## AR(2)
phi0 <- 0
phi1 <- 1 #0.7
phi2 <- 0 #-0.3
y <- rep(NA, 100)
y[1] <- rnorm(1)
y[2] <- rnorm(1)


for(t in 3:100) {
  y[t] <- phi0 + phi1*y[t-1] + phi2*y[t-2] + rnorm(1)
}
plot(y, type="l")


acf(y)
pacf(y)

y.1 <- c(NA, y[1:99])
y.2 <- c(NA, NA, y[1:98])
dati <- as.data.frame(cbind(y, y.1, y.2))

ar2mod <- lm(y~y.1+y.2, dati)
summary(ar2mod)

## MA(2)
n <- 100
theta1 <- 0.7
theta2 <- -0.8
y <- rep(NA, n)
e <- rep(NA, n)
y[1] <- e[1] <- rnorm(1)
y[2] <- e[2] <- rnorm(1)
for(i in 3:n) {
  e[i] <- rnorm(1)
  y[i] <- e[i] - theta1*e[i-1] - theta2*e[i-2]
}

plot(y, type="l")
mean(y)  
acf(y)  
pacf(y)