E=rnorm(1000)
plot(acf(E),lwd=5)
plot(pacf(E),lwd=5)

E=rnorm(10000)
X=rep(0,10000)
phi=-.7
1/(1-phi^2)
for(t in 2:10000) X[t]=phi*X[t-1]+E[t]
plot(X[1:200],type="l")
plot(X,type="l")
plot(acf(X),lwd=5)
plot(pacf(X),lwd=5)

X=rep(0,10000)
phi1=0.4
phi2=0
phi3=-0.5
for(t in 4:10000) X[t]=phi1*X[t-1]+
  phi2*X[t-2]+phi3*X[t-3]+E[t]
plot(X[1:200],type="l")
plot(X,type="l")
plot(acf(X),lwd=5)
plot(pacf(X),lwd=5)



X=rep(0,10000)
phi1=+1.6
phi2=-.8
for(t in 3:10000) X[t]=phi1*X[t-1]+
  phi2*X[t-2]+E[t]
plot(X,type="l")
plot(pacf(X),lwd=5)