library(openxlsx)

sample1<-read.xlsx("http://kanggc.iptime.org/book/data/gdp-q.xlsx")

y.ts<-ts(sample1$GDP, start=c(2013,1), frequency=4)
y.ts

lagy4<-lag(y.ts, k=-4)
lagy4

gy4<-(y.ts-lagy4)/lagy4*100
gy4

ly.ts<-log(y.ts)
ly.ts

gly4<-(ly.ts-lag(ly.ts, k=-4))*100
gly4

plot(gy4, type="l", lwd=3, col="red", main="Exact Growth Rate vs. Approx. Growth Rate of GDP")
lines(gly4, lwd=3, lty=6, col="green")