Type:	Package
Title:	Bayesian Global Vector Autoregressions
Version:	2.5.8
Author:	Maximilian Boeck [aut, cre], Martin Feldkircher [aut], Florian Huber [aut], Darjus Hosszejni [ctb]
Maintainer:	Maximilian Boeck <maximilian.boeck@fau.de>
Description:	Estimation of Bayesian Global Vector Autoregressions (BGVAR) with different prior setups and the possibility to introduce stochastic volatility. Built-in priors include the Minnesota, the stochastic search variable selection and Normal-Gamma (NG) prior. For a reference see also Crespo Cuaresma, J., Feldkircher, M. and F. Huber (2016) "Forecasting with Global Vector Autoregressive Models: a Bayesian Approach", Journal of Applied Econometrics, Vol. 31(7), pp. 1371-1391 <doi:10.1002/jae.2504>. Post-processing functions allow for doing predictions, structurally identify the model with short-run or sign-restrictions and compute impulse response functions, historical decompositions and forecast error variance decompositions. Plotting functions are also available. The package has a companion paper: Boeck, M., Feldkircher, M. and F. Huber (2022) "BGVAR: Bayesian Global Vector Autoregressions with Shrinkage Priors in R", Journal of Statistical Software, Vol. 104(9), pp. 1-28 <doi:10.18637/jss.v104.i09>.
Encoding:	UTF-8
License:	GPL-3
Language:	en-US
URL:	https://github.com/mboeck11/BGVAR
BugReports:	https://github.com/mboeck11/BGVAR/issues
Depends:	R (≥ 3.5.0)
SystemRequirements:	GNU make
Imports:	abind, bayesm, coda, GIGrvg, graphics, knitr, MASS, Matrix, methods, parallel, Rcpp (≥ 1.0.3), RcppParallel, readxl, stats, stochvol (≥ 3.0.3), utils, xts, zoo
Suggests:	rmarkdown, testthat (≥ 2.1.0)
LazyData:	true
LinkingTo:	Rcpp, RcppArmadillo, RcppProgress, RcppParallel, stochvol, GIGrvg
RoxygenNote:	7.3.2
VignetteBuilder:	knitr
NeedsCompilation:	yes
Packaged:	2024-09-30 14:08:13 UTC; mboeck
Repository:	CRAN
Date/Publication:	2024-09-30 14:50:05 UTC

BGVAR: Bayesian Global Vector Autoregressions

Description

The Bayesian Global Vector Autoregression (BGVAR) package allows to estimate Global Vector Autoregressions and consists of various tools for predicting and doing structural analysis.

Details

It provides a fully Bayesian implementation of Global Vector Autoregressions. It utilizes Markov chain Monte Carlo (MCMC) samplers to conduct inference by obtaining draws from the posterior distribution of parameters. One of the main advantages is the implementation of different shrinkage prior setups for estimating the model. The packages consists thus of various post-processing functions to carry out predictions or structural analysis. It is possible to perform structural identification via short-run or sign/zero restrictions. The available structural tools comprise impulse response functions, historical decompositions and forecast error variance decompositions. For all the aforementioned tools plotting functions are implemented. Furthermore, various functions of the package are intended to inspect the convergence properties of the MCMC chain and to do model evaluation. The main focus of this paper is to show the functionality of BGVAR. In addition, it provides a brief mathematical description of the model, an overview of the implemented sampling scheme, and several illustrative examples using global macroeconomic data.

See Also

bgvar for estimating a Bayesian GVAR. predict for doing predictions with a Bayesian GVAR. irf for doing impulse response analysis with a Bayesian GVAR.

Adding shocks to 'shockinfo' argument

Description

Adds automatically rows to 'shockinfo' data.frame for appropriate use in irf.

Usage

add_shockinfo(shockinfo=NULL, shock=NULL, restriction=NULL, sign=NULL, horizon=NULL, 
prob=NULL, scale=NULL, global=NULL, horizon.fillup=TRUE)

Arguments

Details

This is only possible for sign restriction, hence if ident="sign" in get_shockinfo().

See Also

irf

Average Pairwise Cross-Sectional Correlations

Description

Computes average pairwise cross-sectional correlations of the data and the country models' residuals.

Usage

avg.pair.cc(object, digits=3)

Arguments

Details

If used for analyzing the country models' residuals, avg.pair.cc computes for each country and a given variable, the average cross-sectional correlation (either for the data or for the residuals). In theory, including foreign variables should soak up cross-sectional residual dependence and correlation of the residuals should be small. Otherwise dynamic analysis, especially using GIRFs, might lead to invalid results. See Dees et al. (2007) for more details.

Value

Returns a list with the following elements

Author(s)

Martin Feldkircher

References

Dees, S., Di Mauro F., Pesaran, M. H. and Smith, L. V. (2007) Exploring the international linkages of the euro area: A global VAR analysis. Journal of Applied Econometrics, Vol. 22, pp. 1-38.

See Also

bgvar for estimation of a bgvar object. residuals for calculating the residuals from a bgvar object and creating a bgvar.res object.

Examples

library(BGVAR)
data(testdata)
model.mn <- bgvar(Data=testdata,W=W.test,plag=1,SV=TRUE,
                  draws=100,burnin=100,prior="MN")
avg.pair.cc(model.mn)

res <- residuals(model.mn)
avg.pair.cc(res)

Estimation of Bayesian GVAR

Description

Estimates a Bayesian GVAR with either the Stochastic Search Variable Selection (SSVS), the Minnesota prior (MN), the Normal-Gamma (NG), or the Horseshoe (HS) prior. All specifications can be estimated with stochastic volatility.

Usage

bgvar(Data, W, plag=1, draws=5000, burnin=5000, prior="NG", SV=TRUE, hold.out=0, thin=1, 
      hyperpara=NULL, eigen=TRUE, Ex=NULL, trend=FALSE, expert=NULL, verbose=TRUE)

Arguments

Details

We provide three priors, the Minnesota labeled MN, the Stochastic Search Variable Selection prior labeled SSVS and the Normal-Gamma prior labeled NG. The first one has been implemented for global VARs in Feldkircher and Huber (2016) and the second one in Crespo Cuaresma et al. (2016), while the last one has been introduced to VAR modeling in Huber and Feldkircher (2019). Please consult these references for more details on the specification. In the following we will briefly explain the difference between the three priors. The Minnesota prior pushes the variables in the country-specific VAR towards their unconditional stationary mean, or toward a situation where there is at least one unit root present. The SSVS prior is a form of a 'spike' and 'slab' prior. Variable selection is based on the probability of assigning the corresponding regression coefficient to the 'slab' component. If a regression coefficient is non informative, the 'spike' component pushes the associated posterior estimate more strongly towards zero. Otherwise, the slab component resembles a non-informative prior that has little impact on the posterior. Following George et. al. (2008) we set the prior variances for the normal distribution in a semi-automatic fashion. This implies scaling the mixture normal with the OLS standard errors of the coefficients for the full model. The NG prior is a form of global-local shrinkage prior. Hence, the local component shrinks each coefficient towards zero if there is no information for the associated dependent variable. Otherwise, the prior exerts a fat-tail structure such that deviations from zero are possible. The global component is present for each lag, thus capturing the idea that higher lags should be shrunk more aggressively towards zero.

Value

Returns a list of class bgvar with the following elements:

args

is a list object that contains the arguments submitted to function bgvar.

xglobal

is a matrix object of dimension T times N (T # of observations, K # of variables in the system).

gW

is the global weight matrix. It is a list, with N entries, each of which contains the weight matrix of each country.

country.res

is a matrix that contains the posterior mean of the country models' residuals. The residuals have been obtained as a running mean and thus always relate to the full set of posterior draws. This implies that in case you have opted for trimming the draws the residuals do not correspond to the posterior draws of the "trimmed" coefficients. This is a storage problem, rather than a statistical problem. Experiments, however, show that residual properties (autocorrelation, cross-sectional correlation) of trimmed and reported residuals are close.

stacked results

S_large

is a three-dimensional array (K times K times draws) of the (block-diagonal) posterior variance covariance matrix.

F_large

is a four-dimensional array (K times K times lags times draws) of the coefficients.

Ginv_large

is a three-dimensional array (K times K times draws) of the inverse of the G matrix.

A_large

is a three-dimensional array (K times K+1 times draws) of the posterior estimates for the K coefficients plus a global constant.

F.eigen

in case eigen="TRUE", returns a vector that contains for each posterior draw the modulus of the largest eigenvalue of the companion matrix.

trim.info

is a character vector. Contains information regarding the nr. of stable draws out of total (thinned) draws. Experience shows that a maximum eigenvalue of 1.05 seems a reasonable choice when working with data in levels to generate stable impulse responses.

cc.results

each entry of this list contains an list object of length N. Each entry in the list corresponds to one country model and contains one of the following posterior medians.

coeffs

contains in each entry the matrix with the posterior median of the estimated coefficients. Columns of the matrix correspond to an equation in the country model (i.e., the dependent variable) and rows to coefficient estimates of the explanatory variables.

sig

contains in each entry the variance-covariance matrix for each point in time. If SV=FALSE all entries along the time dimension are the same.

theta

contains in each entry the estimated prior variances for the coefficients. Explains how much shrinkage is induced on each coefficient depending on the prior setup.

res

contains in each entry a matrix of dimension (T-p times K) with the posterior median of the residuals of the cross-country models.

shrink

in case prior="MN" each entry contains the estimated shrinkage parameters.

PIP

in case prior="SSVS" returns a list object. The first slot in the list PIP.cc, is a list of length N and contains the posterior inclusion probabilities of the country models. The second slot in the list, named PIP.avg yields simple averages (over the country models where a particular variable has been included) of the posterior inclusion probabilities.

lambda2

in case prior="NG" each entry contains the estimated global shrinkage parameters. It is a matrix of dimension (p+1 times 3). Columns refer to the endogenous, weakly exogenous and shrinkage parameters for the covariances. Rows correspond to different degree of shrinkage per lag of the variables starting with the contemporaneous lag (only for weakly exogenous variables). In case of the covariances just one global shrinkage parameter is estimated.

tau

in case prior="NG" each entry contains the estimated parameter that governs the heaviness of the tails of the marginal prior distribution of the coefficients associated to endogenous variables. Structure is the same as lambda2.

Author(s)

Maximilian Boeck, Martin Feldkircher, Florian Huber

References

Boeck, M., Feldkircher, M. and F. Huber (2022) BGVAR: Bayesian Global Vector Autoregressions with Shrinkage Priors in R. Journal of Statistical Software, Vol. 104(9), pp. 1-28.

Crespo Cuaresma, J., Feldkircher, M. and F. Huber (2016) Forecasting with Global Vector Autoregressive Models: A Bayesian Approach. Journal of Applied Econometrics, Vol. 31(7), pp. 1371-1391.

Doan, T. R., Litterman, B. R. and C. A. Sims (1984) Forecasting and Conditional Projection Using Realistic Prior Distributions. Econometric Reviews, Vol. 3, pp. 1-100.

Dovern, J., Feldkircher, M. and F. Huber (2016) Does joint modelling of the world economy pay off? Evaluating multivariate forecasts from a Bayesian GVAR. Journal of Economic Dynamics and Control, Vol. 70, pp. 86-100.

Feldkircher, M. and F. Huber (2016) The International Transmission of US Shocks - Evidence from Bayesian Global Vector Autoregressions. European Economic Review, Vol. 81, pp. 167-188.

Feldkircher, M. Gruber, T. and F. Huber (2020) International effects of a compression of euro area yield curves. Journal of Banking & Finance, Vol. 113, pp. 11-14.

George, E.I., Sun, D. and S. Ni (2008) Bayesian stochastic search for var model restrictions. Journal of Econometrics, Vol. 142, pp. 553-580.

Georgiadis, G. (2015) Examining asymmetries in the transmission of monetary policy in the euro area: Evidence from a mixed cross-section global VAR model. European Economic Review, Vol. 75, pp. 195-215.

Huber, F. and M. Feldkircher (2016) Adaptive Shrinkage in Bayesian Vector Autoregressive Models. Journal of Business and Economic Statistics, Vol. 37(1), pp. 27-39.

Mohaddes, K. and M. Raissi (2018). Compilation, Revision and Updating of the Global VAR (GVAR) Database, 1979Q2-2016Q4. University of Cambridge: Faculty of Economics (mimeo).

Mohaddes, K. and M. Raissi (2019) The US oil supply revolution and the global economy. Empirical Economics, Vol. 57, pp. 515-546.

Pesaran, M.H., Schuermann T. and S.M. Weiner (2004) Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model. Journal of Business and Economic Statistics, Vol. 22, pp. 129-162.

Sims, C. A. (1992) Bayesian Inference for Multivariate Time Series with Trend. Mimeo, presented at the American statistical Association meeting.

Sims, C.A. and T. Zha (1998) Bayesian Methods for Dynamic Multivariate Models. International Economic Review, Vol. 39, pp. 949-968.

Examples

library(BGVAR)
data(testdata)
hyperpara <- list(tau0=0.1,tau1=3,kappa0=0.1,kappa1=7,a_1=0.01,b_1=0.01,p_i=0.5,q_ij=0.5)
model.ssvs <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100,
                    prior="SSVS",SV=FALSE,hyperpara=hyperpara,thin=1)
## Not run: 
library(BGVAR)
# replicate Feldkircher and Huber (2016) using trade based weights
data(eerData)
hyperpara <- list(tau0=0.1,tau1=3,kappa0=0.1,kappa1=7,a_1=0.01,b_1=0.01,p_i=0.5,q_ij=0.5)
model.ssvs <- bgvar(Data=eerData,W=W.trade0012,plag=1,draws=100,burnin=100,
                    prior="SSVS",SV=FALSE,hyperpara=hyperpara,thin=1)
print(model.ssvs)

# use different weight matrices
variable.list<-list();variable.list$real<-c("y","Dp","tb");variable.list$fin<-c("stir","ltir","rer")
model.mn <- bgvar(Data=eerData, W=W.list[c("tradeW.0012","finW0711")], plag=1, draws=200, 
                  burnin=100,prior="MN",SV=TRUE,thin=2,expert=list(variable.list=variable.list))
print(model.mn)

data(monthlyData)
cN = names(EB.weights$weights)
Data = monthlyData[c(cN,"EB","OC")]
W = W[cN,cN]
OC.weights$weights = OC.weights$weights[cN]
OE.weights <- list(EB=EB.weights, OC=OC.weights)
hyperpara<-list(d_lambda = 0.01, e_lambda = 0.01,e_lambda=1.5,d_lambda=1, 
                prmean=0,a_1=0.01,b_1=0.01,tau_theta=.6,sample_tau=FALSE)
model.ssvs <- bgvar(Data=Data,W=W,plag=2,draws=100,burnin=100,prior="SSVS",
                    hyperpara=hyperpara,eigen=TRUE,SV=TRUE,expert=list(OE.weights=OE.weights))
print(model.ssvs)

## End(Not run)

Extract Model Coefficients of Bayesian GVAR

Description

Extracts the global model coefficients for bgvar for certain quantiles of the posterior distribution. coefficients is an alias for it.

Usage

## S3 method for class 'bgvar'
coef(object, ..., quantile = 0.5)

## S3 method for class 'bgvar'
coefficients(object, ..., quantile = 0.5)

Arguments

Value

Returns an q times K times K times p array of the global coefficients, where q is the number of specified quantiles (this dimension is dropped if q=1), K the number of endogenous variables and p number of lags.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100)
coef(model.ng)


coefficients(model.ng)

MCMC Convergence Diagnostics

Description

This function computes Geweke's Convergence diagnostic making use of the coda package.

Usage

conv.diag(object, crit.val=1.96)

Arguments

Details

Geweke (1992) proposed a convergence diagnostic for Markov chains based on a test for equality of the means of the first and last part of a Markov chain (by default we use the first 10% and the last 50%). If the samples are drawn from the stationary distribution of the chain, the two means are equal and Geweke's statistic has an asymptotically standard normal distribution. The test statistic is a standard Z-score: the difference between the two sample means divided by its estimated standard error. The standard error is estimated from the spectral density at zero and so takes into account any autocorrelation.

Value

Returns an object of class bgvar.CD. This is a list with

geweke.z

Z-scores for a test of equality of means between the first and last parts of the chain. A separate statistic is calculated for each variable in each chain.

perc

is the percentage of Z-scores exceeding crit.val (in absolute terms).

Author(s)

Martin Feldkircher

References

Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to calculating posterior moments. Bayesian Statistics 4 (edited by JM Bernado, JO Berger, AP Dawid and AFM Smith). Clarendon Press, Oxford, UK.

See Also

geweke.diag in the coda package. bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.mn <- bgvar(Data=testdata,W=W.test,plag=1,draws=200,burnin=200,prior="MN")
geweke <- conv.diag(model.mn)

Deviance Information Criterion

Description

Computes the Deviance information criterion for an object bgvar.

Usage

dic(object, ...)

## S3 method for class 'bgvar'
dic(object, ...)

Arguments

Value

Returns a numeric value with the corresponding DIC.

Author(s)

Maximilian Boeck

References

Spiegelhalter, D. J. and Best, N. G., Carlin, B. P. and Linde, A. (2002) Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B, Vol. 64(4), pp. 583-639.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.mn <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100,prior="MN")
dic(model.mn)

Example data set to replicate Feldkircher and Huber (2016)

Description

This data set contains 76 quarterly observations by country, spanning the period from 1995Q1 to 2013Q4. The country coverage is 43 countries and the Euro area (EA) as a regional aggregate.

Usage

eerData

Format

The data loads two objects eerData, which is a list object of length N (i.e, the number of countries) and W.trade0012, which is an N times N weight matrix with rowsums summing up to unity and zero elements on its diagonal. The global variable, oil prices, is included in the US country model as e.g., in Dees et al. (2007). The countries are abbreviated using ISO-2 codes. The weight matrix corresponds to average annual bilateral trade flows (including services) over the period from 2000 to 2012.eerData contains the country data, for more details, see below:

W.trade0012

Weight matrix based on trade flows, rowsums equal unity.

W.list

List of ten weight matrices, described in Feldkircher and Huber (2016).

eerData

is a list object of length N containing

y

Real GDP, average of 2005=100. Seasonally adjusted, in logarithms.

Dp

Consumer prices (period-on-period). CPI seasonally adjusted, in logarithm.

stir

Short-term interest rate, typically 3-months money market rate.

ltir

Long-term interest rates, typically 10-year government bond yields.

reer

Real effective exchange rate, deflated by consumer prices.

tb

Trade balance (ratio of real exports to real imports).

poil

Price of oil, seasonally adjusted, in logarithms.

USexpectations

is a time series object containing US expectations data:

y_t+4

Four-quarter ahead expectation of Real GDP growth.

Dp_t+4

Four-quarter ahead expectation of consumer price inflation.

stir_t+4

Four-quarter ahead expectation of short-term interest rates.

Read Data from Excel

Description

Reads a spreadsheet from excel and converts it to a list for use of bgvar.

Usage

excel_to_list(file, first_column_as_time=TRUE, skipsheet=NULL, ...)

Arguments

Details

Note that each sheet has to be named for a respective country. Column names are used as variable names. Reader uses the readxl R package, hence additional arguments can be passed to the function. Furthermore, if first_column_as_time=TRUE then the column name has also to be time.

Value

Returns a list of length N which contains each a matrix of size T times k, where T are time periods and k variables per entity.

Author(s)

Maximilian Boeck

See Also

bgvar for estimation of a bgvar object.

Forecast Error Variance Decomposition

Description

This function calculates the forecast error variance decomposition (FEVDs) for Cholesky and sign-identified shocks.

Usage

fevd(x, rotation.matrix=NULL, var.slct=NULL, verbose=TRUE)

Arguments

Details

Since the calculations are very time consuming, the FEVDs are based on the posterior median only (as opposed to calculating FEVDs for each MCMC sweep). In case the underlying shock has been identified via sign restrictions, the rotation matrix corresponds to the one that fulfills the sign restrictions at the posterior median of the estimated coefficients. More precisely, the algorithm searches for 50 rotation matrices that fulfill the sign restrictions at the posterior median of the coefficients and then singles out the rotation matrix that minimizes the distance to the median of the impulse responses as suggested in Fry and Pagan (2011).

Value

Returns a list with two elements

FEVD

an array of size (K times horizon times N), where K are all variables in the system, horizon is the specified impulse response horizon and N is the size of the decomposed structural variables (if var.slct=NULL then K=N).

xglobal

used data of the model.

Author(s)

Maximilian Boeck, Martin Feldkircher, Florian Huber

See Also

bgvar, irf

Examples

set.seed(123)
library(BGVAR)
data(testdata)
model.eer<-bgvar(Data=testdata,W=W.test,prior="MN",
                 draws=50,burnin=50,plag=1,eigen=TRUE)
                      
# US monetary policy shock
shockinfo <- get_shockinfo("chol")
shockinfo$shock <- "US.stir"; shockinfo$scale <- -100
irf.chol.us.mp<-irf(model.eer,n.ahead=48,shockinfo=shockinfo)

# calculates FEVD for variables US.Dp and EA.y
fevd.us.mp=fevd(irf.chol.us.mp,var.slct=c("US.Dp","EA.y"))

# US monetary policy shock with sign restrictions
shockinfo <- get_shockinfo("sign")
shockinfo <- add_shockinfo(shockinfo, shock="US.stir", 
                           restriction=c("US.y","US.Dp"), 
                           sign=c("<","<"), horizon=c(1,1), 1, 100)
irf.sign.us.mp<-irf(model.eer,n.ahead=24,shockinfo=shockinfo)

# calculates FEVD for variables US.Dp and EA.y
fevd.us.mp=fevd(irf.sign.us.mp,var.slct=c("US.Dp","EA.y"))

Extract Fitted Values of Bayesian GVAR

Description

Extracts the fitted values for bgvar.

Usage

## S3 method for class 'bgvar'
fitted(object, ..., global = TRUE)

Arguments

Value

Returns an T times K matrix, where T is the number of observations and K number of endogenous variables.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100)
fitted(model.ng)

Create shockinfo argument

Description

Creates dummy shockinfo argument for appropriate use in irf function.

Usage

get_shockinfo(ident="chol", nr_rows=1)

Arguments

Details

Depending on the identification scheme a different shockinfo argument in the irf function is needed. To handle this convenient, an appropriate data.frame with is created with this function.

See Also

irf

Generalized Forecast Error Variance Decomposition

Description

This function calculates a complete generalized forecast error variance decomposition (GFEVDs) based on generalized impulse response functions akin to Lanne-Nyberg (2016). The Lanne-Nyberg (2016) corrected GFEVD sum up to unity.

Usage

gfevd(x, n.ahead=24, running=TRUE, applyfun=NULL, cores=NULL, verbose=TRUE)

Arguments

Value

Returns a list with two elements

GFEVD

a three or four-dimensional array, with the first dimension referring to the K time series that are decomposed into contributions of K time series (second dimension) for n.ahead forecast horizons. In case running=TRUE only the posterior mean else also its 16% and 84% credible intervals is contained in the fourth dimension.

xglobal

used data of the model.

Author(s)

Maximilian Boeck, Martin Feldkircher

References

Lanne, M. and H. Nyberg (2016) Generalized Forecast Error Variance Decomposition for Linear and Nonlinear Multivariate Models. Oxford Bulletin of Economics and Statistics, Vol. 78(4), pp. 595-603.

See Also

bgvar.

Examples

library(BGVAR)
data(testdata)
model.eer<-bgvar(Data=testdata, W=W.test, draws=50, burnin=50,
                 plag=1, prior="SSVS", eigen=TRUE)
                      
GFEVD<-gfevd(model.eer, n.ahead=24)

Historical Decomposition

Description

A function that calculates historical decomposition (HD) of the time series and the structural error.

Usage

hd(x, rotation.matrix=NULL, verbose=TRUE)

Arguments

Details

To save computational time as well as due to storage limits, both functions are based on the posterior median (as opposed to calculating HDs and the structural error for each draw of the MCMC chain). In case the shock has been identified via sign restrictions, a rotation matrix has to be selected to calculate both statistics. If not specified otherwise (via R), the algorithm searches for 50 rotation matrices that fulfill the sign restrictions at the posterior median of the coefficients and then singles out the rotation matrix that minimizes the distance to the median of the impulse responses as suggested in Fry and Pagan (2011).

Value

Returns a list with the following objects

hd_array

is a three-dimensional array with the first dimension referring to the K time series, the second to the T observations and the third dimensions containing the contribution of the shocks in explaining historically deviations in the time series from their trend. The third dimension is K+3, since the last three entries contain the contributions of the constant, the initial condition and a residual component that the contributions sum up to the original time series. If a trend i specified in the model the third dimension is K+3 with trend ordered after the constant.

struc.shcok

contains the structural shock.

x

is a matrix object that contains the original time series, which is of dimension K times (T-plag).

Author(s)

Maximilian Boeck, Martin Feldkircher, Florian Huber

References

Fry, R. and A. Pagan (2011) Sign restrictions in Structural Vector Autoregressions: A Critical Review. Journal of Economic Literature, Vol. 49(4), pp. 938-960.

See Also

bgvar and irf.

Examples

library(BGVAR)
data(testdata)
model.eer<-bgvar(Data=testdata, W=W.test, draws=50, burnin=50, 
                 plag=1, prior="SSVS", eigen=TRUE)
                 
# US monetary policy shock
shockinfo <- get_shockinfo("chol")
shockinfo$shock <- "US.stir"; shockinfo$scale <- -100
irf.chol.us.mp<-irf(model.eer,n.ahead=48,shockinfo=shockinfo)

# calculates historical decomposition
HD <- hd(irf.chol.us.mp)

Impulse Response Function

Description

This function calculates three alternative ways of dynamic responses, namely generalized impulse response functions (GIRFs) as in Pesaran and Shin (1998), orthogonalized impulse response functions using a Cholesky decomposition and finally impulse response functions given a set of user-specified sign restrictions.

Usage

irf(x, n.ahead=24, shockinfo=NULL, quantiles=NULL, 
    expert=NULL, verbose=TRUE)

Arguments

Value

Returns a list of class bgvar.irf with the following elements:

posterior

Four-dimensional array (K times n.ahead times number of shocks times Q) that contains Q quantiles of the posterior distribution of the impulse response functions.

shockinfo

Dataframe with details on identification specification.

rot.nr

In case identification is based on sign restrictions (i.e., ident="sign"), this provides the number of rotation matrices found for the number of posterior draws (save*save_thin).

struc.obj

List object that contains posterior quantitites needed when calculating historical decomposition and structural errors via hd.decomp.

A

Median posterior of global coefficient matrix.

Ginv

Median posterior of matrix Ginv, which describes contemporaneous relationships between countries.

S

Posterior median of matrix with country variance-covariance matrices on the main diagonal.

Rmed

Posterior rotation matrix if ident="sign".

model.obj

List object that contains model-specific information, in particular

xglobal

Data of the model.

lags

Lag specification of the model.

IRF_store

Four-dimensional array (K times n.ahead times number of shock times draws) which stores the whole posterior distribution. Exists only if save.store=TRUE.

R_store

Three-dimensional array (K times K times draws) which stores all rotation matrices. Exists only if save.store=TRUE.

Author(s)

Maximilian Boeck, Martin Feldkircher, Florian Huber

References

Arias, J.E., Rubio-Ramirez, J.F, and D.F. Waggoner (2018) Inference Based on SVARs Identified with Sign and Zero Restrictions: Theory and Applications. Econometrica Vol. 86(2), pp. 685-720.

D'Amico, S. and T. B. King (2017) What Does Anticipated Monetary Policy Do? Federal Reserve Bank of Chicago Working paper series, Nr. 2015-10.

Pesaran, H.M. and Y. Shin (1998) Generalized impulse response analysis in linear multivariate models. Economics Letters, Volume 58, Issue 1, p. 17-29.

See Also

bgvar, get_shockinfo, add_shockinfo

Examples

oldpar <- par(no.readonly = TRUE)
# First example, a US monetary policy shock, quarterly data
library(BGVAR)
data(testdata)
# US monetary policy shock
model.eer<-bgvar(Data=testdata, W=W.test, draws=50, burnin=50, 
                 plag=1, prior="SSVS", eigen=TRUE)

# generalized impulse responses
shockinfo<-get_shockinfo("girf")
shockinfo$shock<-"US.stir"; shockinfo$scale<--100

irf.girf.us.mp<-irf(model.eer, n.ahead=24, shockinfo=shockinfo)

# cholesky identification
shockinfo<-get_shockinfo("chol")
shockinfo$shock<-"US.stir"; shockinfo$scale<--100

irf.chol.us.mp<-irf(model.eer, n.ahead=24, shockinfo=shockinfo)

# sign restrictions
shockinfo <- get_shockinfo("sign")
shockinfo <- add_shockinfo(shockinfo, shock="US.stir", restriction=c("US.y","US.Dp"), 
                           sign=c("<","<"), horizon=c(1,1), scale=1, prob=1)
irf.sign.us.mp<-irf(model.eer, n.ahead=24, shockinfo=shockinfo)

# sign restrictions
shockinfo <- get_shockinfo("sign")
shockinfo <- add_shockinfo(shockinfo, shock="US.stir", restriction=c("US.y","US.Dp"), 
sign=c("<","<"), horizon=c(1,1), scale=1, prob=1)
irf.sign.us.mp<-irf(model.eer, n.ahead=24, shockinfo=shockinfo)

#' # sign restrictions with relaxed cross-country restrictions
shockinfo <- get_shockinfo("sign")
# restriction for other countries holds to 75\%
shockinfo <- add_shockinfo(shockinfo, shock="US.stir", restriction=c("US.y","EA.y","UK.y"), 
                           sign=c("<","<","<"), horizon=1, scale=1, prob=c(1,0.75,0.75))
shockinfo <- add_shockinfo(shockinfo, shock="US.stir", restriction=c("US.Dp","EA.Dp","UK.Dp"),
                           sign=c("<","<","<"), horizon=1, scale=1, prob=c(1,0.75,0.75))
irf.sign.us.mp<-irf(model.eer, n.ahead=20, shockinfo=shockinfo)

Convert Input List to Matrix

Description

Converts a list to an appropriate input matrix for use of bgvar.

Usage

list_to_matrix(datalist)

Arguments

Details

Note the naming convention. Columns should indicate entity and variable name, separated by a dot, e.g. US.y.

Value

Returns a matrix of size T times K (number of time periods times number of total variables).

Author(s)

Maximilian Boeck

See Also

bgvar for estimation of a bgvar object.

Extract Log-likelihood of Bayesian GVAR

Description

Extracts Log-Likelihood for bgvar.

Usage

## S3 method for class 'bgvar'
logLik(object, ..., quantile = 0.5)

Arguments

Value

Returns an vector of dimension q (number of specified quantiles) of global log-likelihoods.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100)
logLik(model.ng)

Compute Log-Predictive Scores

Description

Computes and prints log-predictive score of an object of class bgvar.predict.

Usage

## S3 method for class 'bgvar.pred'
lps(object, ...)

Arguments

Value

Returns an object of class bgvar.lps, which is a matrix of dimension h times K, whereas h is the forecasting horizon and K is the number of variables in the system.

Author(s)

Maximilian Boeck, Martin Feldkircher

Examples

library(BGVAR)
data(testdata)
model.ssvs.eer<-bgvar(Data=testdata,W=W.test,draws=100,burnin=100,
                      plag=1,prior="SSVS",eigen=TRUE,hold.out=8)
fcast <- predict(model.ssvs.eer,n.ahead=8,save.store=TRUE)
lps <- lps(fcast)

Convert Input Matrix to List

Description

Converts a big input matrix to an appropriate list for use of bgvar.

Usage

matrix_to_list(datamat)

Arguments

Details

Note the naming convention. Columns should indicate entity and variable name, separated by a dot, e.g. US.y.

Value

returns a list of length N (number of entities).

Author(s)

Maximilian Boeck

See Also

bgvar for estimation of a bgvar object.

Monthly EU / G8 countries macroeconomic dataset

Description

This data set contains monthly observations on industrial production, consumer price indices, short- and long-term interest rates, the nominal exchange rate against the euro and equity prices. The time period covered is from January 2001 to June 2021 and the country coverage amounts to 31 countries – roughly corresponding to EU member states and G-8 countries, a country model to model common monetary policy in the euro area and an oil price model.

Usage

monthlyData

Format

The data loads four objects monthly.data, which is a list object of length N+2 (i.e, the number of countries, the ECB country model and an oil price model), W, which is an N times N weight matrix with rowsums summing up to unity and zero elements on its diagonal. The countries are abbreviated using ISO-2 codes. The weight matrix corresponds to average annual input output flows for the N countries over the period from 2000 to 2014. The data are from the world input output table database (https://www.rug.nl/ggdc/valuechain/wiod/) and are fully described in Timmerman et al. (2015). Akin to Georgiadis (2015), interest setting in the euro area is modeled by a Taylor rule that includes ppp-weighted output and prices of euro area countries. The euro area interest rate enters other country models as an additional exogeneous variable. For more details, see below:

W

N times N weight matrix, rowsums equal unity and the i,jth element reflecting flows from unit i to unit j.

EB.weights

To model the common monetary policy in the euro area, it is possible to augment the GVAR countries by a country model for the ECB. It is important that this country model is labeled 'EB'. Akin to Georgidas (2015) we use a Taylor rule to determine interest rates in the euro area. The Taylor rule typically relates short-term interest rates to a weighted average of output (ip and prices p). EB.weights is a list whith the first slot containing a vector of weights to aggregate single euro area countrys' output and price figures. In the example using the monthlyData set, we use purchasing power parity weights, averaged over the sample period. The second slot contains a character vector that specifies the variables which should enter the Taylor rule (typicall output and prices).

OC.weights

This feature is very similar to EB.weights above and should be specified if an own-standing unit model for the oil price should be included – as opposed to having oil prices attached to a particular country model, as is standard in the literature. It is important that the country model is labeled 'OC'. Again, OC.weights is a list of length 2, the first slot should be a vector of weights to aggregate variables, second one the variables to aggregate. The vector of weights should have country names attached to it. In the example using the monthlyData set, we use purchasing power parity weights to aggregate world output to resemble demand for oil.

monthlyData

is a list object of length N containing

y

Industrial production index, in real terms, logarithmic transform and seasonally adjusted.

p

Harmonized Consumer Price Index (HCPI) for EU member states, for other countries Consumer Price Index. Data in logarithmic transform and seasonally adjusted.

stir

Short-term interest rate, typically 3 months money market rate.

EAstir

Short-term interest rate, typically 3 months money market rate (3 months euribor).

ltir

Long term interest rates, typically 10-year government bond yields.

eur_er

Nominal exchange rate against the euro in logarithmic transform. An increase implies an appreciation of the euro.

eq

Equity price index, in logarithmic transform.

poil

Price of oil, seasonally adjusted, in logarithms.

qoil

World oil production of crude oil, in thousands of barrels per day, in logarithms.

References

Georgiadis, G. (2015) Examining asymmetries in the transmission of monetary policy in the euro area: Evidence from a mixed cross-section global VAR model. In: European Economic Review, Vol. 75, pp. 195-215.

Timmer, M. P., Dietzenbacher, E., Los, B., Stehrer, R. and de Vries, G. J. (2015) An Illustrated User Guide to the World Input–Output Database: the Case of Global Automotive Production. In: Review of International Economics, Vol. 23, pp. 575–605.

pesaranData

Description

This data set contains quarterly observations by country, spanning the period from 1979Q2 to 2019Q4. It can be downloaded from https://www.mohaddes.org/gvar. The country coverage is 28 countries.

Usage

pesaranData

Format

The data loads pesaranData, which is a list object of length N (i.e, the number of countries) and contains the country-level data as described in Mohaddes and Raissi (2020). The countries are abbreviated using ISO-2 codes. Furthermore, we also provide two datasets with first differences of some variables in pesaranDiff. dominant contains data that is considered global. tA is a three-dimensional array that contains N times N annual trade flow matrices over the period from 1980 to 2016. This array can be used to construct weight matrices. For more details, see below:

W.8016

Weight matrix for the pesaran.level and pesaran.diff data sets, based on averaged trade flows covering the period 1980 to 2016 (based on tA).

tA

Three-dimensional array that contains the yearly, bilateral trade flows, which were used to construct W.8016.

peseranData

List object of length N containing

y

Real GDP.

Dp

Consumer price inflation.

r

Short-term interest rate, typically 3-months money market rate.

lr

Long-term interest rate.

eq

Equity prices.

ep

Exchange rate vis a vis the US dollar, deflated by the domestic CPI.

pesaranDiff

List object of length N containing

y

Growth rate of real GDP.

Dp

First differences of consumer price inflation.

r

First differences of short-term interest rate, typically 3-months money market rate.

lr

Long-term interest rate.

eq

Equity prices.

ep

Exchange rate vis a vis the US dollar, deflated by the domestic CPI.

dominant

Data set containing global variables:

poil

Oil prices.

pmetal

Metal price index.

pmat

Agricultural price index.

References

Mohaddes, K. and M. Raissi (2018). Compilation, Revision and Updating of the Global VAR (GVAR) Database, 1979Q2-2016Q4. University of Cambridge: Faculty of Economics (mimeo).

Graphical Summary of Output Created with bgvar

Description

Plotting function for fitted values, residuals, predictions, impulse responses and forecast error variance decompositions created with the BGVAR package.

Usage

## S3 method for class 'bgvar'
plot(x, ..., resp = NULL, global = TRUE)

## S3 method for class 'bgvar.resid'
plot(x, ..., resp = NULL, global = TRUE)

## S3 method for class 'bgvar.pred'
plot(x, ..., resp = NULL, cut = 40, quantiles = c(0.1, 0.16, 0.5, 0.84, 0.9))

## S3 method for class 'bgvar.irf'
plot(
  x,
  ...,
  resp = NULL,
  shock = 1,
  quantiles = c(0.1, 0.16, 0.5, 0.84, 0.9),
  cumulative = FALSE
)

## S3 method for class 'bgvar.fevd'
plot(x, ..., resp, k.max = 10)

Arguments

Value

No return value.

Author(s)

Maximilian Boeck, Martin Feldkircher

Examples

library(BGVAR)
data(testdata)
model.ssvs <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100,
                    prior="SSVS",eigen=TRUE)

# example for class 'bgvar'
plot(model.ssvs, resp=c("EA.y","US.Dp"))


# example for class 'bgvar.resid'
res <- residuals(model.ssvs)
plot(res, resp="EA.y")


# example for class 'bgvar.pred'
fcast <- predict(model.ssvs,n.ahead=8)
plot(fcast, resp="y", cut=20)


# example for class 'bgvar.irf'
shockinfo <- get_shockinfo("chol")
shockinfo$shock <- "US.stir"; shockinfo$scale <- +1
irf.chol<-irf(model.ssvs, n.ahead=24, shockinfo=shockinfo)
plot(irf.chol, resp="US")


# example for class 'bgvar.fevd'
fevd.us=fevd(irf.chol,var.slct=c("US.stir"))
plot(fevd.us, resp="US.stir", k.max=10)

Predictions

Description

A function that computes predictions and conditional predictions based on a object of class bgvar.

Usage

## S3 method for class 'bgvar'
predict(
  object,
  ...,
  n.ahead = 1,
  constr = NULL,
  constr_sd = NULL,
  quantiles = NULL,
  save.store = FALSE,
  verbose = TRUE
)

Arguments

Details

Predictions are performed up to an horizon of n.ahead. Note that conditional forecasts need a fully identified system. Therefore this function utilizes short-run restrictions via the Cholesky decomposition on the global solution of the variance-covariance matrix of the Bayesian GVAR.

Value

Returns an object of class bgvar.pred with the following elements

fcast

is a K times n.ahead times Q-dimensional array that contains Q quantiles of the posterior predictive distribution.

xglobal

is a matrix object of dimension T times N (T # of observations, K # of variables in the system).

n.ahead

specified forecast horizon.

lps.stats

is an array object of dimension K times 2 times n.ahead and contains the mean and standard deviation of the log-predictive scores for each variable and each forecast horizon.

hold.out

if h is not set to zero, this contains the hold-out sample.

Author(s)

Maximilian Boeck, Martin Feldkircher, Florian Huber

References

Jarocinski, M. (2010) Conditional forecasts and uncertainty about forecasts revisions in vector autoregressions. Economics Letters, Vol. 108(3), pp. 257-259.

Waggoner, D., F. and T. Zha (1999) Conditional Forecasts in Dynamic Multivariate Models. Review of Economics and Statistics, Vol. 81(4), pp. 639-561.

Examples

library(BGVAR)
data(testdata)
model.ssvs <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100,
                    prior="SSVS")
fcast <- predict(model.ssvs, n.ahead=8)

# conditional predictions
# et up constraints matrix of dimension n.ahead times K
constr <- matrix(NA,nrow=8,ncol=ncol(model.ssvs$xglobal))
colnames(constr) <- colnames(model.ssvs$xglobal)
constr[1:5,"US.Dp"] <- model.ssvs$xglobal[76,"US.Dp"]

# add uncertainty to conditional forecasts
constr_sd <- matrix(NA,nrow=8,ncol=ncol(model.ssvs$xglobal))
colnames(constr_sd) <- colnames(model.ssvs$xglobal)
constr_sd[1:5,"US.Dp"] <- 0.001

fcast_cond <- predict(model.ssvs, n.ahead=8, constr=constr, constr_sd=constr_sd)

Residual Autocorrelation Test

Description

An F-test for serial autocorrelation in the residuals.

Usage

resid.corr.test(obj, lag.cor=1, alpha=0.95, dig1=5, dig2=3)

Arguments

Details

It is the F-test of the familiar Lagrange Multiplier (LM) statistic (see Godfrey 1978a, 1978b), also known as the 'modified LM' statistic. The null hypothesis is that rho, the autoregressive parameter on the residuals, equals 0 indicating absence of serial autocorrelation. For higher order serial correlation, the null is that all rho's jointly are 0. The test is implemented as in Vanessa Smith's and Alessandra Galesi's ”GVAR toolbox 2.0 User Guide”, page 129.

Value

Returns a list with the following objects

Fstat

contains a list of length N with the associated F-statistic for each variable in each country.

resTest

contains a matrix of size 2N times K+3, with the F-statistics for each country and each variable.

p.res

contains a table which summarizes the output.

pL

contains a list of length N with the associated p-values for each variable in each country.

Author(s)

Martin Feldkircher

References

Godfrey, L.G. (1978a) Testing Against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables. Econometrica, 46, pp. 1293-1302. Godfrey, L.G. (1978b) Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables. Econometrica, 46, pp. 1303-1310. Smith, L. V. and A. Galesi (2014) GVAR Toolbox 2.0 User Guide, available at https://sites.google.com/site/gvarmodelling/gvar-toolbox.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,draws=100,burnin=100)
resid.corr.test(model.ng)

Extract Residuals of Bayesian GVAR

Description

Calculate residuals of the global model and the country models.

Usage

## S3 method for class 'bgvar'
residuals(object, ...)

## S3 method for class 'bgvar'
resid(object, ...)

Arguments

Details

This function calculates residuals of the global and the country models based on a bgvar object. Country models' residuals are equivalent to output generated by the print.bgvar function in case no trimming has been used. If trimming was invoked to discard unstable draws output of both functions might differ since print.bgvar calculates residuals as a running mean to save storage which is based on the whole set of posterior draws (including discarded draws). In this case it is recommended to recalculate the residuals with residuals.bgvar and re-do the serial autocorrelation or average pairwise cross-correlation analysis using functions resid.corr.test and avg.pair.cc.

Value

Returns a list with the following arguments

global

A (T-p) times K times draws/thin array containing the residuals of the global model.

country

A (T-p) times K times draws/thin array containing the residuals of the country models.

Data

A (T-p) times K matrix containing the data of the model.

Author(s)

Maximilian Boeck, Martin Feldkircher

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100)
resid(model.ng)


resid(model.ng)

Compute Root Mean Squared Errors

Description

Computes and prints root mean squared errors (RMSEs) of an object of class bgvar.predict.

Usage

## S3 method for class 'bgvar.pred'
rmse(object, ...)

Arguments

Value

Returns an object of class bgvar.rmse, which is a matrix of dimension h times K, whereas h is the forecasting horizon and K is the number of variables in the system.

Author(s)

Maximilian Boeck, Martin Feldkircher

Examples

library(BGVAR)
data(testdata)
model.ssvs.eer<-bgvar(Data=testdata,W=W.test,draws=100,burnin=100,
                      plag=1,prior="SSVS",eigen=TRUE,hold.out=8)
fcast <- predict(model.ssvs.eer,n.ahead=8,save.store=TRUE)
rmse <- rmse(fcast)

Summary of Bayesian GVAR

Description

Output gives model information as well as some descriptive statistics on convergence properties, likelihood, serial autocorrelation in the errors and the average pairwise autocorrelation of cross-country residuals.

Usage

## S3 method for class 'bgvar'
summary(object, ...)

Arguments

Value

No return value.

Author(s)

Maximilian Boeck

See Also

bgvar to estimate a bgvar object. avg.pair.cc to compute average pairwise cross-country correlation of cross-country residuals separately. resid.corr.test to compute F-test on first-order autocorrelation of cross-country residuals separately.

Example data set to show functionality of the package

Description

This data set is a subset of eerData containing just three countries with 76 quarterly observations, spanning the period from 1995Q1 to 2013Q4. The country coverage are the United States, the United Kingdom and the Euro area (EA) as a regional aggregate.

Usage

testdata

Format

The data loads two objects eerDatasmall, which is a list object of length N (i.e, the number of countries) and W.trade0012, which is an N times N weight matrix with rowsums summing up to unity and zero elements on its diagonal. The global variable, oil prices, is included in the US country model as e.g., in Dees et al. (2007). The countries are abbreviated using ISO-2 codes. The weight matrix corresponds to average annual bilateral trade flows (including services) over the period from 2000 to 2012.eerDatasmall contains the country data, for more details, see below:

W.test

Weight matrix based on trade flows, rowsums equal unity.

testdata

List object of length N containing

y

Real GDP, average of 2005=100. Seasonally adjusted, in logarithms.

Dp

Consumer prices (period-on-period). CPI seasonally adjusted, in logarithm.

stir

Short-term interest rate, typically 3-months money market rate.

ltir

Long-term interest rates, typically 10-year government bond yields.

reer

Real effective exchange rate, deflated by consumer prices.

tb

Trade balance (ratio of real exports to real imports).

poil

Price of oil, seasonally adjusted, in logarithms.

Extract Variance-covariance Matrix of Bayesian GVAR

Description

Extracts the global variance-covariance matrix for bgvar for certain quantiles of the posterior distribution.

Usage

## S3 method for class 'bgvar'
vcov(object, ..., quantile = 0.5)

Arguments

Value

Returns an q times K times K array of the global variance-covariance matrix, where q is the number of specified quantiles (this dimension is dropped if q=1) and K the number of endogenous variables.

See Also

bgvar for estimation of a bgvar object.

Examples

library(BGVAR)
data(testdata)
model.ng <- bgvar(Data=testdata,W=W.test,plag=1,draws=100,burnin=100)
vcov(model.ng)