The following table contains quarterly data on upper midwest car sales (CS) in the United States for

Question:

The following table contains quarterly data on upper midwest car sales (CS) in the United States for 1987Q1 through 2007Q4:

a. Prepare a time-series plot of upper midwest car sales from 1987Q1 through 2007Q4.
b. On the basis of these data, calculate the centered moving average (CSCMA) and the centered moving-average trend (CSCMAT). Plot CS, CSCMA, and CSCMAT on a single time-series plot.
c. Calculate a seasonal factor (SF = CS/CSCMA) for each quarter from 1987Q3 through 2007Q2. Calculate the seasonal indices (SI) for this series.
d. Determine the cycle factors CF = CSCMA/CSCMAT for the period from 1987Q3 through 2007Q2 and plot them along with a horizontal line at 1.
e. Evaluate the cycle factor (CF) and project it forward from 2007Q3 through 2008Q4.
f. Prepare a time-series decomposition forecast of CS (CSFTSD = CSCMAT X SI X CF).
g. Calculate the historic RMSE as a measure of fit; then calculate the RMSE for the 2008Q1-2008Q4 forecast horizon as a measure of accuracy, given that the actual values of CS for 2008 were:
2008Q1€¦€¦€¦€¦€¦€¦.301.1
2008Q2€¦€¦€¦€¦€¦€¦.336.7
2008Q3€¦€¦€¦€¦€¦€¦.341.8
2008Q4€¦€¦€¦€¦€¦€¦.293.5
h. Prepare a Winters' exponential smoothing forecast of CS using data from 1987Q1 through 2007Q4 as the basis for a forecast of 2008Q1-2008Q4. Compare these results in terms of fit and accuracy with the results from the time-series decomposition forecast.