Data Analysis with Microsoft Excel: Updated for Office 2007

442 Statistical Methods

5 Click the Output button, and send the output to a new sheet named

Temperature ACF. Click OK twice to close the dialog box and calcu-

late the ACF function. Figure 11-7 shows the output from the ACF

command.

Figure 11-7
Autocorrelation

of the

temperature

data

significant

autocorrelations

upper and lower

95% confidence values 95% confidence interval

The output shown in Figure 11-7 lists the lags from 1 to 20 and gives the

corresponding autocorrelations in the next column.

The lower and upper ranges of the autocorrelations are shown in the next

two columns and indicate how low or high the correlation needs to be for

statistical significance at the 5% level. Autocorrelations that lie outside

this range are shown in red in the worksheet. The plot of the ACF values

and confidence widths gives a visual picture of the patterns in the data.

The two curves indicate the width of the 95% confi dence interval of the

autocorrelations.

The autocorrelations are very high for the lower lag numbers, and they

remain significant (that is, they lie outside the 95% confidence width

boundaries) through lag 9. Specifi cally, the correlation between the mean

annual temperature and the mean annual temperature of the previous year

is 0.829 (cell B2). The correlation between the current temperature and the

lag 2 value is 0.738 (cell B3), and so forth. This is typical for a series that

has a strong trend upward or downward. Given the increase in the global

temperatures during the latter half of the twentieth century, it shouldn’t be