hc.forecast: Forecast density estimation of hard condition forecasts for...
In MSBVAR: Markov-Switching, Bayesian, Vector Autoregression Models

Description Usage Arguments Details Value Author(s) References See Also Examples

Implements a "hard condition" forecast density estimator for VAR/BVAR/B-SVAR models as described in Waggoner and Zha (1999). A "hard condition" forecast is one where the forecast path of one or more variables in a VAR is constrained to be an exact value. The forecast densities are estimated as the posterior sample for the VAR 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.

1 2	hc.forecast(varobj, yconst, nsteps, burnin, gibbs, exog = NULL)

`varobj`	VAR object produced for an unrestricted VAR or BVAR using `szbvar` or `reduced.form.var`
`yconst`	nsteps x m matrix of the constrained forecasts that matches the variables in the endogenous variables of the VAR object. Unconstrained forecasts should be set to NA or zero.
`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.

"Hard conditions" are restrictions of the future forecast path of a variable in a VAR. Once a variable has been constrained along the forecast path, the paths of the other variables in the VAR forecasts must be re-estimated to satisfy the forecast constraint, since the constrained variable has a forecast variance of zero (it is assumed known). Thus, an MCMC algorithm must be used to determine the posterior of the forecasts and a consistent set of VAR parameter estimates that satisfy the forecast constraints. This function accounts for the uncertainty of the VAR parameters by sampling from them in the computation of the VAR forecasts.

A list with two components:

`forecast`	gibbs x nsteps x m array of the samples of the VAR forecasts
`orig.y`	T x m time series object of the original endogenous variables

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.

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

plot.forecast for plotting, forecast for unconditional forecasting of forecast means, uc.forecast for MCMC estimation of forecast densities for unconstrained or unconditional forecasts

## 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)   

# 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)