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 brvbar brvbar brvbar brvbar brvbar brvbar 301 1 2008Q2 brvbar brvbar brvbar brvbar brvbar brvbar 336 7 2008Q3 brvbar brvbar brvbar brvbar brvbar brvbar 341 8 2008Q4 brvbar brvbar brvbar brvbar brvbar brvbar 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 Upper Midwest Car Sales (CS) Year 92 O1 04 1987 1988 1989 1990 1991 1992 1993 1994 1995 407 6 328 7 456 3 485 0 555 0 662 7 641 2 542 8 588 1 589 2 586 1 691 6 653 9 722 2 629 3 603 9 461 3 476 6 407 2 418 6 371 1 381 3 624 3 564 3 682 7 591 1 632 7 558 9 626 5 643 2 699 4 793 4 754 8 788 6 738 6 653 6 548 0 528 2 498 5 470 2 425 5 441 6 422 6 557 5 538 3 581 3 616 9 576 6 581 7 590 9 593 9 734 4 864 9 883 6 769 9 732 0 606 1 306 2 369 4 436 7 412 5 509 7 529 7 475 0 537 8 580 1 612 2 753 8 840 8 797 7 725 5 598 8 539 7 480 4 452 6 403 7 375 7 313 5 1997 1998 2000 2001 2002 2003 2004 2005 480 4 474 3 470 7 397 3 006 2007

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

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.

Upper Midwest Car Sales (CS) Year 92 O1 04 1987 1988 1989 1990 1991 1992 1993 1994 1995 407.6 328.7 456.3 485.0 555.0 662.7 641.2 542.8 588.1 589.2 586.1 691.6 653.9 722.2 629.3 603.9 461.3 476.6 407.2 418.6 371.1 381.3 624.3 564.3 682.7 591.1 632.7 558.9 626.5 643.2 699.4 793.4 754.8 788.6 738.6 653.6 548.0 528.2 498.5 470.2 425.5 441.6 422.6 557.5 538.3 581.3 616.9 576.6 581.7 590.9 593.9 734.4 864.9 883.6 769.9 732.0 606.1 306.2 369.4 436.7 412.5 509.7 529.7 475.0 537.8 580.1 612.2 753.8 840.8 797.7 725.5 598.8 539.7 480.4 452.6 403.7 375.7 313.5 1997 1998 2000 2001 2002 2003 2004 2005 480.4 474.3 470.7 397.3 006 2007

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