambda1, lambda3, lambda4, lambda5,
                            mu5, mu6, ident, qm = 4)
A0.posterior <- gibbs.A0(varobj, N1, N2)
impulse.sample <- mc.irf(varobj, A0.posterior, nsteps)