Suppose a savings and loan association wants to forecast

Question

Suppose a savings and loan association wants to forecast the delinquency rate on home mortgages. Using monthly data, the following trend model is estimated where DR_t = the percentage of mortgage payments delinquent in time period t, and t = 1,..,48 (January 2010 through December 2013). The following estimation results are obtained:

DEPENDENT VARIABLE:	DRT	R-SQUARE	F-RATIO	P-VALUE ON F
OBSERVATIONS:	48	0.7982	181.93	0.0001
VARIABLE		PARAMETER ESTIMATE	STANDARD ERROR	T-RATIO	P-VALUE
INTERCEPT		2.60	0.74	3.51	0.0010
T		0.030	0.010	3.00	0.0043

a. Does this estimate indicate a significant upward trend in the delinquency rate on home mortgages? In the space below, perform the appropriate t-test at the 5 per­cent significance level.

b. Perform an F-test to determine if the model is statistically significant at the 5 percent level of significance.

c. Calculate the predicted delinquency rates for January 2014 and March 2014.

DR_{Jan 2014} = ________ percent

DR_{Mar 2014} = ________ percent

Show your work here:

The trend analysis above indicates that the delinquency rate is rapidly becoming a serious problem for this savings and loan. A management consultant suggests that the trend analysis may be overstating the upward trend because it fails to account for the fact that the months of December and January are consistently much worse months than the rest. The consultant suggests estimating the following model:

where D is equal to one for the months of December and January, and zero otherwise. The estimation results are:

DEPENDENT VARIABLE:	DRT	R-SQUARE	F-RATIO	P-VALUE ON F
OBSERVATIONS:	48	0.9876	1794.0	0.0001
VARIABLE		PARAMETER ESTIMATE	STANDARD ERROR	T-RATIO	P-VALUE
INTERCEPT		2.200	0.780	2.82	0.0071
T		0.018	0.004	4.50	0.0001
D		0.810	0.210	3.86	0.0004

d. Does the new model indicate a significant upward trend in the delinquency rate? Perform the appropriate t-test.

e. Perform a t-test to determine whether December and January are signifi­cantly worse months for mortgage payments.

f. Predict the delinquency rates for January 2014 and March 2014.

DR_{Jan 2014} = ________ percent

DR_{Mar 2014} = ________ percent

Show your work here:

g. Compare your forecasts in parts c and f. Explain why they differ.