Nothing
R/lineVar.R
In tsDyn: Nonlinear Time Series Models with Regime Switching
Defines functions
toLatex.VAR
vcov.VAR
print.summary.VAR
summary.VAR
print.VAR
VECM
lineVar
Documented in
lineVar
VECM
#'Multivariate linear models: VAR and VECM
#'
#'Estimate either a VAR or a VECM.
#'
#'This function provides basic functionalities for VAR and VECM models. More
#'comprehensive functions are in package \pkg{vars}. A few differences appear
#'in the VECM estimation: \describe{
#' \item{Engle-Granger estimator}{The Engle-Granger estimator is available}
#' \item{Presentation}{Results are printed in a different ways, using a matrix form}
#' \item{lateX export}{The matrix of coefficients can be exported to latex,
#' with or without standard-values and significance stars}
#' }
#'
#'Two estimators are available: the Engle-Granger two-steps
#'approach (\code{2OLS}) or the Johansen (\code{ML}). For the 2OLS,
#'deterministic regressors (or external variables if \code{LRinclude} is of
#'class numeric) can be added for the estimation of the cointegrating value and
#'for the ECT. This is only working when the beta value is not pre-specified.
#'
#' The argument \code{beta} is only for \code{\link{VECM}}, look at the specific help page for more details.
#'
#'@param data multivariate time series (first row being first=oldest value)
#'@param lag Number of lags to include in each regime
#'@param r Number of cointegrating relationships
#'@param include Type of deterministic regressors to include
#'@param model Model to estimate. Either a VAR or a VECM
#'@param I For VAR only: whether in the VAR the variables are to be taken in
#'levels (original series) or in difference, or similarly to the univariate ADF
#'case.
#'@param beta for VECM only: user-specified cointegrating value.
#'If NULL, will be estimated using the estimator specified in \code{estim}
#'@param LRinclude Possibility to include in the long-run relationship and the
#'ECT a trend, a, constant, etc. Can also be a matrix with exogeneous regressors
#'@param estim Type of estimator for the VECM: '2OLS' for the two-step approach
#'or 'ML' for Johansen MLE
#'@param exogen Inclusion of exogenous variables (first row being first=oldest
#'value). Is either of same size than data (then automatically cut) or than
#'end-sample.
#'@return Fitted model data
#'@author Matthieu Stigler
#'@seealso \code{\link{VECM}} which is just a wrapper for \code{lineVar(..., model="VECM")}.
#'Methods \code{\link{predict.VAR}}, \code{\link{VARrep}}, \code{\link{regime}}, \code{\link{irf}} and \code{\link{toLatex}}.
#'
#'\code{\link{TVAR}} and \code{\link{TVECM}} for the corresponding threshold
#'models. \code{\link{linear}} for the univariate AR model.
#'@keywords ts
#'@export
#'@examples
#'
#'data(zeroyld)
#'
#'#Fit a VAR
#'VAR <- lineVar(zeroyld, lag=1)
#'VAR
#'summary(VAR)
#'
#'#compare results with package vars:
#'if(require(vars)) {
#' a<-VAR(zeroyld, p=1)
#' coef_vars <- t(sapply(coef(a), function(x) x[c(3,1,2),1]))
#' all.equal(coef(VAR),coef_vars, check.attributes=FALSE)
#'}
#'
#'###VECM
#'VECM.EG <- lineVar(zeroyld, lag=2, model="VECM")
#'VECM.EG
#'summary(VECM.EG)
#'
#'VECM.ML <- lineVar(zeroyld, lag=2, model="VECM", estim="ML")
#'VECM.ML
#'summary(VECM.ML)
#'
#'
#'###Check Johansen MLE
#'myVECM <- lineVar(zeroyld, lag=1, include="const", model="VECM", estim="ML")
#'summary(myVECM, digits=7)
#'#comparing with vars package
#'if(require(vars)){
#' a<-ca.jo(zeroyld, spec="trans")
#' summary(a)
#' #same answer also!
#'}
#'
#'##export to Latex
#'toLatex(VECM.EG)
#'toLatex(summary(VECM.EG))
#'options("show.signif.stars"=FALSE)
#'toLatex(summary(VECM.EG), parenthese="Pvalue")
#'options("show.signif.stars"=TRUE)
#'
#'
#'
lineVar<-function(data, lag, r=1,include = c( "const", "trend","none", "both"), model=c("VAR", "VECM"),
I=c("level", "diff", "ADF"),beta=NULL, estim=c("2OLS", "ML"),
LRinclude=c("none", "const", "trend","both"), exogen=NULL){
y <- as.matrix(data)
Torigin <- nrow(y) #Size of original sample
T <- nrow(y) #Size of start sample
if(length(lag)==1){
p <- lag
notAllLags<-FALSE
Lags<-1:p
} else {
notAllLags<-TRUE
p<-max(lag)
Lags<-lag
}
t <- T-p #Size of end sample
k <- ncol(y) #Number of variables
t<-T-p #Size of end sample
if(is.null(colnames(data)))
colnames(data)<-paste("Var", c(1:k), sep="")
###Check args
include<-match.arg(include)
LRinclude<-match.arg(LRinclude)
if(lag==0) {
warning("Lag=0 not fully implemented, methods not expected to work: fevd, predict, irf,...")
}
if(LRinclude%in%c("const", "both") & include !="none") {
warning("When `LRinclude` is either 'const' or 'both', `include` can only be `none`.\n Setting include='none'.")
include <- "none"
}
ninclude<-switch(include, "const"=1, "trend"=1,"none"=0, "both"=2)
model<-match.arg(model)
estim<-match.arg(estim)
I<-match.arg(I)
if(!r%in%1:(k-1)) stop("Arg r, the number of cointegrating relationships, should be between 1 and K-1\n")
if(model=="VECM"&estim=="2OLS"&r>1){
warning("Estimation of more than 1 coint relationship is not possible with estim '2OLS'. Switched to Johansen 'ML'\n")
estim<-"ML"
}
minPara<-p*k+ninclude
if(!t>minPara) stop("Not enough observations. Try reducing lag number\n")
###Construct variables
Y <- y[(p+1):T,] #
X <- embed(y, p+1)[, -seq_len(k)] #Lags matrix
#Set up of dependent and independent variables matrices
if(notAllLags)
X<-X[,sort(rep((Lags*k-k+1), k))+0:(k-1)]
DeltaY<-diff(y)[(p+1):(T-1),]
Xminus1<-embed(y,p+2)[,(k+1):(k+k)]
DeltaX<-embed(diff(y),p+1)[,-(1:k)]
if(model=="VAR"){
if(I=="level"){
Z<-X
Y<-Y
} else if(I=="diff"){
Z<-DeltaX
Y<-DeltaY
t<-t-1
} else if(I=="ADF"){
Z<-cbind(Xminus1, DeltaX)
Y<-DeltaY
t<-t-1
}
} else if(model=="VECM"){
Z<-DeltaX
Y<-DeltaY
t<-t-1
}
###Regressors matrix
incReg <- switch(include,
"const" = matrix(1, nrow=t, ncol=1),
"trend" = matrix(seq_len(t), ncol=1),
"both" = cbind(rep(1,t),seq_len(t)),
"none"=NULL)
Z <-if(lag==0) incReg else cbind(incReg, Z)
if(!is.null(exogen)){
if(is.data.frame(exogen)|is.vector(exogen)) exogen <- as.matrix(exogen)
n_exo <- NROW(exogen)
if(n_exo!=t){
if(n_exo!=T) warning("exogen is of size ", n_exo, "while full/end-sample size is of size", T,"/", nrow(Z), "series shortened")
exogen <- myTail(exogen, t, keepnums=FALSE)# changed form addrownums
}
Z <- if(lag==0 & include=="none") exogen else cbind(Z, exogen)
}
##VECM: Long-run relationship OLS estimation
if(model=="VECM"&estim=="2OLS"){
#beta has to be estimated
beta.estimated <- is.null(beta)
if(is.null(beta) ){
## build LRplus: deterministic/exogeneous regressor in coint
if(is.character(LRinclude)){
LRplus <-switch(LRinclude, "none"=NULL,"const"=rep(1,T),"trend"=seq_len(T),"both"=cbind(rep(1,T),seq_len(T)))
LRinc_name <- switch(LRinclude, "const"="const", "trend"="trend", "both"=c("const", "trend"), "none"=NULL)
LRinc_dim <- switch(LRinclude, "const"=1, "trend"=1, "both"=2, "none"=0)
} else if(inherits(LRinclude, c("matrix", "numeric"))) {
LRplus <- LRinclude
} else{
stop("Argument LRinclude not correctly indicated")
}
## run coint regression
if(LRinclude=="none"){
cointLM<-lm(y[,1] ~ y[,-1]-1)
} else {
cointLM<-lm(y[,1] ~ y[,-1]-1+ LRplus)
Xminus1 <- cbind(Xminus1, tail(LRplus,nrow(Xminus1)))
}
betaLT<-coint<-c(1,-cointLM$coef)
betaLT_std <- c(1,summary(cointLM)$coef[,2])
names(betaLT_std)<-c(colnames(data), LRinc_name)
## case beta pre-estimated
} else {
if(length(beta)!=k-1) stop("Arg 'beta' should be of length k-1")
if(LRinclude!="none")
warning("Arg LRinclude not taken into account when beta is given by user")
LRinc_name <- NULL
LRinc_dim <- 0
coint<-c(1, -beta)
betaLT<-c(1,-beta)
}
coint_export<-matrix(coint, nrow=k+LRinc_dim , dimnames=list(c(colnames(data),LRinc_name), "r1"))
betaLT<-matrix(betaLT, nrow=k+LRinc_dim , dimnames=list(c(colnames(data),LRinc_name),"r1"))
ECTminus1<-Xminus1%*%betaLT
Z<-cbind(ECTminus1,Z)
}
##VECM: ML (Johansen ) estimation of cointegrating vector
else if(model=="VECM"&estim=="ML"){
beta.estimated<- is.null(beta)
if(lag==0 & include=="none" & is.null(exogen)){
u <- Y
v <- Xminus1
} else {
#Auxiliary regression 1
reg_res1<-lm.fit(Z,Y)
u<-residuals(reg_res1)
#Auxiliary regression 2
reg_res2<-lm.fit(Z,Xminus1)
v<-residuals(reg_res2)
}
#Auxiliary regression 3
if(LRinclude!="none"){
add <- switch(LRinclude, "const"=matrix(1, nrow=t),
"trend"=matrix(1:t, nrow=t),
"both"=cbind(1,1:t))
reg_res3 <- if(lag==0) add else residuals(lm.fit(Z,add))
v<-cbind(v,reg_res3) # equ 20.2.46 in Hamilton
}
#Moment matrices
S00<-crossprod(u)
S11<-crossprod(v)
S01<-crossprod(u,v)
if(beta.estimated){
SSSS<-solve(S11)%*%t(S01)%*%solve(S00)%*%S01
eig<-eigen(SSSS)
ve<-Re(eig$vectors)
va<-Re(eig$values)
#normalize eigenvectors
ve_no<-apply(ve,2, function(x) x/c(sqrt(t(x)%*%S11%*%x)))
ve_2<-t(t(ve_no)/diag(ve_no))
ve_3<-ve_2[,1:r, drop=FALSE]
## Phillips triangular normalisation (Juselius (2006, p. 216))
C2 <- matrix(0, nrow = nrow(ve_2) - r, ncol = r)
C <- rbind(diag(r), C2)
ve_4 <- ve_3 %*% solve(t(C) %*% ve_3)
#compute A (speed adjustment)
z0<-t(u)%*%v%*%tcrossprod(ve_no[,1:r])
###Slope parameters
if(LRinclude!="none"){
ECTminus1<-cbind(Xminus1,add)%*%ve_4
}else{
ECTminus1<-Xminus1%*%ve_4
}
coin_ve_names <- switch(LRinclude, "const"="const", "trend"="trend", "both"=c("const", "trend"), "none"=NULL)
dimnames(ve_4)<-list(c(colnames(data), coin_ve_names), paste("r", 1:r, sep=""))
betaLT<-ve_4
# if beta restricted:
} else {
betaLT <- as.matrix(beta)
if(ncol(betaLT)!=r) stop("Argument 'beta' should have as many columns as 'r'")
if(ncol(betaLT)==1&&nrow(betaLT)==k-1) betaLT <- rbind(1,betaLT)
if(nrow(betaLT)!=k) stop("Argument 'beta' should have as many rows as 'k'")
ECTminus1 <- Xminus1%*%betaLT
## restricted ML:
S11_r <- t(betaLT)%*%S11%*%betaLT ## equa 20.3.11 Hamilton 1994, p. 649
S01_r <- S01 %*%betaLT ## equa 20.3.12 Hamilton 1994, p. 649
SSSS_r <-solve(S11_r)%*%t(S01_r)%*%solve(S00)%*%S01_r
eig_r<-eigen(SSSS_r)
va<-Re(eig_r$values)
}
Z<-cbind(ECTminus1,Z)
}#end model=="VECM"&estim=="ML"
###Slope parameters, residuals and fitted
lmReg <- lm.fit(Z,Y)
B <- t(lmReg$coefficients )
fitted <- lmReg$fitted.values
res <- lmReg$residuals
###naming of variables and parameters
npar<-ncol(B)*nrow(B)
rownames(B)<-paste("Equation",colnames(data))
if(p>0){
LagNames<-c(paste(rep(colnames(data),length(Lags)), -rep(Lags, each=k)))
if(I=="ADF") LagNames <- paste("D", LagNames,sep="_")
} else {
LagNames <- NULL
}
ECT<- if(model=="VECM") paste("ECT", if(r>1) 1:r else NULL, sep="") else NULL
Xminus1Names<- if(I=="ADF") paste(colnames(data),"-1",sep="") else NULL
BnamesInter<-switch(include,"const"="Intercept","none"=NULL,"trend"="Trend","both"=c("Intercept","Trend"))
if(!is.null(exogen)){
exo_names <- colnames(as.matrix(exogen))
exp_res <- "-[0-9]+|\\.l[0-9]+|ECT|Intercept|Trend"
if(any(grepl(exp_res, exo_names))) {
warning("Exogen contains reserved names (", exp_res, ". Changed to exo_x")
exo_names[grepl(exp_res, exo_names)] <- paste("exo", 1:sum(grepl(exp_res, exo_names)), sep="_")
}
if(any(is.null(exo_names))) exo_names <- paste("exo", 1:NCOL(exogen), sep="_")
} else {
exo_names <- NULL
}
Bnames<-c(ECT,BnamesInter,Xminus1Names, LagNames, exo_names)
colnames(B)<-Bnames
###Y and regressors matrix to be returned
naX<-rbind(matrix(NA, ncol=ncol(Z), nrow=T-t), Z)
rownames(naX)<-rownames(data)
YnaX<-cbind(data, naX)
colnames(YnaX)<-c(colnames(data),Bnames)
###Return outputs
model.specific<-list()
model.specific$nthresh<-0
if(model=="VECM"){
model.specific$beta<- betaLT
model.specific$coint <- betaLT
model.specific$r<-r
model.specific$estim<-estim
model.specific$LRinclude<-LRinclude
model.specific$beta.estimated<-beta.estimated
model.specific$estim <- estim
if(estim=="ML"){
model.specific$S00<-S00
model.specific$lambda<-va
}
}
inputArgs <- list()
inputArgs$I <- I
inputArgs$estim <- estim
inputArgs$LRinclude <- LRinclude
inputArgs$call <- match.call()
z<-list(residuals=res,
coefficients=B, k=k, t=t,T=T, npar=npar, nparB=ncol(B), type="linear",
fitted.values=fitted,
model.x=Z,
include=include,
lag=lag,
model=YnaX,
df.residual=t-npar/k,
exogen = !is.null(exogen),
num_exogen = if(!is.null(exogen)) NCOL(exogen) else 0,
model.specific=model.specific,
qr=lmReg$qr,
inputArgs = inputArgs)
if(model=="VAR"){
class(z)<-c("VAR","nlVar")
} else {
class(z)<-c("VECM","VAR", "nlVar")
I<-"diff"
}
attr(z, "varsLevel")<-I
attr(z, "model")<-model
return(z)
}
#### VECM function: wrapper to lineVar
#' Estimation of Vector error correction model (VECM)
#'
#' Estimate a VECM by either Engle-Granger (2OLS) or Johansen (MLE) method.
#'
#' This function is just a wrapper for the \code{\link{lineVar}}, with
#' model="VECM".
#'
#' More comprehensive functions for VECM are in package \pkg{vars}.
#' Differences with that package are: \describe{ \item{Engle-Granger
#' estimator}{The Engle-Granger estimator is available}
#' \item{Presentation}{Results are printed in a different ways, using a matrix
#' form} \item{lateX export}{The matrix of coefficients can be exported to
#' latex, with or without standard-values and significance stars}
#' \item{Prediction}{The \code{predict} method contains a \code{newdata}
#' argument allowing to compute rolling forecasts.} }
#'
#' Two estimators are available: the Engle-Granger two step approach
#' (\code{2OLS}) or the Johansen (\code{ML}). For the 2OLS, deterministic
#' regressors (or external variables if \code{LRinclude} is of class numeric) can be
#' added for the estimation of the cointegrating value and for the ECT. This is
#' only working when the beta value is not pre-specified.
#'
#' The arg beta is the cointegrating value, the cointegrating vector will be
#' taken as: (1, -beta).
#'
#' Note that the lag specification corresponds to the lags in the VECM
#' representation, not in the VAR (as is done in package vars or software
#' GRETL). Basically, a VAR with 2 lags corresponds here to a VECM with 1 lag.
#' The lag can be set to 0, although some methods (irf, fevd) won't work for this case.
#'
#' #'The arg \code{beta} allows to specify constrained cointegrating values, leading to
#' \eqn{ECT= \beta^{'}X_{t-1}}. It should be specified as a \eqn{K \times r} matrix. In case of
#' \eqn{r=1}, can also be specified as a vector. Note that the vector should be normalised,
#' with the first value to 1, and the next values showing the opposite sign in the long-run relationship \eqn{- \beta}.
#' In case the vector has \eqn{K-1} values, this is what \code{lineVar} is doing, setting \eqn{(1, - \beta)}.
#' Note finally one should provide values for all
#' the coefficients (eventually except for special case of r=1 and k-1), if you want to provide only part of the
#' parameters, and let the others be estimated, look at the functions in package urca.
#'
#'The eigenvector matrix \eqn{\beta} is normalised using the Phillips triangular representation,
#'see Hamilton (1994, p. 576) and Juselius (2006, p. 216), see \code{\link{coefA}} for more details.
#'
#' @param data multivariate time series (first row being first=oldest value)
#' @param lag Number of lags (in the VECM representation, see Details)
#' @param r Number of cointegrating relationships
#' @param include Type of deterministic regressors to include
#'@param beta for VECM only: user-specified cointegrating values, the cointegrating vector will be
#' taken as: (1, -\code{beta})
#'If NULL, will be estimated using the estimator specified in \code{estim}
#'@param LRinclude Type of deterministic regressors to include in the long-term
#'relationship. Can also be a matrix with exogeneous regressors (2OLS only).
#'@param estim Type of estimator: \code{2OLS} for the two-step approach or
#'\code{ML} for Johansen MLE
#'@param exogen Inclusion of exogenous variables (first row being first=oldest
#'value). Is either of same size than data (then automatically cut) or than
#'end-sample.
#'
#'@return An object of class \code{VECM} (and higher classes \code{VAR} and
#'\code{nlVar}) with methods:
#'\describe{
#'\item{Usual methods:}{Print, summary, residuals, fitted, vcov}
#'\item{Fit criteria:}{AIC, BIC, \code{\link{MAPE}}, \code{\link{mse}}, \code{\link[=logLik.VECM]{logLik}}
#'(the latter only for models estimated with MLE)}
#'\item{Prediction:}{predict and \code{\link{predict_rolling}}}
#'\item{coef extraction:}{Extract cointegrating/adjustment coefficients, \code{\link{coefA}}, \code{\link{coefB}} \code{\link{coefPI}}}
#'\item{VAR/VECM methods:}{Impulse response function (\code{\link{irf.VECM}}) and forecast error variance
#'decomposition (\code{\link[=fevd.nlVar]{fevd}})}
#'\item{LaTeX:}{toLatex} }
#'
#'@author Matthieu Stigler
#'
#'@references
#' Hamilton (1994) Time Series Analysis, Princeton University Press
#'
#' Juselius (2006) The Cointegrated VAR model, Oxford University Press
#'@seealso \code{\link{coefA}}, \code{\link{coefB}} and \code{\link{coefPI}}
#'to extract the relevant parameter matrices.
#'
#'\code{\link{lineVar}} \code{\link{TVAR}} and \code{\link{TVECM}} for
#'the corresponding threshold models. \code{\link{linear}} for the univariate AR
#'model.
#'@keywords ts
#'@export
#'@examples
#'
#'data(zeroyld)
#'data<-zeroyld
#'
#'#Fit a VECM with Engle-Granger 2OLS estimator:
#'vecm.eg<-VECM(zeroyld, lag=2)
#'
#'#Fit a VECM with Johansen MLE estimator:
#'vecm.jo<-VECM(zeroyld, lag=2, estim="ML")
#'
#'#compare results with package vars:
#'if(require(vars)) {
#' data(finland)
#' #check long coint values
#' all.equal(VECM(finland, lag=2, estim="ML", r=2)$model.specific$beta,
#' cajorls(ca.jo(finland, K=3, spec="transitory"), r=2) $beta, check.attributes=FALSE)
#' # check OLS parameters
#' all.equal(t(coefficients(VECM(finland, lag=2, estim="ML", r=2))),
#' coefficients(cajorls(ca.jo(finland, K=3, spec="transitory"), r=2)$rlm), check.attributes=FALSE)
#'
#'}
#'
#'
#'##export to Latex
#'toLatex(vecm.eg)
#'toLatex(summary(vecm.eg))
#'options("show.signif.stars"=FALSE)
#'toLatex(summary(vecm.eg), parenthese="Pvalue")
#'options("show.signif.stars"=TRUE)
#'
#'
#'
VECM<-function(data, lag,r=1, include = c( "const", "trend","none", "both"), beta=NULL, estim=c("2OLS", "ML"),LRinclude=c("none", "const", "trend","both"), exogen=NULL)
lineVar(data, lag, r=r,include = include, model="VECM" ,beta=beta, estim=estim,LRinclude=LRinclude,exogen=exogen)
###Testing
if(FALSE) { #usage example
###Hansen Seo data
library(tsDyn)
environment(lineVar)<-environment(star)
environment(summary.VAR)<-environment(star)
environment(toLatex.VAR)<-environment(star)
#data(zeroyld)
dat<-zeroyld
#tests
aVAR<-lineVar(dat[1:100,], lag=c(1,2), include="both", model="VAR")
#lag2, 2 thresh, trim00.05: 561.46
class(aVAR)
aVAR
print(aVAR)
logLik(aVAR)
AIC(aVAR)
BIC(aVAR)
deviance(aVAR)
coef(aVAR)
summary(aVAR)
toLatex(aVAR)
toLatex(summary(aVAR))
}
#' @export
print.VAR <- function(x,...){
print(coef(x))
}
#' @export
summary.VAR<-function(object, digits=4,...){
x<-object
r<-4
t<-x$t
k<-x$k
Sigma<-matrix(1/(object$df.residual)*crossprod(x$residuals),ncol=k)
betas <- x$coefficients
XX <- crossprod(x$model.x)
# cov.unscaled <- try(solve(XX), silent=TRUE)
cov.unscaled <- chol2inv(object$qr$qr)
if(inherits(cov.unscaled, "try-error")) {
Qr <- qr(x$model.x)
p1 <- 1:Qr$rank
cov.unscaled <- chol2inv(Qr$qr[p1, p1, drop = FALSE])
warning("Potential numerical unstability, beware of standard errors\n")
}
VarCovB <- Sigma %x% cov.unscaled
StDevB<-matrix(sqrt(diag(VarCovB)), nrow=k, byrow = TRUE)
Tvalue<-betas/StDevB
Pval <- 2* pt(abs(Tvalue), df=x$df.residual, lower.tail=FALSE)
symp <- symnum(Pval, corr=FALSE,cutpoints = c(0, .001,.01,.05, .1, 1), symbols = c("***","** ","* ",". "," "))
stars<-matrix(symp, nrow=nrow(Pval))
ab<-matrix(paste(myformat(betas,digits),"(", myformat(StDevB,digits),")",stars,sep=""), nrow=nrow(Pval))
dimnames(ab)<-dimnames(betas)
## assemble
coMat <- cbind(ct(betas), ct(StDevB), ct(Tvalue), ct(Pval))
colnames(coMat) <- c("Estimate", "Std. Error", "t value", "Pr(>|t|)")
rownames(coMat) <- paste(rep(eqNames(x), each=ncol(betas)),
gsub(" ", "", colnames(betas)), sep=":")
x$bigcoefficients<-ab
x$cov.unscaled<-cov.unscaled
x$sigma<-Sigma
x$StDev<-StDevB
x$Pvalues<-Pval
x$coefMat <- coMat
x$stars<-stars
x$starslegend<-symp
x$aic<-AIC.nlVar(x)
x$bic<-BIC.nlVar(x)
x$SSR<-deviance.nlVar(x)
class(x)<-c("summary.VAR", "VAR")
return(x)
}
#' @export
print.summary.VAR<-function(x,...){
cat("#############\n###Model", attr(x,"model"),"\n#############")
cat("\nFull sample size:",x$T, "\tEnd sample size:", x$t)
cat("\nNumber of variables:", x$k,"\tNumber of estimated slope parameters", x$npar)
cat("\nAIC",x$aic , "\tBIC", x$bic, "\tSSR", x$SSR)
if(attr(x,"model")=="VECM"){
cat("\nCointegrating vector ", if(x$model.specific$beta.estimated) paste("(estimated by ", x$model.specific$estim, "):\n", sep="") else "(fixed by user):\n", sep="")
print(t(x$model.specific$beta))
}
cat("\n\n")
print(noquote(x$bigcoefficients))
}
#' @export
vcov.VAR<-function(object, ...){
sum<-summary.VAR(object)
so<-sum$sigma %x% sum$cov.unscaled
co.names<-gsub(" ", "", colnames(coef(object)))
eq.names <- eqNames(object)
together.names<-paste(rep(eq.names,each= length(co.names)), co.names, sep=":")
dimnames(so)<-list(together.names, together.names)
so
}
#' @export
toLatex.VAR<-function(object,..., digits=4, parenthese=c("StDev","Pvalue"), label){
x<-object
if(attr(x,"model")=="VECM"&&x$model.specific$LRinclude!="none") stop("toLatex not implemented now for models with arg 'LRinclude' different from 'none'")
parenthese<-match.arg(parenthese)
if(inherits(x,"summary.VAR")){
a<-myformat(x$coefficients,digits, toLatex=TRUE)
inp<-switch(parenthese, "StDev"= x$StDev, "Pvalue"= x$Pvalues )
b<-myformat(inp ,digits,toLatex=TRUE)
if(getOption("show.signif.stars"))
stars<-paste("^{",x$stars,"}", sep="")
else
stars<-NULL
coeftoprint<-matrix(paste(a,"(",b,")",stars, sep=""),ncol=ncol(a), nrow=nrow(a))
}#end if x is of class summary
else{
coeftoprint <-myformat(x$coefficients, digits, toLatex=TRUE)}
varNames<-rownames(x$coefficients)
res<-character()
res[1]<-"%insert in the preamble and uncomment the line you want for usual /medium /small matrix"
res[2]<-"%\\usepackage{amsmath} \\newenvironment{smatrix}{\\begin{pmatrix}}{\\end{pmatrix}} %USUAL"
res[3]<-"%\\usepackage{amsmath} \\newenvironment{smatrix}{\\left(\\begin{smallmatrix}}{\\end{smallmatrix}\\right)} %SMALL"
res[4]<-"%\\usepackage{nccmath} \\newenvironment{smatrix}{\\left(\\begin{mmatrix}}{\\end{mmatrix}\\right)} %MEDIUM"
res[5]<-"\\begin{equation}"
if(!missing(label)) res[5]<- paste(res[5], "\\label{", label, "}", sep="")
res[6]<- "\\begin{smatrix} %explained vector"
###explained vector
if(attr(x, "varsLevel")=="diff")
res[7]<-TeXVec(paste("slashDelta X_{t}^{",seq(1, x$k),"}", sep=""))
else
res[7]<-TeXVec(paste("X_{t}^{",seq(1, x$k),"}", sep=""))
res[8]<- "\\end{smatrix}="
###ECT
ninc<-switch(x$include, "const"=1, "trend"=1,"none"=0, "both"=2)
if(attr(x,"model")=="VECM"){
r<-x$model.specific$r
len<-length(res)
if(r==1){
res[len+1]<-"+\\begin{smatrix} %ECT"
res[len+2]<-TeXVec(coeftoprint[,1]) #see nlVar-methods.R
res[len+3]<-"\\end{smatrix}ECT_{-1}"
}else{
res[len+1]<-"+\\begin{smatrix} %ECT"
res[(len+2):(len+x$k+1)]<-TeXMat(coeftoprint[,1:r]) #see nlVar-methods.R
res[len+x$k+2]<-"\\end{smatrix}ECT_{-1}"
}
}
###Const
a<-if(attr(x,"model")=="VECM") r else 0
res<-include(x, res, coeftoprint, skip=a) #nlVar-methods.R
###Lags
res<-LagTeX(res, x, coeftoprint, ninc+a) #nlVar-methods.R
res[length(res)+1]<-"\\end{equation}"
res<-gsub("slash", "\\", res, fixed=TRUE)
res<-res[res!="blank"]
return(structure(res, class="Latex"))
}
if(FALSE){
###TODO
#check if const/trend/both in LR rel and VECM makes sense!
#check for standaard deviation of coint vector whith ML estim!
#consistency between ML and OLS coint estimator?
}
if(FALSE) { #usage example
###Hansen Seo data
library(tsDyn)
#data(zeroyld)
dat<-zeroyld
environment(lineVar)<-environment(star)
environment(summary.VAR)<-environment(star)
aVAR<-lineVar(dat, lag=1, include="both", model="VAR")
aVAR<-lineVar(dat, lag=1, include="const", model="VECM", estim="ML", beta=0.98)
#lag2, 2 thresh, trim00.05: 561.46
aVAR
summary(aVAR)
sqrt(diag(summary(aVAR, cov=0)$sigma))
vcov.VAR(aVAR)
vcovHC.VAR(aVAR)
logLik(aVAR)
AIC(aVAR)
BIC(aVAR)
deviance(aVAR)
coef(aVAR)
environment(toLatex.VAR)<-environment(star)
toLatex(aVAR)
toLatex(summary(aVAR))
###Check VAR: comparing with vars
myVAR<-lineVar(dat, lag=1)
library(vars)
var<-VAR(dat, lag=1)
vaco1<-coef(var)$short.run[c(3,1,2),1]
vaco2<-coef(var)$long.run[c(3,1,2),1]
round(coef(myVAR),8)==round(rbind(vaco1, vaco2),8)
###Check Johansen MLE
myVECM<-lineVar(dat, lag=1, include="const", model="VECM", estim="ML")
summary(myVECM, digits=7)
#comparing with Hansen paper:reported in Gauss procedure is:
#coint vector: 1.02206: ok!
#coeff:
#comparing with vars package
a<-ca.jo(dat, spec="trans")
summary(a)
#same answer also!
set.seed(123)
rn <- rnorm(2*nrow(dat))
ex_1_n <- ex_1 <- rn[1:nrow(dat)]
ex_2_n <- ex_2 <- matrix(rn, ncol=2)
names(ex_1_n) <- "exoVar"
colnames(ex_2_n) <- c("exoVar1", "exoVar2")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_1)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_1_n)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
colnames(ex_2_n) <- c("exoVar1", "a -1")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
colnames(ex_2_n) <- c("a.l2", "Trend")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
}
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Defines functions toLatex.VAR vcov.VAR print.summary.VAR summary.VAR print.VAR VECM lineVar
Documented in lineVar VECM
#'Multivariate linear models: VAR and VECM
#'
#'Estimate either a VAR or a VECM.
#'
#'This function provides basic functionalities for VAR and VECM models. More
#'comprehensive functions are in package \pkg{vars}. A few differences appear
#'in the VECM estimation: \describe{
#' \item{Engle-Granger estimator}{The Engle-Granger estimator is available}
#' \item{Presentation}{Results are printed in a different ways, using a matrix form}
#' \item{lateX export}{The matrix of coefficients can be exported to latex,
#' with or without standard-values and significance stars}
#' }
#'
#'Two estimators are available: the Engle-Granger two-steps
#'approach (\code{2OLS}) or the Johansen (\code{ML}). For the 2OLS,
#'deterministic regressors (or external variables if \code{LRinclude} is of
#'class numeric) can be added for the estimation of the cointegrating value and
#'for the ECT. This is only working when the beta value is not pre-specified.
#'
#' The argument \code{beta} is only for \code{\link{VECM}}, look at the specific help page for more details.
#'
#'@param data multivariate time series (first row being first=oldest value)
#'@param lag Number of lags to include in each regime
#'@param r Number of cointegrating relationships
#'@param include Type of deterministic regressors to include
#'@param model Model to estimate. Either a VAR or a VECM
#'@param I For VAR only: whether in the VAR the variables are to be taken in
#'levels (original series) or in difference, or similarly to the univariate ADF
#'case.
#'@param beta for VECM only: user-specified cointegrating value.
#'If NULL, will be estimated using the estimator specified in \code{estim}
#'@param LRinclude Possibility to include in the long-run relationship and the
#'ECT a trend, a, constant, etc. Can also be a matrix with exogeneous regressors
#'@param estim Type of estimator for the VECM: '2OLS' for the two-step approach
#'or 'ML' for Johansen MLE
#'@param exogen Inclusion of exogenous variables (first row being first=oldest
#'value). Is either of same size than data (then automatically cut) or than
#'end-sample.
#'@return Fitted model data
#'@author Matthieu Stigler
#'@seealso \code{\link{VECM}} which is just a wrapper for \code{lineVar(..., model="VECM")}.
#'Methods \code{\link{predict.VAR}}, \code{\link{VARrep}}, \code{\link{regime}}, \code{\link{irf}} and \code{\link{toLatex}}.
#'
#'\code{\link{TVAR}} and \code{\link{TVECM}} for the corresponding threshold
#'models. \code{\link{linear}} for the univariate AR model.
#'@keywords ts
#'@export
#'@examples
#'
#'data(zeroyld)
#'
#'#Fit a VAR
#'VAR <- lineVar(zeroyld, lag=1)
#'VAR
#'summary(VAR)
#'
#'#compare results with package vars:
#'if(require(vars)) {
#' a<-VAR(zeroyld, p=1)
#' coef_vars <- t(sapply(coef(a), function(x) x[c(3,1,2),1]))
#' all.equal(coef(VAR),coef_vars, check.attributes=FALSE)
#'}
#'
#'###VECM
#'VECM.EG <- lineVar(zeroyld, lag=2, model="VECM")
#'VECM.EG
#'summary(VECM.EG)
#'
#'VECM.ML <- lineVar(zeroyld, lag=2, model="VECM", estim="ML")
#'VECM.ML
#'summary(VECM.ML)
#'
#'
#'###Check Johansen MLE
#'myVECM <- lineVar(zeroyld, lag=1, include="const", model="VECM", estim="ML")
#'summary(myVECM, digits=7)
#'#comparing with vars package
#'if(require(vars)){
#' a<-ca.jo(zeroyld, spec="trans")
#' summary(a)
#' #same answer also!
#'}
#'
#'##export to Latex
#'toLatex(VECM.EG)
#'toLatex(summary(VECM.EG))
#'options("show.signif.stars"=FALSE)
#'toLatex(summary(VECM.EG), parenthese="Pvalue")
#'options("show.signif.stars"=TRUE)
#'
#'
#'
lineVar<-function(data, lag, r=1,include = c( "const", "trend","none", "both"), model=c("VAR", "VECM"),
I=c("level", "diff", "ADF"),beta=NULL, estim=c("2OLS", "ML"),
LRinclude=c("none", "const", "trend","both"), exogen=NULL){
y <- as.matrix(data)
Torigin <- nrow(y) #Size of original sample
T <- nrow(y) #Size of start sample
if(length(lag)==1){
p <- lag
notAllLags<-FALSE
Lags<-1:p
} else {
notAllLags<-TRUE
p<-max(lag)
Lags<-lag
}
t <- T-p #Size of end sample
k <- ncol(y) #Number of variables
t<-T-p #Size of end sample
if(is.null(colnames(data)))
colnames(data)<-paste("Var", c(1:k), sep="")
###Check args
include<-match.arg(include)
LRinclude<-match.arg(LRinclude)
if(lag==0) {
warning("Lag=0 not fully implemented, methods not expected to work: fevd, predict, irf,...")
}
if(LRinclude%in%c("const", "both") & include !="none") {
warning("When `LRinclude` is either 'const' or 'both', `include` can only be `none`.\n Setting include='none'.")
include <- "none"
}
ninclude<-switch(include, "const"=1, "trend"=1,"none"=0, "both"=2)
model<-match.arg(model)
estim<-match.arg(estim)
I<-match.arg(I)
if(!r%in%1:(k-1)) stop("Arg r, the number of cointegrating relationships, should be between 1 and K-1\n")
if(model=="VECM"&estim=="2OLS"&r>1){
warning("Estimation of more than 1 coint relationship is not possible with estim '2OLS'. Switched to Johansen 'ML'\n")
estim<-"ML"
}
minPara<-p*k+ninclude
if(!t>minPara) stop("Not enough observations. Try reducing lag number\n")
###Construct variables
Y <- y[(p+1):T,] #
X <- embed(y, p+1)[, -seq_len(k)] #Lags matrix
#Set up of dependent and independent variables matrices
if(notAllLags)
X<-X[,sort(rep((Lags*k-k+1), k))+0:(k-1)]
DeltaY<-diff(y)[(p+1):(T-1),]
Xminus1<-embed(y,p+2)[,(k+1):(k+k)]
DeltaX<-embed(diff(y),p+1)[,-(1:k)]
if(model=="VAR"){
if(I=="level"){
Z<-X
Y<-Y
} else if(I=="diff"){
Z<-DeltaX
Y<-DeltaY
t<-t-1
} else if(I=="ADF"){
Z<-cbind(Xminus1, DeltaX)
Y<-DeltaY
t<-t-1
}
} else if(model=="VECM"){
Z<-DeltaX
Y<-DeltaY
t<-t-1
}
###Regressors matrix
incReg <- switch(include,
"const" = matrix(1, nrow=t, ncol=1),
"trend" = matrix(seq_len(t), ncol=1),
"both" = cbind(rep(1,t),seq_len(t)),
"none"=NULL)
Z <-if(lag==0) incReg else cbind(incReg, Z)
if(!is.null(exogen)){
if(is.data.frame(exogen)|is.vector(exogen)) exogen <- as.matrix(exogen)
n_exo <- NROW(exogen)
if(n_exo!=t){
if(n_exo!=T) warning("exogen is of size ", n_exo, "while full/end-sample size is of size", T,"/", nrow(Z), "series shortened")
exogen <- myTail(exogen, t, keepnums=FALSE)# changed form addrownums
}
Z <- if(lag==0 & include=="none") exogen else cbind(Z, exogen)
}
##VECM: Long-run relationship OLS estimation
if(model=="VECM"&estim=="2OLS"){
#beta has to be estimated
beta.estimated <- is.null(beta)
if(is.null(beta) ){
## build LRplus: deterministic/exogeneous regressor in coint
if(is.character(LRinclude)){
LRplus <-switch(LRinclude, "none"=NULL,"const"=rep(1,T),"trend"=seq_len(T),"both"=cbind(rep(1,T),seq_len(T)))
LRinc_name <- switch(LRinclude, "const"="const", "trend"="trend", "both"=c("const", "trend"), "none"=NULL)
LRinc_dim <- switch(LRinclude, "const"=1, "trend"=1, "both"=2, "none"=0)
} else if(inherits(LRinclude, c("matrix", "numeric"))) {
LRplus <- LRinclude
} else{
stop("Argument LRinclude not correctly indicated")
}
## run coint regression
if(LRinclude=="none"){
cointLM<-lm(y[,1] ~ y[,-1]-1)
} else {
cointLM<-lm(y[,1] ~ y[,-1]-1+ LRplus)
Xminus1 <- cbind(Xminus1, tail(LRplus,nrow(Xminus1)))
}
betaLT<-coint<-c(1,-cointLM$coef)
betaLT_std <- c(1,summary(cointLM)$coef[,2])
names(betaLT_std)<-c(colnames(data), LRinc_name)
## case beta pre-estimated
} else {
if(length(beta)!=k-1) stop("Arg 'beta' should be of length k-1")
if(LRinclude!="none")
warning("Arg LRinclude not taken into account when beta is given by user")
LRinc_name <- NULL
LRinc_dim <- 0
coint<-c(1, -beta)
betaLT<-c(1,-beta)
}
coint_export<-matrix(coint, nrow=k+LRinc_dim , dimnames=list(c(colnames(data),LRinc_name), "r1"))
betaLT<-matrix(betaLT, nrow=k+LRinc_dim , dimnames=list(c(colnames(data),LRinc_name),"r1"))
ECTminus1<-Xminus1%*%betaLT
Z<-cbind(ECTminus1,Z)
}
##VECM: ML (Johansen ) estimation of cointegrating vector
else if(model=="VECM"&estim=="ML"){
beta.estimated<- is.null(beta)
if(lag==0 & include=="none" & is.null(exogen)){
u <- Y
v <- Xminus1
} else {
#Auxiliary regression 1
reg_res1<-lm.fit(Z,Y)
u<-residuals(reg_res1)
#Auxiliary regression 2
reg_res2<-lm.fit(Z,Xminus1)
v<-residuals(reg_res2)
}
#Auxiliary regression 3
if(LRinclude!="none"){
add <- switch(LRinclude, "const"=matrix(1, nrow=t),
"trend"=matrix(1:t, nrow=t),
"both"=cbind(1,1:t))
reg_res3 <- if(lag==0) add else residuals(lm.fit(Z,add))
v<-cbind(v,reg_res3) # equ 20.2.46 in Hamilton
}
#Moment matrices
S00<-crossprod(u)
S11<-crossprod(v)
S01<-crossprod(u,v)
if(beta.estimated){
SSSS<-solve(S11)%*%t(S01)%*%solve(S00)%*%S01
eig<-eigen(SSSS)
ve<-Re(eig$vectors)
va<-Re(eig$values)
#normalize eigenvectors
ve_no<-apply(ve,2, function(x) x/c(sqrt(t(x)%*%S11%*%x)))
ve_2<-t(t(ve_no)/diag(ve_no))
ve_3<-ve_2[,1:r, drop=FALSE]
## Phillips triangular normalisation (Juselius (2006, p. 216))
C2 <- matrix(0, nrow = nrow(ve_2) - r, ncol = r)
C <- rbind(diag(r), C2)
ve_4 <- ve_3 %*% solve(t(C) %*% ve_3)
#compute A (speed adjustment)
z0<-t(u)%*%v%*%tcrossprod(ve_no[,1:r])
###Slope parameters
if(LRinclude!="none"){
ECTminus1<-cbind(Xminus1,add)%*%ve_4
}else{
ECTminus1<-Xminus1%*%ve_4
}
coin_ve_names <- switch(LRinclude, "const"="const", "trend"="trend", "both"=c("const", "trend"), "none"=NULL)
dimnames(ve_4)<-list(c(colnames(data), coin_ve_names), paste("r", 1:r, sep=""))
betaLT<-ve_4
# if beta restricted:
} else {
betaLT <- as.matrix(beta)
if(ncol(betaLT)!=r) stop("Argument 'beta' should have as many columns as 'r'")
if(ncol(betaLT)==1&&nrow(betaLT)==k-1) betaLT <- rbind(1,betaLT)
if(nrow(betaLT)!=k) stop("Argument 'beta' should have as many rows as 'k'")
ECTminus1 <- Xminus1%*%betaLT
## restricted ML:
S11_r <- t(betaLT)%*%S11%*%betaLT ## equa 20.3.11 Hamilton 1994, p. 649
S01_r <- S01 %*%betaLT ## equa 20.3.12 Hamilton 1994, p. 649
SSSS_r <-solve(S11_r)%*%t(S01_r)%*%solve(S00)%*%S01_r
eig_r<-eigen(SSSS_r)
va<-Re(eig_r$values)
}
Z<-cbind(ECTminus1,Z)
}#end model=="VECM"&estim=="ML"
###Slope parameters, residuals and fitted
lmReg <- lm.fit(Z,Y)
B <- t(lmReg$coefficients )
fitted <- lmReg$fitted.values
res <- lmReg$residuals
###naming of variables and parameters
npar<-ncol(B)*nrow(B)
rownames(B)<-paste("Equation",colnames(data))
if(p>0){
LagNames<-c(paste(rep(colnames(data),length(Lags)), -rep(Lags, each=k)))
if(I=="ADF") LagNames <- paste("D", LagNames,sep="_")
} else {
LagNames <- NULL
}
ECT<- if(model=="VECM") paste("ECT", if(r>1) 1:r else NULL, sep="") else NULL
Xminus1Names<- if(I=="ADF") paste(colnames(data),"-1",sep="") else NULL
BnamesInter<-switch(include,"const"="Intercept","none"=NULL,"trend"="Trend","both"=c("Intercept","Trend"))
if(!is.null(exogen)){
exo_names <- colnames(as.matrix(exogen))
exp_res <- "-[0-9]+|\\.l[0-9]+|ECT|Intercept|Trend"
if(any(grepl(exp_res, exo_names))) {
warning("Exogen contains reserved names (", exp_res, ". Changed to exo_x")
exo_names[grepl(exp_res, exo_names)] <- paste("exo", 1:sum(grepl(exp_res, exo_names)), sep="_")
}
if(any(is.null(exo_names))) exo_names <- paste("exo", 1:NCOL(exogen), sep="_")
} else {
exo_names <- NULL
}
Bnames<-c(ECT,BnamesInter,Xminus1Names, LagNames, exo_names)
colnames(B)<-Bnames
###Y and regressors matrix to be returned
naX<-rbind(matrix(NA, ncol=ncol(Z), nrow=T-t), Z)
rownames(naX)<-rownames(data)
YnaX<-cbind(data, naX)
colnames(YnaX)<-c(colnames(data),Bnames)
###Return outputs
model.specific<-list()
model.specific$nthresh<-0
if(model=="VECM"){
model.specific$beta<- betaLT
model.specific$coint <- betaLT
model.specific$r<-r
model.specific$estim<-estim
model.specific$LRinclude<-LRinclude
model.specific$beta.estimated<-beta.estimated
model.specific$estim <- estim
if(estim=="ML"){
model.specific$S00<-S00
model.specific$lambda<-va
}
}
inputArgs <- list()
inputArgs$I <- I
inputArgs$estim <- estim
inputArgs$LRinclude <- LRinclude
inputArgs$call <- match.call()
z<-list(residuals=res,
coefficients=B, k=k, t=t,T=T, npar=npar, nparB=ncol(B), type="linear",
fitted.values=fitted,
model.x=Z,
include=include,
lag=lag,
model=YnaX,
df.residual=t-npar/k,
exogen = !is.null(exogen),
num_exogen = if(!is.null(exogen)) NCOL(exogen) else 0,
model.specific=model.specific,
qr=lmReg$qr,
inputArgs = inputArgs)
if(model=="VAR"){
class(z)<-c("VAR","nlVar")
} else {
class(z)<-c("VECM","VAR", "nlVar")
I<-"diff"
}
attr(z, "varsLevel")<-I
attr(z, "model")<-model
return(z)
}
#### VECM function: wrapper to lineVar
#' Estimation of Vector error correction model (VECM)
#'
#' Estimate a VECM by either Engle-Granger (2OLS) or Johansen (MLE) method.
#'
#' This function is just a wrapper for the \code{\link{lineVar}}, with
#' model="VECM".
#'
#' More comprehensive functions for VECM are in package \pkg{vars}.
#' Differences with that package are: \describe{ \item{Engle-Granger
#' estimator}{The Engle-Granger estimator is available}
#' \item{Presentation}{Results are printed in a different ways, using a matrix
#' form} \item{lateX export}{The matrix of coefficients can be exported to
#' latex, with or without standard-values and significance stars}
#' \item{Prediction}{The \code{predict} method contains a \code{newdata}
#' argument allowing to compute rolling forecasts.} }
#'
#' Two estimators are available: the Engle-Granger two step approach
#' (\code{2OLS}) or the Johansen (\code{ML}). For the 2OLS, deterministic
#' regressors (or external variables if \code{LRinclude} is of class numeric) can be
#' added for the estimation of the cointegrating value and for the ECT. This is
#' only working when the beta value is not pre-specified.
#'
#' The arg beta is the cointegrating value, the cointegrating vector will be
#' taken as: (1, -beta).
#'
#' Note that the lag specification corresponds to the lags in the VECM
#' representation, not in the VAR (as is done in package vars or software
#' GRETL). Basically, a VAR with 2 lags corresponds here to a VECM with 1 lag.
#' The lag can be set to 0, although some methods (irf, fevd) won't work for this case.
#'
#' #'The arg \code{beta} allows to specify constrained cointegrating values, leading to
#' \eqn{ECT= \beta^{'}X_{t-1}}. It should be specified as a \eqn{K \times r} matrix. In case of
#' \eqn{r=1}, can also be specified as a vector. Note that the vector should be normalised,
#' with the first value to 1, and the next values showing the opposite sign in the long-run relationship \eqn{- \beta}.
#' In case the vector has \eqn{K-1} values, this is what \code{lineVar} is doing, setting \eqn{(1, - \beta)}.
#' Note finally one should provide values for all
#' the coefficients (eventually except for special case of r=1 and k-1), if you want to provide only part of the
#' parameters, and let the others be estimated, look at the functions in package urca.
#'
#'The eigenvector matrix \eqn{\beta} is normalised using the Phillips triangular representation,
#'see Hamilton (1994, p. 576) and Juselius (2006, p. 216), see \code{\link{coefA}} for more details.
#'
#' @param data multivariate time series (first row being first=oldest value)
#' @param lag Number of lags (in the VECM representation, see Details)
#' @param r Number of cointegrating relationships
#' @param include Type of deterministic regressors to include
#'@param beta for VECM only: user-specified cointegrating values, the cointegrating vector will be
#' taken as: (1, -\code{beta})
#'If NULL, will be estimated using the estimator specified in \code{estim}
#'@param LRinclude Type of deterministic regressors to include in the long-term
#'relationship. Can also be a matrix with exogeneous regressors (2OLS only).
#'@param estim Type of estimator: \code{2OLS} for the two-step approach or
#'\code{ML} for Johansen MLE
#'@param exogen Inclusion of exogenous variables (first row being first=oldest
#'value). Is either of same size than data (then automatically cut) or than
#'end-sample.
#'
#'@return An object of class \code{VECM} (and higher classes \code{VAR} and
#'\code{nlVar}) with methods:
#'\describe{
#'\item{Usual methods:}{Print, summary, residuals, fitted, vcov}
#'\item{Fit criteria:}{AIC, BIC, \code{\link{MAPE}}, \code{\link{mse}}, \code{\link[=logLik.VECM]{logLik}}
#'(the latter only for models estimated with MLE)}
#'\item{Prediction:}{predict and \code{\link{predict_rolling}}}
#'\item{coef extraction:}{Extract cointegrating/adjustment coefficients, \code{\link{coefA}}, \code{\link{coefB}} \code{\link{coefPI}}}
#'\item{VAR/VECM methods:}{Impulse response function (\code{\link{irf.VECM}}) and forecast error variance
#'decomposition (\code{\link[=fevd.nlVar]{fevd}})}
#'\item{LaTeX:}{toLatex} }
#'
#'@author Matthieu Stigler
#'
#'@references
#' Hamilton (1994) Time Series Analysis, Princeton University Press
#'
#' Juselius (2006) The Cointegrated VAR model, Oxford University Press
#'@seealso \code{\link{coefA}}, \code{\link{coefB}} and \code{\link{coefPI}}
#'to extract the relevant parameter matrices.
#'
#'\code{\link{lineVar}} \code{\link{TVAR}} and \code{\link{TVECM}} for
#'the corresponding threshold models. \code{\link{linear}} for the univariate AR
#'model.
#'@keywords ts
#'@export
#'@examples
#'
#'data(zeroyld)
#'data<-zeroyld
#'
#'#Fit a VECM with Engle-Granger 2OLS estimator:
#'vecm.eg<-VECM(zeroyld, lag=2)
#'
#'#Fit a VECM with Johansen MLE estimator:
#'vecm.jo<-VECM(zeroyld, lag=2, estim="ML")
#'
#'#compare results with package vars:
#'if(require(vars)) {
#' data(finland)
#' #check long coint values
#' all.equal(VECM(finland, lag=2, estim="ML", r=2)$model.specific$beta,
#' cajorls(ca.jo(finland, K=3, spec="transitory"), r=2) $beta, check.attributes=FALSE)
#' # check OLS parameters
#' all.equal(t(coefficients(VECM(finland, lag=2, estim="ML", r=2))),
#' coefficients(cajorls(ca.jo(finland, K=3, spec="transitory"), r=2)$rlm), check.attributes=FALSE)
#'
#'}
#'
#'
#'##export to Latex
#'toLatex(vecm.eg)
#'toLatex(summary(vecm.eg))
#'options("show.signif.stars"=FALSE)
#'toLatex(summary(vecm.eg), parenthese="Pvalue")
#'options("show.signif.stars"=TRUE)
#'
#'
#'
VECM<-function(data, lag,r=1, include = c( "const", "trend","none", "both"), beta=NULL, estim=c("2OLS", "ML"),LRinclude=c("none", "const", "trend","both"), exogen=NULL)
lineVar(data, lag, r=r,include = include, model="VECM" ,beta=beta, estim=estim,LRinclude=LRinclude,exogen=exogen)
###Testing
if(FALSE) { #usage example
###Hansen Seo data
library(tsDyn)
environment(lineVar)<-environment(star)
environment(summary.VAR)<-environment(star)
environment(toLatex.VAR)<-environment(star)
#data(zeroyld)
dat<-zeroyld
#tests
aVAR<-lineVar(dat[1:100,], lag=c(1,2), include="both", model="VAR")
#lag2, 2 thresh, trim00.05: 561.46
class(aVAR)
aVAR
print(aVAR)
logLik(aVAR)
AIC(aVAR)
BIC(aVAR)
deviance(aVAR)
coef(aVAR)
summary(aVAR)
toLatex(aVAR)
toLatex(summary(aVAR))
}
#' @export
print.VAR <- function(x,...){
print(coef(x))
}
#' @export
summary.VAR<-function(object, digits=4,...){
x<-object
r<-4
t<-x$t
k<-x$k
Sigma<-matrix(1/(object$df.residual)*crossprod(x$residuals),ncol=k)
betas <- x$coefficients
XX <- crossprod(x$model.x)
# cov.unscaled <- try(solve(XX), silent=TRUE)
cov.unscaled <- chol2inv(object$qr$qr)
if(inherits(cov.unscaled, "try-error")) {
Qr <- qr(x$model.x)
p1 <- 1:Qr$rank
cov.unscaled <- chol2inv(Qr$qr[p1, p1, drop = FALSE])
warning("Potential numerical unstability, beware of standard errors\n")
}
VarCovB <- Sigma %x% cov.unscaled
StDevB<-matrix(sqrt(diag(VarCovB)), nrow=k, byrow = TRUE)
Tvalue<-betas/StDevB
Pval <- 2* pt(abs(Tvalue), df=x$df.residual, lower.tail=FALSE)
symp <- symnum(Pval, corr=FALSE,cutpoints = c(0, .001,.01,.05, .1, 1), symbols = c("***","** ","* ",". "," "))
stars<-matrix(symp, nrow=nrow(Pval))
ab<-matrix(paste(myformat(betas,digits),"(", myformat(StDevB,digits),")",stars,sep=""), nrow=nrow(Pval))
dimnames(ab)<-dimnames(betas)
## assemble
coMat <- cbind(ct(betas), ct(StDevB), ct(Tvalue), ct(Pval))
colnames(coMat) <- c("Estimate", "Std. Error", "t value", "Pr(>|t|)")
rownames(coMat) <- paste(rep(eqNames(x), each=ncol(betas)),
gsub(" ", "", colnames(betas)), sep=":")
x$bigcoefficients<-ab
x$cov.unscaled<-cov.unscaled
x$sigma<-Sigma
x$StDev<-StDevB
x$Pvalues<-Pval
x$coefMat <- coMat
x$stars<-stars
x$starslegend<-symp
x$aic<-AIC.nlVar(x)
x$bic<-BIC.nlVar(x)
x$SSR<-deviance.nlVar(x)
class(x)<-c("summary.VAR", "VAR")
return(x)
}
#' @export
print.summary.VAR<-function(x,...){
cat("#############\n###Model", attr(x,"model"),"\n#############")
cat("\nFull sample size:",x$T, "\tEnd sample size:", x$t)
cat("\nNumber of variables:", x$k,"\tNumber of estimated slope parameters", x$npar)
cat("\nAIC",x$aic , "\tBIC", x$bic, "\tSSR", x$SSR)
if(attr(x,"model")=="VECM"){
cat("\nCointegrating vector ", if(x$model.specific$beta.estimated) paste("(estimated by ", x$model.specific$estim, "):\n", sep="") else "(fixed by user):\n", sep="")
print(t(x$model.specific$beta))
}
cat("\n\n")
print(noquote(x$bigcoefficients))
}
#' @export
vcov.VAR<-function(object, ...){
sum<-summary.VAR(object)
so<-sum$sigma %x% sum$cov.unscaled
co.names<-gsub(" ", "", colnames(coef(object)))
eq.names <- eqNames(object)
together.names<-paste(rep(eq.names,each= length(co.names)), co.names, sep=":")
dimnames(so)<-list(together.names, together.names)
so
}
#' @export
toLatex.VAR<-function(object,..., digits=4, parenthese=c("StDev","Pvalue"), label){
x<-object
if(attr(x,"model")=="VECM"&&x$model.specific$LRinclude!="none") stop("toLatex not implemented now for models with arg 'LRinclude' different from 'none'")
parenthese<-match.arg(parenthese)
if(inherits(x,"summary.VAR")){
a<-myformat(x$coefficients,digits, toLatex=TRUE)
inp<-switch(parenthese, "StDev"= x$StDev, "Pvalue"= x$Pvalues )
b<-myformat(inp ,digits,toLatex=TRUE)
if(getOption("show.signif.stars"))
stars<-paste("^{",x$stars,"}", sep="")
else
stars<-NULL
coeftoprint<-matrix(paste(a,"(",b,")",stars, sep=""),ncol=ncol(a), nrow=nrow(a))
}#end if x is of class summary
else{
coeftoprint <-myformat(x$coefficients, digits, toLatex=TRUE)}
varNames<-rownames(x$coefficients)
res<-character()
res[1]<-"%insert in the preamble and uncomment the line you want for usual /medium /small matrix"
res[2]<-"%\\usepackage{amsmath} \\newenvironment{smatrix}{\\begin{pmatrix}}{\\end{pmatrix}} %USUAL"
res[3]<-"%\\usepackage{amsmath} \\newenvironment{smatrix}{\\left(\\begin{smallmatrix}}{\\end{smallmatrix}\\right)} %SMALL"
res[4]<-"%\\usepackage{nccmath} \\newenvironment{smatrix}{\\left(\\begin{mmatrix}}{\\end{mmatrix}\\right)} %MEDIUM"
res[5]<-"\\begin{equation}"
if(!missing(label)) res[5]<- paste(res[5], "\\label{", label, "}", sep="")
res[6]<- "\\begin{smatrix} %explained vector"
###explained vector
if(attr(x, "varsLevel")=="diff")
res[7]<-TeXVec(paste("slashDelta X_{t}^{",seq(1, x$k),"}", sep=""))
else
res[7]<-TeXVec(paste("X_{t}^{",seq(1, x$k),"}", sep=""))
res[8]<- "\\end{smatrix}="
###ECT
ninc<-switch(x$include, "const"=1, "trend"=1,"none"=0, "both"=2)
if(attr(x,"model")=="VECM"){
r<-x$model.specific$r
len<-length(res)
if(r==1){
res[len+1]<-"+\\begin{smatrix} %ECT"
res[len+2]<-TeXVec(coeftoprint[,1]) #see nlVar-methods.R
res[len+3]<-"\\end{smatrix}ECT_{-1}"
}else{
res[len+1]<-"+\\begin{smatrix} %ECT"
res[(len+2):(len+x$k+1)]<-TeXMat(coeftoprint[,1:r]) #see nlVar-methods.R
res[len+x$k+2]<-"\\end{smatrix}ECT_{-1}"
}
}
###Const
a<-if(attr(x,"model")=="VECM") r else 0
res<-include(x, res, coeftoprint, skip=a) #nlVar-methods.R
###Lags
res<-LagTeX(res, x, coeftoprint, ninc+a) #nlVar-methods.R
res[length(res)+1]<-"\\end{equation}"
res<-gsub("slash", "\\", res, fixed=TRUE)
res<-res[res!="blank"]
return(structure(res, class="Latex"))
}
if(FALSE){
###TODO
#check if const/trend/both in LR rel and VECM makes sense!
#check for standaard deviation of coint vector whith ML estim!
#consistency between ML and OLS coint estimator?
}
if(FALSE) { #usage example
###Hansen Seo data
library(tsDyn)
#data(zeroyld)
dat<-zeroyld
environment(lineVar)<-environment(star)
environment(summary.VAR)<-environment(star)
aVAR<-lineVar(dat, lag=1, include="both", model="VAR")
aVAR<-lineVar(dat, lag=1, include="const", model="VECM", estim="ML", beta=0.98)
#lag2, 2 thresh, trim00.05: 561.46
aVAR
summary(aVAR)
sqrt(diag(summary(aVAR, cov=0)$sigma))
vcov.VAR(aVAR)
vcovHC.VAR(aVAR)
logLik(aVAR)
AIC(aVAR)
BIC(aVAR)
deviance(aVAR)
coef(aVAR)
environment(toLatex.VAR)<-environment(star)
toLatex(aVAR)
toLatex(summary(aVAR))
###Check VAR: comparing with vars
myVAR<-lineVar(dat, lag=1)
library(vars)
var<-VAR(dat, lag=1)
vaco1<-coef(var)$short.run[c(3,1,2),1]
vaco2<-coef(var)$long.run[c(3,1,2),1]
round(coef(myVAR),8)==round(rbind(vaco1, vaco2),8)
###Check Johansen MLE
myVECM<-lineVar(dat, lag=1, include="const", model="VECM", estim="ML")
summary(myVECM, digits=7)
#comparing with Hansen paper:reported in Gauss procedure is:
#coint vector: 1.02206: ok!
#coeff:
#comparing with vars package
a<-ca.jo(dat, spec="trans")
summary(a)
#same answer also!
set.seed(123)
rn <- rnorm(2*nrow(dat))
ex_1_n <- ex_1 <- rn[1:nrow(dat)]
ex_2_n <- ex_2 <- matrix(rn, ncol=2)
names(ex_1_n) <- "exoVar"
colnames(ex_2_n) <- c("exoVar1", "exoVar2")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_1)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_1_n)
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
colnames(ex_2_n) <- c("exoVar1", "a -1")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
colnames(ex_2_n) <- c("a.l2", "Trend")
lineVar(dat, lag=1, include="both", model="VAR", exogen=ex_2_n)
}
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