library(astsa)

library(TSA)

#1
data(deere3)


m1.deere3=arima(deere3,order=c(1,0,0)) #AR(1)
plot(m1.deere3, n.ahead=10,type='b',xlab='Time',ylab='Deere3')
abline(h=coef(m1.deere3)[names(coef(m1.deere3))=='intercept'])

predict(m1.deere3, n.ahead=10)



#2 

data(days)

m1.days=arima(days,order=c(0,0,2))  #MA(2)
plot(m1.days, n.ahead=10,type='b',xlab='Time',ylab='Duration')
abline(h=coef(m1.days)[names(coef(m1.days))=='intercept'])

predict(m1.days, n.ahead=10)

days.adj=days; days.adj[c(63,106,129)]=35; 

m2.days=arima(days.adj,order=c(0,0,2))
plot(m2.days, n.ahead=10,type='b',xlab='Time',ylab='Duration')
abline(h=coef(m2.days)[names(coef(m2.days))=='intercept'])

predict(m2.days, n.ahead=10)

#3

data(robot)


m1.robot=arima(robot,order=c(0,1,1))  #IMA(1,1)
plot(m1.robot, n1=315, n.ahead=5,type='b',xlab='Time',ylab='Robot')
abline(h=coef(m1.robot)[names(coef(m1.robot))=='intercept'])

predict(m1.robot, n.ahead=5)

### Note: the 'sarima.for' function will produce results like:

sarima.for(robot, 5, 0,1,1)

x11()

m1.robot=arima(robot,order=c(1,0,1))  #ARMA(1,1)
plot(m1.robot, n1=315, n.ahead=5,type='b',xlab='Time',ylab='Robot')
abline(h=coef(m1.robot)[names(coef(m1.robot))=='intercept'])

predict(m1.robot, n.ahead=5)

#4

data(electricity)

month.=season(electricity) 
# the period sign is included to make the printout from
# the commands two lines below clearer
model.s=lm(log(electricity)~time(electricity) + month.-1) # -1 removes the intercept term 
summary(model.s)

#Predicted January 2006 logged value:

2.526e-02*2006-3.783e+01

#or equivalently:
future.time<-2006
as.numeric( coef(model.s) %*% c(future.time,1,0,0,0,0,0,0,0,0,0,0,0) )

#Predicted Feb. 2006 logged value:

2.526e-02*2006.083-3.795e+01

#or equivalently:
future.time<-2006.083
as.numeric( coef(model.s) %*% c(future.time,0,1,0,0,0,0,0,0,0,0,0,0) )

#Predicted March 2006 logged value:

2.526e-02*2006.167-3.792e+01

#or equivalently:
future.time<-2006.167
as.numeric( coef(model.s) %*% c(future.time,0,0,1,0,0,0,0,0,0,0,0,0) )

#Predicted January 2006 value:

exp(2.526e-02*2006-3.783e+01)

#or equivalently:
future.time<-2006
exp(as.numeric( coef(model.s) %*% c(future.time,1,0,0,0,0,0,0,0,0,0,0,0) ))

#Predicted Feb. 2006 value:

exp(2.526e-02*2006.083-3.795e+01)

#or equivalently:
future.time<-2006.083
exp(as.numeric( coef(model.s) %*% c(future.time,0,1,0,0,0,0,0,0,0,0,0,0) ))

#Predicted March 2006 value:

exp(2.526e-02*2006.167-3.792e+01)

#or equivalently:
future.time<-2006.167
exp(as.numeric( coef(model.s) %*% c(future.time,0,0,1,0,0,0,0,0,0,0,0,0) ))