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##
## Augmented-Dickey-Fuller Test
##
ur.df <- function (y, type = c("none", "drift", "trend"), lags = 1, selectlags = c("Fixed", "AIC", "BIC"))
{
selectlags<-match.arg(selectlags)
type <- match.arg(type)
if (ncol(as.matrix(y)) > 1)
stop("\ny is not a vector or univariate time series.\n")
if (any(is.na(y)))
stop("\nNAs in y.\n")
y <- as.vector(y)
lag <- as.integer(lags)
if (lag < 0)
stop("\nLags must be set to an non negative integer value.\n")
CALL <- match.call()
DNAME <- deparse(substitute(y))
x.name <- deparse(substitute(y))
lags <- lags + 1
z <- diff(y)
n <- length(z)
x <- embed(z, lags)
z.diff <- x[, 1]
z.lag.1 <- y[lags:n]
tt <- lags:n
if (lags > 1) {
if(selectlags!="Fixed"){
critRes<-rep(NA, lags)
for(i in 2:(lags)){
z.diff.lag = x[, 2:i]
if (type == "none")
result <- lm(z.diff ~ z.lag.1 - 1 + z.diff.lag)
if (type == "drift")
result <- lm(z.diff ~ z.lag.1 + 1 + z.diff.lag)
if (type == "trend")
result <- lm(z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
critRes[i]<-AIC(result, k = switch(selectlags, "AIC" = 2, "BIC" = log(length(z.diff))))
}
lags<-which.min(critRes)
}
z.diff.lag = x[, 2:lags]
if (type == "none") {
result <- lm(z.diff ~ z.lag.1 - 1 + z.diff.lag)
tau <- coef(summary(result))[1, 3]
teststat <- as.matrix(tau)
colnames(teststat) <- 'tau1'
}
if (type == "drift") {
result <- lm(z.diff ~ z.lag.1 + 1 + z.diff.lag)
tau <- coef(summary(result))[2, 3]
phi1.reg <- lm(z.diff ~ -1 + z.diff.lag)
phi1 <- anova(phi1.reg, result)$F[2]
teststat <- as.matrix(t(c(tau, phi1)))
colnames(teststat) <- c('tau2', 'phi1')
}
if (type == "trend") {
result <- lm(z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
tau <- coef(summary(result))[2, 3]
phi2.reg <- lm(z.diff ~ -1 + z.diff.lag)
phi3.reg <- lm(z.diff ~ z.diff.lag)
phi2 <- anova(phi2.reg, result)$F[2]
phi3 <- anova(phi3.reg, result)$F[2]
teststat <- as.matrix(t(c(tau, phi2, phi3)))
colnames(teststat) <- c('tau3', 'phi2', 'phi3')
}
}
else {
if (type == "none") {
result <- lm(z.diff ~ z.lag.1 - 1)
tau <- coef(summary(result))[1, 3]
teststat <- as.matrix(tau)
colnames(teststat) <- 'tau1'
}
if (type == "drift") {
result <- lm(z.diff ~ z.lag.1 + 1)
phi1.reg <- lm(z.diff ~ -1)
phi1 <- anova(phi1.reg, result)$F[2]
tau <- coef(summary(result))[2, 3]
teststat <- as.matrix(t(c(tau, phi1)))
colnames(teststat) <- c('tau2', 'phi1')
}
if (type == "trend") {
result <- lm(z.diff ~ z.lag.1 + 1 + tt)
phi2.reg <- lm(z.diff ~ -1)
phi3.reg <- lm(z.diff ~ 1)
phi2 <- anova(phi2.reg, result)$F[2]
phi3 <- anova(phi3.reg, result)$F[2]
tau <- coef(summary(result))[2, 3]
teststat <- as.matrix(t(c(tau, phi2, phi3)))
colnames(teststat) <- c('tau3', 'phi2', 'phi3')
}
}
rownames(teststat) <- 'statistic'
testreg <- summary(result)
res <- residuals(testreg)
if(n < 25)
rowselec <- 1
if(25 <= n & n < 50)
rowselec <- 2
if(50 <= n & n < 100)
rowselec <- 3
if(100 <= n & n < 250)
rowselec <- 4
if(250 <= n & n < 500)
rowselec <- 5
if(n >= 500)
rowselec <- 6
if (type == "none"){
cval.tau1 <- rbind(
c(-2.66, -1.95, -1.60),
c(-2.62, -1.95, -1.61),
c(-2.60, -1.95, -1.61),
c(-2.58, -1.95, -1.62),
c(-2.58, -1.95, -1.62),
c(-2.58, -1.95, -1.62))
cvals <- t(cval.tau1[rowselec, ])
testnames <- 'tau1'
}
if (type == "drift"){
cval.tau2 <- rbind(
c(-3.75, -3.00, -2.63),
c(-3.58, -2.93, -2.60),
c(-3.51, -2.89, -2.58),
c(-3.46, -2.88, -2.57),
c(-3.44, -2.87, -2.57),
c(-3.43, -2.86, -2.57))
cval.phi1 <- rbind(
c(7.88, 5.18, 4.12),
c(7.06, 4.86, 3.94),
c(6.70, 4.71, 3.86),
c(6.52, 4.63, 3.81),
c(6.47, 4.61, 3.79),
c(6.43, 4.59, 3.78))
cvals <- rbind(
cval.tau2[rowselec, ],
cval.phi1[rowselec, ])
testnames <- c('tau2', 'phi1')
}
if (type == "trend"){
cval.tau3 <- rbind(
c(-4.38, -3.60, -3.24),
c(-4.15, -3.50, -3.18),
c(-4.04, -3.45, -3.15),
c(-3.99, -3.43, -3.13),
c(-3.98, -3.42, -3.13),
c(-3.96, -3.41, -3.12))
cval.phi2 <- rbind(
c(8.21, 5.68, 4.67),
c(7.02, 5.13, 4.31),
c(6.50, 4.88, 4.16),
c(6.22, 4.75, 4.07),
c(6.15, 4.71, 4.05),
c(6.09, 4.68, 4.03))
cval.phi3 <- rbind(
c(10.61, 7.24, 5.91),
c( 9.31, 6.73, 5.61),
c( 8.73, 6.49, 5.47),
c( 8.43, 6.49, 5.47),
c( 8.34, 6.30, 5.36),
c( 8.27, 6.25, 5.34))
cvals <- rbind(
cval.tau3[rowselec, ],
cval.phi2[rowselec, ],
cval.phi3[rowselec, ])
testnames <- c('tau3', 'phi2', 'phi3')
}
colnames(cvals) <- c("1pct", "5pct", "10pct")
rownames(cvals) <- testnames
new("ur.df", y = y, model = type, cval=cvals, lags=lag, teststat = teststat, testreg=testreg, res=res, test.name="Augmented Dickey-Fuller Test")
}
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