GVAR: Global Vector Auto-Regressive Modelling

In GVAR: Vector Error Correction Model (VECM), VECM with exogenous I(1) variables, Global VAR (GVAR)

Description

GVAR computes VECMs for all regions and stacks the models to a Global Vector Autoregressive Model

Usage

GVAR(Data, tw = NULL, p, q = p, r = NULL, weight, Case, exo.var = FALSE,
     d = NULL, lex = NULL, endo = NULL, ord = NULL, we = NULL, method = "max.eigen", caseTest = FALSE, weTest = FALSE)

Arguments

Data	timeseries data as list (each entry is a matrix of a subsystem of variables, if exo.var=TRUE the last entry are exogeneous variables)
tw	time window, vector of start and end point, if NULL the maximum time interval will be used
p	scalar/vector of endogenous lags, if a scalar is provided the same lag length is used for all subsystems
q	scalar/vector of (weakly) exogeneous lags, if a scalar is provided the same lag length is used for all subsystems
r	scalar/vector of cointegrating relations, if a scalar is provided the same cointegration rank is used for all subsystems, if set to NULL the cointegration rank will be determind by method
weight	weight matrix, the diagonal elements need to be zero
Case	single value/vector of cases (I to V), where case I is a zero intercept, zero trend model, case II is a restricted intercept, zero trend model, III is a unrestricted intercept, zero trend model, IV is a unrestricted intercept restricted trend model and V is a unrestricted intercept, unrestricted trend model; if a single value is provided the same structure is used for all subsystems
exo.var	if TRUE strictly exogeneous variables are included in the model
d	list showing which strictly exogeneous variables enter the subsystem equations, if NULL all variables in the last entry of data will be used for all subsystems
lex	scalar/vector of strictly exogeneous lags, if a scalar is provided the same lag length is used for all subsystems
endo	list of endogenous variables used in each subsystem, if NULL all variables in data will be used
ord	vector used if variables in the different subsystem don't appear in the same order, order of each subsystem is concatenated to one vector, if NULL the variables in data are assumed to be ordered identically in all subsystems
we	list with numbers of weakly exogeneous variables included in each VECM, corresponds to numbers in ord, if NULL every variable appearing in all subsystems will be used
method	select cointegrating rank by max. eigenvalue (max.eigen) or trace statistic (trace)
caseTest	provide test statistics regarding the intercept/trend structure
weTest	perform F test for weak exogenity

Details

The function computes a VECM for every subsystem before stacking the results to a GVAR model.

Specification of input here.

Value

An object of class GVAR containing the following items:

subsys	subsystem names
Data	data
we.vecms	VECMs of the subsystems
X	data as one single matrix
bigT	length of time series data
r	vector of cointegration ranks of the VECMs
Case	vector of intercept/trend behaviour of the VECMs
W	multiplier matrix to generate endogenous and weakly exogenous variables from X
G	multiplier matrix for the current variables
H	multiplier matrix for the lagged variables
Upsilon.0	multiplier matrix for the current strictly exogenous variables
Upsilon	multiplier matrix for the lagged strictly exogenous variables
c.0	multiplier matrix for the intercept
c.1	multiplier matrix for the trend
caseTest	test statistics for case selection
weight	weight matrix used to calculate the weakly exogenous variables
U	residuals of the GVAR
U.cov	residual covariance matrix
arguments	arguments passed to GVAR function, including lags, variable types,...

Author(s)

Martin Summer, Klaus Rheinberger, Rainer Puhr

References

Stephane Dees, Filippo di Mauro, Hashem Pesaran, and L. Vanessa Smith. Exploring the international linkages of the Euro area: A global VAR analysis. Journal of applied Econometrics, 22(1), 2007.

Soeren Johansen. Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models. Advanced Texts in Econometrics. Oxford University Press, 1995.

M. Hashem Pesaran, Yongcheol Shin, and Richard J. Smith. Structural analysis of vector error correction models with exogenous I(1) variables. Journal of Econometrics, 97:293-343, 2000.

See Also

est.we.mdls

Examples

data(pesaran26)
c.names <- names(Data)[-length(Data)]

p <- c(2,2,2,1,2,2,1,2,2,2,2,1,2,1,1,2,2,2,2,2,2,1,2,2,2,2)
q <- c(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
lex <- q

endo <- ord <- we <- d <- vector("list",length=length(c.names))
names(endo) <- names(ord) <- names(we) <- names(d) <- c.names
# base country: usa
endo[[1]] <- c(1:3,5:7)
ord[[1]] <- c(1:3,5:7)
we[[1]] <- c(1:2,4)
d[[1]] <- NULL
# countries with 6 endogenous variables:
for (j in c("EuroArea", "Japan", "UK", "Sweden", "Switzerland", "Norway", "Australia", "Canada", "NewZealand", "Korea", "Safrica")) 
{i <- which(c.names==j); endo[[i]] <- ord[[i]] <- 1:6}
# countries with 5 endogenous variables:
for (j in c("Argentina", "Chile", "Malaysia", "Philippines", "Singapore", "Thailand", "India")) 
{i <- which(c.names==j); endo[[i]] <- ord[[i]] <- 1:5}
# countries with 4 endogenous variables:
for (j in c("China", "Brazil", "Mexico", "Peru", "Indonesia", "Turkey")) 
{i <- which(c.names==j); endo[[i]] <- ord[[i]] <- c(1:2,4:5)}
# Saudi Arabia
endo[[21]] <- ord[[21]] <- c(1:2,4)

# all countries but us
for (i in 2:length(we))
{
  we[[i]] <- c(1:3,5,6)
  d[[i]] <- 1
}

Case <- "IV"
r <- c(2,1,1,4,3,3,3,2,2,1,2,3,3,4,4,3,3,4,1,2,3,3,2,1,1,1)

res.GVAR <- GVAR(Data=Data,r=r,p=p,q=q,weight=weight,Case=Case,exo.var=TRUE,d=d,lex=lex,ord=ord,we=we,endo=endo,method="max.eigen")

# view vecm models
res.GVAR$we.vecms

GVAR documentation built on May 2, 2019, 6:30 p.m.