Homework 6
==========
*Firstname Lastname (Replace this part with your name)*
```{r}
library("forecast")
```
For this assignment, we analyze the `chaos1` and `chaos2` series.
```{r}
chaos1 <- read.csv("http://ptrckprry.com/course/forecasting/data/chaos1.csv")$value
chaos2 <- read.csv("http://ptrckprry.com/course/forecasting/data/chaos2.csv")$value
time <- 1:50
```
Problem 1
---------
```{r}
# print the value of x1 for chaos1
```
**Check that `x1 = f(x0)`, for `chaos1`.**
Problem 2
---------
```{r}
# Plot chaos1 and chaos2 in separate plots.
```
**Do the series look random?**
**Are they in fact random?**
**Do the series look stationary?**
Problem 3
---------
```{r}
# Plot the ACF and PACF for chaos1
```
**Based on these, suggest an ARMA model.**
**Would this model provide the best possible forecasts?**
Problem 4
---------
```{r}
# Plot both chaos1 and chaos2 on the same plot
```
**Do the paths look similar?**
**Should they look similar when t is close to 1?**
**What should happen if `chaos1` and `chaos2` happen to get very close
together at some later time?**
Problem 5
---------
```{r}
# Plot x2, ..., x50 versus x1, ..., x49 for chaos1
# (Replace ???? and uncomment the following line)
# plot(????, ????, type="p")
# Hint:
# If x is a vector of length 50, then
# x[-1] is equal to c(x[2], x[3], ..., x[50])
# x[-50] is equal to c(x[1], x[2], ..., x[49])
```
**Does this plot reveal the map (in other words, the function *f*) which
generated the data?**
**Do you see why this *f* is called the tent map?**
**Does this plot help us to see that `{ x_t }` is not an AR(1) series? How?**