library(openxlsx)
excel_sample1<-read.xlsx("http://kanggc.iptime.org/book/data/sample1-n.xlsx")
year<-excel_sample1$year
gdp<-excel_sample1$gdp
consumption<-excel_sample1$consumption

graphics.off()
par("mar")
par(mar=c(1,1,1,1))

y.ts<-ts(gdp, start=2000, end=2016, frequency=1) 
c.ts<-ts(consumption, start=2000, end=2016, frequency=1) 

lagy<-lag(y.ts, k=-1) 
lagc<-lag(c.ts, k=-1) 

gy<-(y.ts-lagy)/lagy  
gc<-(c.ts-lagc)/lagc  

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

gly<-ly.ts-lag(ly.ts, k=-1) 
glc<-lc.ts-lag(lc.ts, k=-1)

(y<-cbind(gy, gly))
(c<-cbind(gc, glc))


par(mfrow=c(2,1))

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

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