# 2.1 Linear Models (Solution to Homework)

# Ex 2.13 Plot the path of (\eps_t) and (\tilde \eps_t) for t = 1,...,100 and compare!
t <- 1:100
eps <- rnorm(100)
t.eps <- eps
t.eps[seq(3,100,by=2)] <- (eps[seq(2,98,by=2)]^2-1)/sqrt(2)
plot(eps,type="l")
lines(t.eps,col="red")

# Ex 2.14: Plot the path of a random walk with normal N(mu,sig^2) distributed for each of the cases
# mu < 0, mu = 0 and mu > 0.
t <- 1:100
eps <- rnorm(100,-0.5)
plot(cumsum(eps),type="l")

eps <- rnorm(100,0)
plot(cumsum(eps),type="l")

eps <- rnorm(100,0.2)
plot(cumsum(eps),type="l")