Problem

Mortgage Rates. The file on the CD named MRATES4 contains monthly 30-year conventional mor...

Mortgage Rates. The file on the CD named MRATES4 contains monthly 30-year conventional mortgage rates from January 1985 to December 2002. (These figures are found on the web site www.economagic.com and are obtained from the Federal Home Mortgage Corporation).

Figure 4.21 provides a time-series plot of the rates. The following model is to be used to forecast mortgage rates:

yi = β0 + β1yi–1 + ei

where yi is the mortgage rate at time i and yi–1 is the rate at lime i–1. The regression results are shown in Figure 4.22. Note that RATEL1 in the output represents the one-period lagged variable, yi–1. Use the output to answer the following questions:

a. What is the estimated regression equation?
b. Is there a relationship between current and previous period mortgage rates? State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance.
c. What percentage of the variation in mortgage rates has been explained by the regression?
d. Use the estimated equation to produce a forecast of the mortgage rate in January 2003. Find out what the actual rate was and compare it to the forecast. How well did the equation do? Repeat this process for the remainder of 2003. Discuss any difficulties you encounter in forecasting more than 1 month ahead.
e. Test whether the intercept of the equation is equal to zero. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance.
f. Test whether the slope of the equation is equal to 1. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a 5% level of significance.

FIGURE 4.21: Time-Series Plot of Mortgage Rates.