# R code for HW 6

# Problem 1:  

library(TSA); data(JJ)

#(a)
plot(JJ,type='o')
plot(log(JJ),type='o')

#(b)
plot(diff(log(JJ)),type='o')


#(c)
acf(diff(log(JJ)))

# (d)

 plot(diff(diff(log(JJ)),4),type='o')

# (e)
acf(diff(diff(log(JJ)),4))
pacf(diff(diff(log(JJ)),4))

# (f)

m1.jj=arima(log(JJ),order=c(0,1,1),seasonal=list(order=c(0,1,1),period=4))
m1.jj

#(g)
tsdiag(m1.jj)

#(h)
predict(m1.jj,n.ahead=8)

plot(m1.jj,n.ahead=8,col='red',xlab='Year',type='o',
ylab=expression(Earnings),
main=expression(Forecasts~~'for'~~the~~JJ~~Model))

## Problem 2:

# (a)

data(boardings)
log.boardings = boardings[,1]
plot(log.boardings,ylab='Log(boardings)',xlab='Year', )
points(y=log.boardings,x=time(boardings),pch=as.vector(season(boardings)))

# (b)

acf(log.boardings)

# (c)

m1.bd=arima(log.boardings,order=c(0,0,3),seasonal=list(order=c(1,0,0),period=12))
m1.bd

# (d)

m1.bd1=arima(log.boardings,order=c(0,0,4),seasonal=list(order=c(1,0,0),period=12))
m1.bd1

## Problem 3

data(bluebirdlite)

log.sales=bluebirdlite[,1]
price=bluebirdlite[,2]
chip.m1=lm(log.sales~price,data=bluebirdlite)
summary(chip.m1)

prewhiten(log.sales,price)  # shows lag=0 cross-correlation

# ACF tails off:
acf(residuals(chip.m1),ci.type='ma')

# PACF cuts off after lag 4:
pacf(residuals(chip.m1))

# Suggests AR(4) ?

# EACF suggests ARMA(1,1)?
eacf(residuals(chip.m1))


chip.m2=arima(log.sales,order=c(1,0,1),xreg=data.frame(price))
chip.m2

chip.m3=arima(log.sales,order=c(4,0,0),xreg=data.frame(price))
chip.m3

# Overfit:
chip.m4=arima(log.sales,order=c(4,0,1),xreg=data.frame(price))
chip.m4

# Worse!  Stay with ARMA(4,0).

# model diagnostics can be done by running the tsdiag command.
tsdiag(chip.m3)  # looks good.

## Problem 4:

data(deere1)
m1.deere = arima(deere1,order=c(2,0,0))
m1.deere

tsdiag(m1.deere)

detectAO(m1.deere)
detectIO(m1.deere)

m2.deere = arima(deere1,order=c(2,0,0), io=c(27))
m2.deere

tsdiag(m2.deere)