1. (Calculating Forecasts from Trend Models) You work for the International Monetary Fund in Washington DC, monitoring Singapore’s real consumption expenditures. Using a sample of real consumption data (measured in billions of 2005 Singapore dollars), yt, t = 1990 : Q1, · · · , 2006 : Q4, you estimate the linear consumption trend model, yt = β0 + β1T IMEt + εt , where εt ∼ N(0, σ2 ), obtaining the estimates βˆ
0 = 0.51, βˆ
1 = 2.30, and s
2 = 16. Based upon your estimated trend model, construct feasible point, interval(95%) and density forecasts for 2010 : Q1.
2. (Constructing Seasonal Models) Describe how you would construct a purely seasonal model for the following monthly series. In particular, what dummy variable(s) would you use to capture the relevant effects?
a. A sporting goods store finds that detrended monthly sales are roughly the same for each month in a given three-month season. For example, sales are similar in the winter months of January, February and March, in the spring months of April, May and June, and so on.
b. A campus bookstore finds that detrended sales are roughly the same for all first, all second, all third, and all fourth months of each trimester. For example, sales are similar in January, May, and September, the first months of the first, second, and third trimesters, respectively.
c. A Christmas ornament store is only open in November and December, so sales are zero in all other months.
3. (Calendar Effects) You run a large catering firm, specializing in Sunday brunches and weddings. You model the firm’s monthly income as yt = β0 +δSSt +δW Wt +εt , where y is monthly income, and S and W are calendar effect variables indicating the number of Sundays and weddings in a month.
a. What are the units of β0, δS, and δW ?
b. How could you estimate the average income the firm receives per wedding?
c. Over the past thirty years, you have regularly increased your prices to keep pace with inflation. How would you modify the model to account for the effects of such increases?
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