Kim Brite and Larry Short have developed a series of exclusive mobile-home parks in which each unit occupies a site at least 100 X 150 feet. Each site is well landscaped to provide privacy and a pleasant living environment. Kim and Larry are considering opening more such facilities, but to help manage their cash flow they need better forecasts of mobile-home shipments (MHS), since MHS appears to influence their vacancy rates and the rate at which they can fill newly opened parks. They have 16 years of data on mobile-home shipments, beginning with 1988Q1 and ending with 2003Q4, as shown:

Assuming that Kim Brite and Larry Short have hired you as a forecasting consultant:

a. Provide a time-series plot of the actual MHS data along with the deseasonalized data. Write a brief memo in which you report the nature and extent of the seasonality in the data. Include seasonal indices in your report.

b. Develop a long-term linear trend for the data, based on the centered moving averages. Let time equal 1 for 1988Q1 in your trend equation. On the basis of this trend, does the future look promising for Brite and Short?

c. One of the things Ms. Brite and Mr. Short are concerned about is the degree to which MHS is subject to cyclical fluctuations. Calculate cycle factors and plot them in a time-series graph, including projections of the cycle factor through 2004. In evaluating the cycle factor, sec whether interest rates appear to have any effect on the cyclical pattern. The rate for 1988Q1 through 2003Q4 is provided in the following table, should you wish to use this measure of interest rates.

d. Demonstrate for Ms. Brite and Mr. Short how well your time-series decomposition model follows the historical pattern in the data by plotting the actual values of MHS and those estimated by the model in a single time-series plot.

e. Prepare a forecast for 2004 and calculate the root-mean-squared error (RMSE), given the actual values of MHS for 2004 shown:

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Mobile Home Shipments (MHS) (000s) Year Q1 Q2 Q3 Q4 1988 56.6 49.1 58.5 57.5 1989 54.9 70.1 65.8 50.2 1990 53.3 67.9 63.1 55.3 1991 63.3 81.5 81.7 69.2 1992 66.2 67.8 82.7 79.0 1993 62.3 79.3 76.5 65.5 1994 58.1 66.8 63.4 56.1 1995 51.9 62.8 64.7 53.5 1996 47.0 60.5 59.2 51.6 1997 48.1 55.1 50.3 44.5 43.3 1998 51.7 50.5 42.6 1999 35.4 47.4 47.2 40.9 43.0 52.8 2000 57.0 57.6 2001 56.4 64.3 67.1 66.4 2002 69.1 78.7 78.7 77.5 86.8 86.4 2003 79.2 87.6