4. Estimating the volume of loans that will be made at a credit union is crucial to effective cash management in those institutions. In the table that follows are quarterly data for a real credit union located in a midwestern city. Credit unions are ﬁnancial institutions similar to banks, but credit unions are not-for-proﬁt ﬁrms whose members are the actual owners (remember their slogan, “It’s where you belong”). The members may be both depositors in and borrowers from the credit union.
a. Estimate a multiple-regression model to estimate loan demand and calculate its root mean squared error.
b. Estimate a time-series decomposition model to estimate loan demand with the same data and calculate its root-mean-squared error.
c. Combine the models in parts (a) and (b) and determine whether the combined model performs better than either or both of the original models. Try to explain why you obtained the results you did.
5. HeathCo Industries, a producer of a line of skiwear, has been the subject of exercises in several earlier chapters of the text. The data for its sales and two potential causal variables, income (INCOME) and the northern-region unemployment rate (NRUR), are repeated in the following table:
a. Develop a multiple-regression model of SALES as a function of both INCOME and NRUR:
Use this model to forecast sales for 2008Q1–2008Q4 (call your regression forecast series SFR), given that INCOME and NRUR for 2004 have been forecast to be:
b. Calculate the RMSE for your regression model for both the historical period (1998Q1–2007Q4) and the forecast horizon (2008Q1–2008Q4).
c. Now prepare a forecast through the historical period and the forecast horizon (2008Q1–2008Q4) using Winters’ exponential smoothing. Call this forecast series SFW, and ﬁll in the RMSEs for SFW:
d. Solely on the basis of the historical data, which model appears to be the best? Why?
e. Now prepare a combined forecast (SCF) using the regression technique described in this chapter. In the standard regression:
Is the intercept essentially zero? Why? If it is, do the following regression as a basis for developing SCF:
f. Calculate the RMSEs for SCF:
Did combining models reduce the RMSE in the historical period? What about the actual forecast?
6. Your company produces a favorite summertime food product, and you have been placed in charge of forecasting shipments of this product. The historical data below represent your company’s past experience with the product.
a. Since the data appear to have both seasonality and trend, you should estimate a Winters’ model and calculate its root-mean-squared error.
b. You also have access to a survey of the potential purchasers of your product. This information has been collected for some time, and it has proved to be quite accurate for predicting shipments in the past. Calculate the root-mean-squared error of the purchasers’ survey data.
c. After checking for bias, combine the forecasts in parts (a) and (b) and determine if a combined model may forecast better than either single model.