Exercise

An AR(1) model

Now consider the AR(1) model $$Y_t - 0.05 = \phi(Y_{t-1} - 0.05)$$ with $|\phi| < 0$ and $\epsilon_t ~ iid$ $N(0,(0.1)^2)$.

Assume that $\phi = 0.5$ and rewrite the code in such a way that it simulates data from the AR(1) model and that it displays the three corresponding graphs from the previous exercise correctly.

Instructions

100 XP

Assign to ar1_sim 250 observations simulated from the described AR(1) model.
Assign to acf_ar1_model the theoretical autocorrelations up to lag 10.
Create the three plot functions from the previous exercise but now for the AR(1) model instead of the MA(1) model. Have a look at the code of the previous exercise if you are unsure.