# Uploading package from Shumway and Stoffer's book
install.packages("astsa")
library(astsa) 

# Simple plots of Jonshon & Johnson returns
plot(jj, type="o", ylab="Quarterly Earnings per Share")
plot(diff(jj), type="o", ylab="Quarterly Earnings per Share")

# All data sets available in the package
data()
par(mfrow=c(2,3))
ts.plot(nyse)
ts.plot(salmon)
ts.plot(chicken)
ts.plot(UnempRate)
ts.plot(birth)
ts.plot(flu)

# Playing around with DJIA - ACF
y = djia[,4]
ts.plot(y)
y = diff(log(y))

par(mfrow=c(2,2))
ts.plot(y)
acf(y)
ts.plot(y^2)
acf(y^2)

# Box-Ljung test for DJIA and DJIA^2
Box.test(y,lag=30,type="Ljung")
Box.test(y^2,lag=30,type="Ljung")


# ACF for Canadian lynx and air passengers data
par(mfrow=c(2,2))
plot(Lynx)
acf(Lynx)
plot(diff(log(AirPassengers)))
acf(diff(log(AirPassengers)))


# White noise and AR(1) processes
set.seed(12435)
e = rnorm(100,0,1)
y = rep(0,100)
for (t in 2:100)
  y[t] = 0.98*y[t-1]+e[t]

par(mfrow=c(2,2))
ts.plot(e)
acf(e)
ts.plot(y)
acf(y)

# Stationary region for AR(2) processes
# -------------------------------------
phi1 <- seq(from = -2.5, to = 2.5, length = 51)
plot(phi1,1+phi1,lty="dashed",type="l",
     xlab="",ylab="",cex.axis=.8,ylim=c(-1.5,1.5))
abline(a = -1, b = 0, lty="dashed")
abline(a = 1, b = -1, lty="dashed")
title(ylab=expression(phi[2]),xlab=expression(phi[1]),cex.lab=.8)
polygon(x = phi1[6:46], y = 1-abs(phi1[6:46]), col="gray")
lines(phi1,-phi1^2/4)
text(0,-.5,expression(phi[2]<phi[1]^2/4),cex=.7)
text(1.2,.5,expression(phi[2]>1-phi[1]),cex=.7)
text(-1.75,.5,expression(phi[2]>1+phi[1]),cex=.7)
points(1.75,-0.8,pch=16,col=1)
points(0.9,0.05,pch=16,col=2)