Mr. Carl Lipke is the marketing VP for a propane gas distributor. He would like to have a forecast of sales on a quarterly basis, and he has asked you to prepare a time-series decomposition model. The data for 1996 through 2007 follow: Propane Gas Sales in Millions of Pounds (total at end-month of each quarter)
Year March June September December
1996 6.44 4.85 4.67 5.77
1997 6.22 4.25 4.14 5.34
1998 6.07 4.36 4.07 5.84
1999 6.06 4.24 4.20 5.43
2000 6.56 4.25 3.92 5.26
2001 6.65 4.42 4.09 5.51
2002 6.61 4.25 3.98 5.55
2003 6.24 4.34 4.00 5.36
2004 6.40 3.84 3.53 4.74
2005 5.37 3.57 3.32 5.09
2006 6.03 3.98 3.57 4.92
2007 6.16 3.79 3.39 4.51
a. To help Mr. Lipke see how propane gas sales have varied over the 12-year period, prepare a time-series plot of the raw data and the deseasonalized data (i. e., the centered moving averages).
b. Prepare seasonal indices for quarters 1 through 4 based on the normalized averages of the seasonal factors (the seasonal factors equal actual values divided by the corresponding centered moving averages). Write a short paragraph in which you explain to Carl Lipke exactly what these indices mean.
c. Estimate the long-term trend for the sales series by using a bivariate linear regression of the centered moving average as a function of time, where TIME = 1 for 1996Q1.
d. Develop cycle factors for the sales data, and plot them on a graph that extends from 1996Q1 through 2007Q4. Analyze the plot of the cycle factor and project it through the four quarters of 2008. Write a brief explanation of why you forecast the cycle factor as you did.
e. Plot the values of sales that would be estimated by this model along with the original data. Does the model appear to work well for this data series?
f. Prepare a forecast for 2008Q1 through 2008Q4 from your time-series decomposition model. Write your forecast values in the accompanying table. Given the actual values shown in the table, calculate the root-mean-squared error (RMSE) for 2008.