R/ablrtest.R

In urca: Unit Root and Cointegration Tests for Time Series Data

##
## ablrtest
##
ablrtest <- function(z, H, A, r){
    if(!inherits(z , "ca.jo")){
      stop("\nPlease, provide object of class 'ca.jo' as 'z'.\n")
    }
    r <- as.integer(r)
    A <- as.matrix(A)
    H <- as.matrix(H)
    if(!(nrow(A)==z@P)){
      stop("\nRow number of 'A' is unequal to VAR order.\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
    }
    if(!(nrow(H)==P)){
      stop("\nRow number of 'H' is unequal to VAR order.\n")
    }
    type <- "Estimation and testing under linear restrictions on alpha and beta"
    N <- nrow(z@Z0)
    B <- qr.Q(qr(A), complete=TRUE)[,-c(1:ncol(A))]
    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
    Sab <- t(A)%*%S00%*%B
    Skb <- t(S0K)%*%B
    Sbb <- t(B)%*%S00%*%B
    Sbbinv <- solve(Sbb)
    RA <- z@R0%*%A - z@R0%*%B%*%Sbbinv%*%t(Sab)
    RK <- z@RK - z@R0%*%B%*%Sbbinv%*%t(Skb)
    Saa.b <- crossprod(RA, RA)/N
    Sak.b <- crossprod(RA, RK)/N
    Ska.b <- crossprod(RK, RA)/N
    Skk.b <- crossprod(RK, RK)/N
    Ctemp <- chol(t(H)%*%Skk.b%*%H, pivot=TRUE)
    pivot <- attr(Ctemp, "pivot")
    oo <- order(pivot)
    C <- t(Ctemp[,oo])
    Cinv <- solve(C)
    Saa.binv <- solve(Saa.b)
    valeigen <- eigen(Cinv%*%t(H)%*%Ska.b%*%Saa.binv%*%Sak.b%*%H%*%t(Cinv))
    lambda.res <- valeigen$values
    e <- valeigen$vector
    V <- H%*%t(Cinv)%*%e
    Vorg <- V
    idx <- 1:r
    V <- sapply(idx, function(x) V[ , x] / V[1,x])
    PHI <- solve(t(A)%*%A)%*%Sak.b%*%Vorg
    ALPHA <- as.matrix(A%*%PHI)
    ALPHAorg <- ALPHA
    ALPHA <- sapply(idx, function(x) ALPHA[ , x] * Vorg[1,x])
    PI <- ALPHA %*% t(V)
    GAMMA <- M01%*%M11inv - PI%*%MK1%*%M11inv
    DELTA.bb <- Sbb
    DELTA.ab <- Sab - t(A)%*%ALPHA%*%t(V)%*%Skb
    DELTA.aa.b <- Saa.b - t(A)%*%ALPHA%*%t(ALPHA)%*%A
    lambda <- z@lambda
    teststat <- N*sum(log((1-lambda.res[1:r])/(1-lambda[1:r])))
    df <- r*(z@P - ncol(A)) + r*(z@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=A, B=B, type=type, teststat=teststat, pval=pval, lambda=lambda.res, Vorg=Vorg, V=V, W=ALPHA, PI=PI, DELTA=NULL, DELTA.bb=DELTA.bb, DELTA.ab=DELTA.ab, DELTA.aa.b=DELTA.aa.b, GAMMA=GAMMA, test.name="Johansen-Procedure")
}