# # Time Series and Forecasting

## # Creating a ts object

Time series data can be stored as a `ts`

object. `ts`

objects contain information about seasonal frequency that is used by ARIMA functions. It also allows for calling of elements in the series by date using the `window`

command.

```
#Create a dummy dataset of 100 observations
x <- rnorm(100)
#Convert this vector to a ts object with 100 annual observations
x <- ts(x, start = c(1900), freq = 1)
#Convert this vector to a ts object with 100 monthly observations starting in July
x <- ts(x, start = c(1900, 7), freq = 12)
#Alternatively, the starting observation can be a number:
x <- ts(x, start = 1900.5, freq = 12)
#Convert this vector to a ts object with 100 daily observations and weekly frequency starting in the first week of 1900
x <- ts(x, start = c(1900, 1), freq = 7)
#The default plot for a ts object is a line plot
plot(x)
#The window function can call elements or sets of elements by date
#Call the first 4 weeks of 1900
window(x, start = c(1900, 1), end = (1900, 4))
#Call only the 10th week in 1900
window(x, start = c(1900, 10), end = (1900, 10))
#Call all weeks including and after the 10th week of 1900
window(x, start = c(1900, 10))
```

It is possible to create `ts`

objects with multiple series:

```
#Create a dummy matrix of 3 series with 100 observations each
x <- cbind(rnorm(100), rnorm(100), rnorm(100))
#Create a multi-series ts with annual observation starting in 1900
x <- ts(x, start = 1900, freq = 1)
#R will draw a plot for each series in the object
plot(x)
```

## # Exploratory Data Analysis with time-series data

```
data(AirPassengers)
class(AirPassengers)
```

1 "ts"

In the spirit of Exploratory Data Analysis (EDA) a good first step is to look at a plot of your time-series data:

```
plot(AirPassengers) # plot the raw data
abline(reg=lm(AirPassengers~time(AirPassengers))) # fit a trend line
```

For further EDA we examine cycles across years:

```
cycle(AirPassengers)
```

```
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1949 1 2 3 4 5 6 7 8 9 10 11 12
1950 1 2 3 4 5 6 7 8 9 10 11 12
1951 1 2 3 4 5 6 7 8 9 10 11 12
1952 1 2 3 4 5 6 7 8 9 10 11 12
1953 1 2 3 4 5 6 7 8 9 10 11 12
1954 1 2 3 4 5 6 7 8 9 10 11 12
1955 1 2 3 4 5 6 7 8 9 10 11 12
1956 1 2 3 4 5 6 7 8 9 10 11 12
1957 1 2 3 4 5 6 7 8 9 10 11 12
1958 1 2 3 4 5 6 7 8 9 10 11 12
1959 1 2 3 4 5 6 7 8 9 10 11 12
1960 1 2 3 4 5 6 7 8 9 10 11 12
```

```
boxplot(AirPassengers~cycle(AirPassengers)) #Box plot across months to explore seasonal effects
```

#### # Remarks

Forecasting and time-series analysis may be handled with commonplace functions from the `stats`

package, such as `glm()`

or a large number of specialized packages. The CRAN Task View for time-series analysis provides a detailed listing of key packages by topic with short descriptions.