MSBVAR (version 0.1.1)

mc.irf.var: 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 both Bayesian and frequentist VARs estimated with the szbvar() and 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.var(varobj, nsteps, draws)

Value

An mc.irf.var 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 responses

Details

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).

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. 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 as plot.mc.irf.var for plotting methods and error band construction for the posterior of the impulse response functions

Examples

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.var(fit.BVAR, nsteps=10, draws=5000)

    # Plot the responses
    plot.mc.irf.var(posterior.impulses, method=c("Sims-Zha2"), component=1,
                     probs=c(0.16,0.84), varnames=varnames)