Purpose
Does Augmented ADF solve the problem where residuals can be correlated ?

I am going to run the same code and include higher order lags and see how many of them are stationary ?

> sector.tests <- samesector
> sector.tests$uroot <- 0
> sector.tests$kpss <- 0
> npairs <- dim(samesector)[1]
> pair <- 1
> for (pair in 1:npairs) {
+     a <- samesector[pair, "tickeri"]
+     b <- samesector[pair, "tickerj"]
+     y1 <- (security.db1[, a])
+     x1 <- (security.db1[, b])
+     temp1 <- (grangertest(y1 ~ x1, order = 1))[2, 4]
+     if (temp1 < 0.05) {
+         y1 <- (security.db1[, a])
+         x1 <- (security.db1[, b])
+         fit.1 <- lm(y1 ~ x1 + 0)
+         error <- residuals(fit.1)
+         time <- 1:length(error)
+         fit.2 <- lm(error ~ time)
+         if (coef(summary(fit.2))[1, 4] > 0.05 & coef(summary(fit.2))[2,
+             4] > 0.05) {
+             type.1 <- "nc"
+             type.2 <- "mu"
+             error.transf <- error
+         }
+         if (coef(summary(fit.2))[1, 4] < 0.05 & coef(summary(fit.2))[2,
+             4] < 0.05) {
+             type.1 <- "ct"
+             type.2 <- "tau"
+             error.transf <- resid(fit.2)
+         }
+         if (coef(summary(fit.2))[1, 4] < 0.05 & coef(summary(fit.2))[2,
+             4] > 0.05) {
+             type.1 <- "c"
+             type.2 <- "mu"
+             error.transf <- error - mean(error)
+         }
+         if (coef(summary(fit.2))[1, 4] > 0.05 & coef(summary(fit.2))[2,
+             4] < 0.05) {
+             type.1 <- "c"
+             type.2 <- "mu"
+             error.transf <- error
+         }
+         t1 <- unitrootTest(error.transf, lags = 1, type = "ct")@test$p.value[1]
+         kpfit <- urkpssTest(error.transf, type.2, "short")
+         if (kpfit@test$test@teststat > kpfit@test$test@cval[2]) {
+             t2 <- 1
+         }
+         else {
+             t2 <- 0
+         }
+         sector.tests$uroot[pair] <- t1
+         sector.tests$kpss[pair] <- t2
+     }
+     temp2 <- (grangertest(x1 ~ y1, order = 1))[2, 4]
+     if (temp1 > 0.05 & temp2 < 0.05) {
+         y1 <- (security.db1[, b])
+         x1 <- (security.db1[, a])
+         fit.1 <- lm(y1 ~ x1 + 0)
+         error <- residuals(fit.1)
+         time <- 1:length(error)
+         fit.2 <- lm(error ~ time)
+         if (coef(summary(fit.2))[1, 4] > 0.05 & coef(summary(fit.2))[2,
+             4] > 0.05) {
+             type.1 <- "nc"
+             type.2 <- "mu"
+             error.transf <- error
+         }
+         if (coef(summary(fit.2))[1, 4] < 0.05 & coef(summary(fit.2))[2,
+             4] < 0.05) {
+             type.1 <- "ct"
+             type.2 <- "tau"
+             error.transf <- resid(fit.2)
+         }
+         if (coef(summary(fit.2))[1, 4] < 0.05 & coef(summary(fit.2))[2,
+             4] > 0.05) {
+             type.1 <- "c"
+             type.2 <- "mu"
+             error.transf <- error - mean(error)
+         }
+         if (coef(summary(fit.2))[1, 4] > 0.05 & coef(summary(fit.2))[2,
+             4] < 0.05) {
+             type.1 <- "c"
+             type.2 <- "mu"
+             error.transf <- error
+         }
+         t1 <- unitrootTest(error.transf, lags = 4, type = type.1)@test$p.value[1]
+         kpfit <- urkpssTest(error.transf, type.2, "short")
+         if (kpfit@test$test@teststat > kpfit@test$test@cval[2]) {
+             t2 <- 1
+         }
+         else {
+             t2 <- 0
+         }
+         sector.tests$uroot[pair] <- t1
+         sector.tests$kpss[pair] <- t2
+     }
+     if (temp1 > 0.05 & temp2 > 0.05) {
+         sector.tests$uroot[pair] <- 999
+         sector.tests$kpss[pair] <- 999
+     }
+ }
> test <- sector.tests[sector.tests$uroot != 999, ]
> dim(test)
[1] 127  12
> length(which(test$uroot < 0.05))
[1] 39

Out of 127 pairs, there are about 39 pairs which pass unit root tests
5 PAIRS ARE KNOCKED OFF when unitrootTest is used with about 4 lags.