# ARIMA Time Series Modeling
require(fpp)

data = read.csv('http://ucanalytics.com/blogs/wp-content/uploads/2015/07/Sales-and-Marketing.csv')

data1<-ts(data[,2],start = c(2011,1),frequency = 12)
Marketing<-ts(data[,3],start = c(2011,1),frequency = 12)

plot(data1)
plot(Marketing)
plot(as.vector(Marketing),as.vector(data1))
cor(Marketing,data1)

data2<-(diff(data1))
adv<-diff(Marketing)
plot(as.vector(adv),as.vector(data2))
cor(data2,adv)
cor(data2[2:47],adv[1:46])
plot(data2[2:47],adv[1:46])

Advert <- cbind(adv[],
                c(NA,adv[1:46]),
                c(NA,NA,adv[1:45]),
                c(NA,NA,NA,adv[1:44]))
colnames(Advert) <- paste("AdLag",0:3,sep="")

plot(as.vector(Advert[,1]),as.vector(data2),xlab = "Marketing Expense",ylab="Tractor Sales")

fit<- auto.arima(data2)
fit1 <- auto.arima(data2[4:47], xreg=Advert[4:47,1], d=0)
fit2 <- auto.arima(data2[4:47], xreg=Advert[4:47,1:2], d=0)
fit3 <- auto.arima(data2[4:47], xreg=Advert[4:47,1:3], d=0)
fit4 <- auto.arima(data2[4:47], xreg=Advert[4:47,1:4], d=0)

summary(fit) 
summary(fit1)
summary(fit2)