MSBVAR (version 0.9-2)

SZ.prior.evaluation: Sims-Zha Bayesian VAR Prior Specification Search

Description

Estimates posterior and in-sample fit measures for a reduced form vector autoregression model with different specifications of the Sims-Zha hyperparameters values.

Usage

SZ.prior.evaluation(Y, p, lambda0, lambda1, lambda3, lambda4, lambda5, mu5, mu6, z = NULL, nu = ncol(Y) + 1, qm, prior = 0, nsteps, y.future)

Arguments

Y

T x m matrix of endogenous variables for the VAR

p

Lag length

lambda0

List of values, e,g, c(0.7, 0.8, 0.9) in [0,1], Overall tightness of the prior (discounting of prior scale).

lambda1

List of values, e,g, c(0.05, 0.1, 0.2) in [0,1], Standard deviation or tightness of the prior around the AR(1) parameters.

lambda3

List of values, e,g, c(0, 1, 2) for Lag decay (>0, with 1=harmonic)

lambda4

List of values, e,g, c(0.15, 0.2, 0.5) for Standard deviation or tightness around the intercept [>0]

lambda5

Single value for the standard deviation or tightness around the exogneous variable coefficients [>0]

mu5

Single value for sum of coefficients prior weight [>=0]

mu6

Single value for dummy Initial observations or cointegration prior [>=0]

z

Exogenous variables

nu

Prior degrees of freedom = m+1

qm

Frequency of the data for lag decay equivalence. Default is 4, and a value of 12 will match the lag decay of monthly to quarterly data. Other values have the same effect as "4"

prior

One of three values: 0 = Normal-Wishart prior, 1 = Normal-flat prior, 2 = flat-flat prior (i.e., akin to MLE)

nsteps

Number of periods in the forecast horizon

y.future

Future values of the series, nsteps x m for computing the root mean squared error and mean absolute error for the fit

Value

A matrix of the results with columns corresponding to the values of "lambda0", "lambda1", "lambda3", "lambda4", "lambda5", "mu5", "mu6", "RMSE", "MAE", "MargLLF","MargPosterior".

Details

This function fits a series of BVAR models for the combinations of lambda0, lambda1, lambda3, and lambda4 provided. For each possible value of these parameters specified, a Sims-Zha prior BVAR model is fit, posterior fit measures are computed, and forecasts are generated over nsteps. These nstep forecasts are then compared to a new set of data in y.future and root mean sqaured error and mean absolute error measures are computed.

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.

See Also

szbvar

Examples

Y <- EuStockMarkets
results <- SZ.prior.evaluation(window(Y, start=c(1998, 1),
                                       end=c(1998,149)),
                               p=3,
                               lambda0=c(1,0.9),
                               lambda1=c(0.1,0.2),
                               lambda3=c(0,1),
                               lambda4=c(0.1,0.25),
                               lambda5=0,
                               mu5=4,
                               mu6=4, z=NULL,
                               nu=ncol(Y)+1, qm=4,
                               prior=0,
                               nstep=20, 
                               y.future=window(Y, start=c(1998,150)))

# Now plot the RMSE and marginal posterior of the data for each of the
# 6 period forecasts as a function of the prior parameters.  This can
# easily be done using a lattice graphic.

library(lattice)

attach(as.data.frame(results))
dev.new()
xyplot(RMSE ~ lambda0 | lambda1 + lambda3)
dev.new()
xyplot(logMDD ~ lambda0 | lambda1 + lambda3)
dev.new()
xyplot(LLF ~ lambda0 | lambda1 + lambda3)