HW1: Problem 2
==============
*Your name goes here*


In this problem we will consider the daily U.S. Dollar-Euro exchange rate,
daily, 4 Jan 1999 to 6 Feb 2017 (*n* = 4636).

```{r}
data <- read.csv("http://ptrckprry.com/course/forecasting/data/euro.csv")
date <- as.Date(data$date)
euro <- data$euro
```


Part A
------

Here is a time-series plot of Euro.

```{r}
# Replace this comment with code to make the plot.
```


**Does a straight-line model seem appropriate?**



Part B
------

Here, we fit two models and predict the value at 7 Feb 2017 (time = 4637).  In
the first model, we fit to observations 1 to 700.  In the second model, we fit
to observations 701 to 4636.

```{r}
time <- 1:length(euro) # create the time variable

# Replace the ???? in the following lines with the appropriate code, then
# uncomment the code.  Make sure you use "time" as the predictor variable,
# note "date".

#model1 <- lm(????, subset=1:700)
#summary(model1)

#model2 <- lm(????, subset=701:4636)
#summary(model2)
```

Here are the predicted values and 95% prediction intervals for the two models:
```{r}
newdata <- data.frame(time = 4637)
# Add code to compute the two prediction intervals
```

**Did both of the forecast intervals succeed in containing the actual value
for 7 Feb 2017?  If not, then use what you learned in Problem~1 to give a
statistical explanation of what went wrong.**


Part C
------

Here, we superimpose the fitted lines from both models on the time series plot.

```{r}
plot(time, euro, t="l")

# Replace the ???? in the following two lines with code to add the two lines:
#
# abline(????, lty=2)
# abline(????, lty=3)

legend("bottomright", inset=0.05,
       legend=c("Fit to 1-700", "Fit to 701-4636"), lty=c(2,3))
```
