01-introduction.Rmd

# Introduction

## Larain

> Use software to produce the time series plot shown in Exhibit 1.2, on page 2.
The data are in the file named larain.

```{r, setup, message = FALSE}
library(TSA)
library(latticeExtra)

data(larain, package = "TSA")
```

```{r}
xyplot(larain, ylab = "Inches", xlab = "Year", type = "o")
```

## Colors

> Produce the time series plot displayed in Exhibit 1.3, on page 3. The data
file is named color.

```{r}
data(color)
xyplot(color, ylab = "Color property", xlab = "Batch", type = "o")
```

## Random, normal time series

> Simulate a completely random process of length 48 with independent, normal
values. Plot the time series plot. Does it look “random”? Repeat this exercise
several times with a new simulation each time.

```{r, fig.show = "hold"}
xyplot(as.ts(rnorm(48)))
xyplot(as.ts(rnorm(48)))
```

As far as we can tell there is no discernable pattern here.

## Random, $\chi^2$-distributed time series

> Simulate a completely random process of length 48 with independent, chi-square
distributed values, each with 2 degrees of freedom. Display the time series
plot. Does it look “random” and nonnormal? Repeat this exercise several times
with a new simulation each time.

```{r, fig.show = "hold"}
xyplot(as.ts(rchisq(48, 2)))
xyplot(as.ts(rchisq(48, 2)))
```

The process appears random, though non-normal.

## *t*(5)-distributed, random values

> Simulate a completely random process of length 48 with independent,
t-distributed values each with 5 degrees of freedom. Construct the time series
plot. Does it look “random” and nonnormal? Repeat this exercise several times
with a new simulation each time.

```{r}
xyplot(as.ts(rt(48, 5)))
xyplot(as.ts(rt(48, 5)))
```

It looks random but not normal, though it should be approximately so,
considering the distribution that we have sampled from.

##  Dubuque temperature series

> Construct a time series plot with monthly plotting symbols for the Dubuque 
temperature series as in Exhibit 1.7, on page 6. The data are in the file named 
tempdub.

```{r}
data(tempdub)
xyplot(tempdub, ylab = "Temperature", xlab = "Year")
```