Problem 31 Page 703

The file P12_ 31. xlsx lists the monthly unemployment rates for several years. A common way to forecast time series is by using regression with lagged variables.
a. Predict future monthly unemployment rates using some combination of the unemployment rates for the last four months. For example, you might use last month’s unemployment rate and the unemployment rate from three months ago as explanatory variables. Make sure all variables that you decide to keep in your final equation are significant at the 15% significance level.
b. Do the residuals in your equation exhibit any autocorrelation?
c. Predict the next month’s unemployment rate.
d. There is a 5% chance that the next month’s unemployment rate will be less than what value?
e. What is the probability the next month’s unemployment rate will be less than 6%, assuming normally distributed residuals?

Source

Bureau of Labor Statistics
These data have not been adjusted for seasonality.

Data

0

.2

5.9

5.9

6

5.9

5.9

5.9

6

6.1

6

6

6

5.8

5.8

5.7

5.7

5.7

5.6

5.5

5.6

4.9

5

4.9

5

4.9

4.9

4.8

4.8

4.8

4.9

5.1

5.2

5.1

5.1

5.1

5.4

5.5

5.5

5.9

6

8.1

9

8.8

8.6

8.4

8.4

7.7

7.6

7.8

7.6

7.7

7.8

7.8

7.6

7.4

7.2

7

7.2

7

6.8

6.8

6.4

6.3

6.1

6

5.9

5.9

6

5.8

5.9

6

5.9

5.9

5.8

5.8

5.6

5.7

5.7

6

5.9

6

5.9

6

6.3

6.3

6.3

6.9

7.5

7.6

7.8

7.7

7.5

7.5

7.5

7.2

7.5

7.4

7.4

7.2

7.5

7.5

7.2

7.4

7.6

7.9

8.3

8.6

9

9.8

10.8

10.4

10.4

10.1

10.1

9.4

8.8

8.5

8.3

8

7.8

7.8

7.7

7.4

7.2

7.5

7.5

7.4

7.2

7.3

7.3

7.2

7.2

7.3

7.2

7.4

7.4

7.1

7.1

7

7

7.2

7.2

7.1

7.2

7.2

7

6.9

7

7

6.9

6.6

6.6

6.6

6.6

6.3

6.3

6.2

6.1

6

5.9

6

5.8

5.7

5.7

5.7

5.7

5.4

5.6

5.4

5.4

5.6

5.4

5.4

5.3

5.3

5.4

5.2

5

5.2

5.2

5.3

5.2

5.2

5.3

5.3

5.4

5.4

5.4

5.3

5.2

5.4

5.4

5.2

5.5

5.7

5.9

5.9

6.2

6.3

6.4

6.6

6.8

6.7

6.9

6.9

6.8

6.9

6.9

7

7

7.3

7.3

7.4

7.4

7.4

7.6

7.8

7.7

7.6

7.6

7.3

7.4

7.4

7.3

7.1

7

7.1

7.1

7

6.9

6.8

6.7

6.8

6.6

6.6

6.6

6.5

6.4

6.1

6.1

6.1

6

5.9

5.8

5.6

5.5

5.6

5.4

5.4

5.8

5.6

5.6

5.7

5.7

5.6

5.5

5.6

5.6

5.6

5.5

5.5

5.6

5.6

5.3

5.5

5.1

5.2

5.2

5.4

5.4

5.3

5.2

5.2

5.1

4.9

5

4.9

4.8

4.9

4.6

4.7

4.6

4.6

4.7

4.4

4.5

4.5

4.6

4.5

4.4

4.4

4.3

4.4

4.3

4.2

4.3

4.3

4.2

4.2

4.1

4

4

4.1

4

4

4

4

4.1

3.9

3.9

3.9

3.9

4.2

4.2

4.3

4.4

4.3

4.5

4.6

4.9

5

5.3

5.5

5.7

5.7

5.7

5.7

5.9

5.8

5.8

5.8

5.7

5.7

5.7

5.9

6

5.8

5.9

5.9

6

6.1

6.3

6.2

6.1

6.1

6

5.8

5.7

5.7

5.6

5.8

5.6

5.6

5.6

5.5

5.4

5.4

5.5

5.4

5.4

5.2

5.4

5.2

5.2

5.1

5.1

5

4.9

5

5

5

4.8

4.7

4.8

4.7

4.7

4.7

4.6

4.7

4.7

4.5

4.4

4.5

4.4

4.6

4.5

4.4

4.5

4.5

4.6

4.7

4.7

4.7

4.8

4.7

4.9

4.9

4.8

5.1

5

5.5

5.6

5.8

6.2

6.2

6.6

6.8

7.2

7.6

8.1

8.5

8.9

9.4

9.7

9.6

9.5

9.5

9.4

9.7

10.4

10.2