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##
## cajolst
##
cajolst <- function (x, trend = TRUE, K = 2, season = NULL)
{
x <- as.matrix(x)
K <- as.integer(K)
if(K < 2){
stop("\nK must be at least K=2.\n")
}
P <- ncol(x)
arrsel <- P
N <- nrow(x)
if (!is.null(season)) {
s <- season - 1
}
else {
s <- 0
}
if (N * P < P + s * P + K * P^2 + P * (P + 1)/2)
stop("\nInsufficient degrees of freedom.\n")
if (P > 5)
warning("\nToo many variables, critical values cannot be computed.\n")
if (!(is.null(season))) {
dum <- (diag(season) - 1/season)[, -season]
dums <- dum
while (nrow(dums) < N) {
dums <- rbind(dums, dum)
}
dums <- dums[1:N, ]
if (NA %in% x) {
idx.NA <- 1:N
ind <- as.logical(sapply(idx.NA, function(z) sum(is.na(x[z,
]) * 1)))
ind2 <- ind * (1:N)
dums <- dums[-ind2, ]
}
}
x2 <- na.omit(x)
Ntot <- nrow(x2)
y <- embed(x2, (K + 1))
rhs <- y[, -c(1:P)]
if (!trend) {
rhs <- y[, -c(1:P)]
}
else {
trd <- seq(K + 1, nrow(y) + K)
rhs <- cbind(trd, y[, -c(1:P)])
}
N <- nrow(y)
if (!(is.null(season))) {
rhs <- cbind(dums[-(1:K), ], rhs)
}
lhs <- y[, 1:P]
idx <- 1:(N - 1)
tau <- function(t) {
dt <- c(rep(0, t), rep(1, N - t))
det(crossprod(resid(lm(lhs ~ dt + rhs))))
}
tau.hat <- sapply(idx, tau)
tau.opt <- which.min(tau.hat) + K
tau.bp <- tau.opt + 1
dt <- c(rep(0, tau.opt), rep(1, N - tau.opt))
if(!trend & is.null(season)){
rhs.aux <- dt
} else {
rhs.aux <- cbind(dt, rhs[, -c((ncol(rhs)-K*ncol(x)+1):ncol(rhs))])
}
reg.opt <- lm(lhs ~ rhs.aux)
dt <- c(rep(0, tau.opt), rep(1, Ntot - tau.opt))
uv <- c(rep(1, Ntot))
if (!trend) {
if (!is.null(season)) {
yfit <- x - uv%*%t(coef(reg.opt)[1, ]) - dt %*% t(coef(reg.opt)[2, ]) - dums %*% coef(reg.opt)[3:(2 + season - 1), ]
}else{
yfit <- x - uv%*%t(coef(reg.opt)[1, ]) - dt %*% t(coef(reg.opt)[2, ])
}
}else if (trend){
trd <- 1:Ntot
if (!is.null(season)) {
yfit <- x - uv%*%t(coef(reg.opt)[1, ]) - dt %*% t(coef(reg.opt)[2, ]) - dums %*% coef(reg.opt)[3:(2 + season - 1), ] - trd %*% t(coef(reg.opt)[season + 2, ])
}else{
yfit <- x - uv%*%t(coef(reg.opt)[1, ]) - dt %*% t(coef(reg.opt)[2, ]) - trd %*% t(coef(reg.opt)[3, ])
}
}
x <- na.omit(yfit)
N <- nrow(x)
spec <- "transitory"
Z <- embed(diff(x), K)
Z0 <- Z[, 1:P]
Z1 <- Z[, -c(1:P)]
ZK <- x[-N, ][K:(N - 1), ]
idx <- 0:(P - 1)
if (trend) {
cvals <- matrix(c(5.423, 13.784, 25.931, 42.083, 61.918, 6.785, 15.826, 28.455, 45.204, 65.662, 10.042, 19.854, 33.757, 51.601, 73.116), nrow=5, ncol=3)
model <- "with linear trend in shift correction"
}else if(!trend){
cvals <- matrix(c(2.996, 10.446, 21.801, 36.903, 55.952, 4.118, 12.276, 24.282, 40.067, 59.749, 6.888, 16.420, 29.467, 46.305, 67.170), nrow=5, ncol=3)
model <- "without linear trend in shift correction"
}
N <- nrow(Z0)
M00 <- crossprod(Z0)/N
M11 <- crossprod(Z1)/N
MKK <- crossprod(ZK)/N
M01 <- crossprod(Z0, Z1)/N
M0K <- crossprod(Z0, ZK)/N
MK0 <- crossprod(ZK, Z0)/N
M10 <- crossprod(Z1, Z0)/N
M1K <- crossprod(Z1, ZK)/N
MK1 <- crossprod(ZK, Z1)/N
M11inv <- solve(M11)
R0 <- Z0 - t(M01 %*% M11inv %*% t(Z1))
RK <- ZK - t(MK1 %*% M11inv %*% t(Z1))
S00 <- M00 - M01 %*% M11inv %*% M10
S0K <- M0K - M01 %*% M11inv %*% M1K
SK0 <- MK0 - MK1 %*% M11inv %*% M10
SKK <- MKK - MK1 %*% M11inv %*% M1K
Ctemp <- chol(SKK, pivot = TRUE)
pivot <- attr(Ctemp, "pivot")
oo <- order(pivot)
C <- t(Ctemp[, oo])
Cinv <- solve(C)
S00inv <- solve(S00)
valeigen <- eigen(Cinv %*% SK0 %*% S00inv %*% S0K %*% t(Cinv))
lambda <- valeigen$values
e <- valeigen$vector
V <- t(Cinv) %*% e
rownames(V) <- colnames(x)
Vorg <- V
V <- sapply(1:P, function(x) V[, x]/V[1, x])
W <- S0K %*% V %*% solve(t(V) %*% SKK %*% V)
PI <- S0K %*% solve(SKK)
DELTA <- S00 - S0K %*% V %*% solve(t(V) %*% SKK %*% V) %*%
t(V) %*% SK0
GAMMA <- M01 %*% M11inv - PI %*% MK1 %*% M11inv
type <- "trace statistic"
teststat <- as.matrix(rev(sapply(idx, function(x) N * sum(log(1 + lambda[(x + 1):P])))))
colnames(teststat) <- "trace"
if (arrsel > 5) {
cval <- NULL
} else {
cval <- round(cvals[1:arrsel, ], 2)
colnames(cval) <- c("10pct", "5pct", "1pct")
rownames(cval) <- c(paste("r <= ", (arrsel - 1):1, " |", sep = ""), "r = 0 |")
}
temp1 <- NULL
for (i in 1:(K - 1)) {
temp <- paste(colnames(x), ".dl", i, sep = "")
temp1 <- c(temp1, temp)
}
colnames(Z1) <- temp1
colnames(ZK) <- paste(colnames(x), "l1", sep=".")
colnames(Z0) <- paste(colnames(x), "d", sep=".")
colnames(V) <- colnames(ZK)
rownames(V) <- colnames(ZK)
colnames(W) <- colnames(V)
rownames(W) <- colnames(x)
colnames(Vorg) <- colnames(V)
rownames(Vorg) <- rownames(V)
rownames(PI) <- colnames(x)
colnames(PI) <- colnames(W)
colnames(R0) <- paste("R0", colnames(Z0), sep = ".")
colnames(RK) <- paste("RK", colnames(ZK), sep = ".")
new("ca.jo", x = x, Z0 = Z0, Z1 = Z1, ZK = ZK, type = type, model = model, ecdet = "none", lag = K, P = arrsel,
season = season, dumvar = NULL, cval = cval, teststat = as.vector(teststat),
lambda = lambda, Vorg = Vorg, V = V, W = W, PI = PI,
DELTA = DELTA, GAMMA = GAMMA, R0 = R0, RK = RK, bp = tau.bp,
test.name = "Johansen-Procedure")
}
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