#Question 2

#part a

#Question 1
data1 = read.table("TPdata.txt",header=TRUE)
time = ts(data1$YER, frequency=4, start=c(1970,1))

#Part a

LYER <- log(data1$YER)
DLYER <- diff(LYER)
LPCR <- log(data1$PCR)
DLPCR <- diff(LPCR)
plot(DLYER, type="l") #YES
plot(DLPCR, type="l") #YES

#Part b

time2 = ts(LYER, frequency=4, start=c(1970,1))
time3 = ts(LPCR, frequency=4, start=c(1970,1))
time2
time3
library(urca)
adf2 = ur.df(time2, type="drift", selectlags="BIC")
summary(adf2) # -1.66 and test stat: -2.88. unit root at 1% sign level for LYER
adf3 = ur.df(time3, type="drift", selectlags="BIC")
summary(adf3) # -3.5787 and test stat: -2.88.(reject) no unit root at 1% sign levelfor LPCR


# Part c
reg= lm(LPCR~LYER)
summary(reg)
e = reg$residuals
adf4 = ur.df(e, type="drift", selectlags="BIC")
summary(adf4) # -2.7343 and test statistic -2.88. no cointegration (reject) the nul at 10% sing level