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?**

