438 Statistical Methods
There does not appear to be any trend in the change in mean annual
temperature over the 128 years represented in the data set. The changes in
temperature values appear as scattered in recent years as they do in years
from the beginning from the chart.Looking at Lagged Values
Often in time series you will want to compare a value observed at one
time point to the value observed one or more time points earlier. In the tem-
perature data, for example, you might be interested in whether the mean
temperature from one year can be used to predict the mean temperature
of the following year. Such prior values are known as lagged values. Lagged
values are an important concept in time series analysis. You can lag observa-
tions for one or more time points. In the example of the global temperature
data, the lag 1 value is the temperature value one year prior, the lag 2 value
is the temperature value two years prior, and so forth.
You can calculate lagged values by letting the values in rows of the lagged
column be equal to values one or more rows above in the unlagged column.
Let’s add a new column to the Temperature worksheet, consisting of annual
temperature averages lagged one year.To create a column of lag 1 values for the global temperature data:1 Click the Temperature sheet tab to return to the data.
2 Right-click the D column header so that the entire column is selected
and the pop-up menu opens. Click Insert in the pop-up menu.
3 Click cell D1, type Lag1 Temps (F), and press Enter.
4 Select the range D3:D129 (not D2:D129).
5 Type =E2 in cell D3 (this is the value from the previous year); then
press Enter.
6 Click the Fill button from the Editing group on the Home tab and
click Down. Excel fi lls in the rest of the column with the one-year
lagged values.Each row of the lagged temperature values is equal to the temperature value
of the previous year. You could have created a column of lag 2 values by select-
ing the range D4:D129 and letting D4 be equal to E2, and so on. Note that for the
lag 2 values you have to start two rows down, as compared to one row down for
the lag 1 values. The lag 3 values would have been put into the range D5:D129.
How do the temperature values compare to those of the previous year? To
see the relationship between each temperature and its one-year lag value,
create a scatterplot.