MSBVAR (version 0.9-2)

uc.forecast: Forecast density estimation unconditional forecasts for VAR/BVAR/BSVAR models via MCMC

Description

Implements unconditional forecast density estimator for VAR/BVAR/BSVAR models described in Waggoner and Zha (1999). The unconditional forecasts place no restriction on the paths of the forecasts (cf. hc.forecast). The forecast densities are estimated as the posterior sample for the VAR/BVAR/BSVAR model using Markov Chain Monte Carlo with data augmentation to account for the uncertainty of the forecasts and the parameters. This function DOES account for parameter uncertainty in the MCMC algorithm.

Usage

uc.forecast(varobj, nsteps, burnin, gibbs, exog = NULL)

Arguments

varobj

VAR or BVAR object produced for a VAR or BVAR using szbvar or reduced.form.var

nsteps

Number of periods in the forecast horizon

burnin

Burnin cycles for the MCMC algorithm

gibbs

Number of cycles of the Gibbs sampler after the burnin that are returned in the output

exog

num.exog x nsteps matrix of the exogenous variable values for the forecast horizon. If left at the NULL default, they are set to zero.

Value

A list with three components:

yforc

Forecast sample

orig.y

Original endogenous variables time series

hyperp

values of the hyperparameters used in the BVAR estimation / MCMC

Details

Produces a posterior sample of unconstrained VAR/BVAR/BSVAR forecasts via MCMC. This function accounts for the uncertainty of the VAR/BVAR/BSVAR parameters by sampling from them in the computation of the VAR/BVAR/BSVAR forecasts and then regenerating the forecasts. Data augmentation is used to account for the impact of the forecast uncertainty on the parameters.

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.

Waggoner, Daniel F. and Tao Zha. 1999. "Conditional Forecasts in Dynamic Multivariate Models" Review of Economics and Statistics, 81(4):639-651.

See Also

hc.forecast

Examples

## Not run: 
# ## Uses the example from Brandt and Freeman 2006.  Will not run unless
# ## you have their data from the Politcal
# ## Analysis website!
# library(MSBVAR)   # Brandt's package for Bayesian VAR models
# 
# # Read the data and set up as a time series
# data <- read.dta("levant.weekly.79-03.dta") 
# attach(data)
# 
# # Set up KEDS data
# KEDS.data <- ts(cbind(a2i,a2p,i2a,p2a,i2p,p2i),
#                 start=c(1979,15),
#                 freq=52,
#                 names=c("A2I","A2P","I2A","P2A","I2P","P2I"))
# 
# # Select the sample we want to use.
# KEDS <- window(KEDS.data, end=c(1988,50))
# 
# 
# ################################################################################
# # Estimate the BVAR models 
# ################################################################################
# 
# # Fit a flat prior model
# KEDS.BVAR.flat <- szbvar(KEDS, p=6, z=NULL, lambda0=1,
#                          lambda1=1, lambda3=1, lambda4=1, lambda5=0,
#                          mu5=0, mu6=0, nu=0, qm=4, prior=2,
#                          posterior.fit=F)
# 
# # Reference prior model -- Normal-IW prior pdf
# KEDS.BVAR.informed <- szbvar(KEDS, p=6, z=NULL, lambda0=0.6,
#                              lambda1=0.1, lambda3=2, lambda4=0.5, lambda5=0,
#                              mu5=0, mu6=0, nu=ncol(KEDS)+1, qm=4, prior=0,
#                              posterior.fit=F)
# 
# # Set up conditional forecast matrix conditions
# nsteps <- 12
# a2i.condition <- rep(mean(KEDS[,1]) + sqrt(var(KEDS[,1])) , nsteps)
# 
# yhat<-matrix(c(a2i.condition,rep(0, nsteps*5)), ncol=6)
# 
# # Set the random number seed so we can replicate the results.
# set.seed(11023)
# 
# # Conditional forecasts
# conditional.forcs.ref <- hc.forecast(KEDS.BVAR.informed, yhat, nsteps,
#                             burnin=3000, gibbs=5000, exog=NULL)
# 
# conditional.forcs.flat <- hc.forecast(KEDS.BVAR.flat, yhat, nsteps,
#                              burnin=3000, gibbs=5000, exog=NULL)
# 
# # Unconditional forecasts
# unconditional.forcs.ref <-uc.forecast(KEDS.BVAR.informed, nsteps,
#                                           burnin=3000, gibbs=5000)
# 
# unconditional.forcs.flat <- uc.forecast(KEDS.BVAR.flat, nsteps,
#                                             burnin=3000, gibbs=5000)
# 
# # Set-up and plot the unconditional and conditional forecasts.  This
# # code pulls for the forecasts for I2P and P2I and puts them into the
# # appropriate array for the figures we want to generate.
# uc.flat <- NULL
# hc.flat <- NULL
# uc.ref <- NULL
# hc.ref <- NULL
# 
# uc.flat$forecast <- unconditional.forcs.flat$forecast[,,5:6]
# hc.flat$forecast <- conditional.forcs.flat$forecast[,,5:6]
# uc.ref$forecast <- unconditional.forcs.ref$forecast[,,5:6]
# hc.ref$forecast <- conditional.forcs.ref$forecast[,,5:6]
# 
# par(mfrow=c(2,2), omi=c(0.25,0.5,0.25,0.25)) 
# plot(uc.flat,hc.flat, probs=c(0.16, 0.84), varnames=c("I2P", "P2I"),
#      compare.level=KEDS[nrow(KEDS),5:6], lwd=2)
# plot(hc.ref,hc.flat, probs=c(0.16, 0.84), varnames=c("I2P", "P2I"),
#      compare.level=KEDS[nrow(KEDS),5:6], lwd=2)
# 
# ## End(Not run)