# R/blrtest.R In urca: Unit Root and Cointegration Tests for Time Series Data

```##
## blrtest
##
blrtest <- function(z, H, r){
if(!(class(z)=="ca.jo")){
stop("\nPlease, provide object of class 'ca.jo' as 'z'.\n")
}
if(r >= z@P || r < 1){
stop("\nCount of cointegrating relationships is out of allowable range.\n")
}
if(z@ecdet == "none"){
P <- z@P
}else{
P <- z@P + 1
}
r <- as.integer(r)
H <- as.matrix(H)
if(!(nrow(H)==P)){
stop("\nRow number of 'H' is unequal to VAR order.\n")
}
type <- "Estimation and testing under linear restrictions on beta"
N <- nrow(z@Z0)
M00 <- crossprod(z@Z0)/N
M11 <- crossprod(z@Z1)/N
MKK <- crossprod(z@ZK)/N
M01 <- crossprod(z@Z0, z@Z1)/N
M0K <- crossprod(z@Z0, z@ZK)/N
MK0 <- crossprod(z@ZK, z@Z0)/N
M10 <- crossprod(z@Z1, z@Z0)/N
M1K <- crossprod(z@Z1, z@ZK)/N
MK1 <- crossprod(z@ZK, z@Z1)/N
M11inv <- solve(M11)
S00 <- M00 - M01%*%M11inv%*%M10
S0K <- M0K - M01%*%M11inv%*%M1K
SK0 <- MK0 - MK1%*%M11inv%*%M10
SKK <- MKK - MK1%*%M11inv%*%M1K
Ctemp <- chol(t(H)%*%SKK%*%H, pivot=TRUE)
pivot <- attr(Ctemp, "pivot")
oo <- order(pivot)
C <- t(Ctemp[,oo])
Cinv <- solve(C)
S00inv <- solve(S00)
valeigen <- eigen(Cinv%*%t(H)%*%SK0%*%S00inv%*%S0K%*%H%*%t(Cinv))
e <- valeigen\$vector
V <- H%*%t(Cinv)%*%e
Vorg <- V
idx <- ncol(V)
V <- sapply(1:idx, function(x) V[,x]/V[1,x])
W <- S0K%*%V%*%solve(t(V)%*%SKK%*%V)
PI <- W %*% t(V)
DELTA <- S00 - S0K%*%V%*%solve(t(V)%*%SKK%*%V)%*%t(V)%*%SK0
GAMMA <- M01%*%M11inv - PI%*%MK1%*%M11inv
lambda.res <- valeigen\$values
lambda <- z@lambda
teststat <- N*sum(log((1-lambda.res[1:r])/(1-lambda[1:r])))
df <- r*(P - ncol(H))
pval <- c(1-pchisq(teststat, df), df)
new("cajo.test", Z0=z@Z0, Z1=z@Z1, ZK=z@ZK, ecdet=z@ecdet, H=H, A=NULL, B=NULL, type=type, teststat=teststat, pval=pval, lambda=lambda.res, Vorg=Vorg, V=V, W=W, PI=PI, DELTA=DELTA, DELTA.bb=NULL, DELTA.ab=NULL, DELTA.aa.b=NULL, GAMMA=GAMMA, test.name="Johansen-Procedure")
}
```

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urca documentation built on May 2, 2019, 2:08 a.m.