Augmented ADF
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) {
+ print(pair)
+ 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 = 4, 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
+ }
+ }
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> test <- sector.tests[sector.tests$uroot != 999, ] > dim(test) [1] 127 12 |
> length(which(test$uroot < 0.05)) [1] 35 |
Out of 127 pairs, there are about 35 pairs which pass unit root tests
9 PAIRS ARE KNOCKED OFF when unitrootTest is used with about 4 lags.