---
title: "Auto-regressive model of order 1"
output: html_document
---

## Simulation of AR(1)

Simulate time series of length 100 from five different AR(1) models with $\alpha_1$ equal to a) -0.9, b) -0.5, c) 0, d) 0.5, e) 0.9 respectively (see Example 3, p. 8 in the slides).
For each model:

- Plot the correlogram 
- Make a plot of the theoretical autocorrelation on top of the correlogram (how well does it fit?)

```{r}
# Hint: Use points(x,y) after the acf to plot y against x on top of the correlogram 
```