Question

The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. Quarter Year 1 Year 2 Year 3 1 1690 1800 1850 2 940 900 1100 3 2625 2900 2930 4 2500 2360 2615

a. Construct a time series plot. What type of pattern exists in the data?

b. Show the four-quarter and centered moving average values for this time series.

c. Compute the seasonal and adjusted seasonal indexes for the four quarters.

d. When does the publisher have the largest seasonal index? Does this result appear reasonable? Explain.

e. Deseasonalize the time series.

f. Compute the linear trend equation for the de-seasonalized data and forecast sales using the linear trend equation. g. Adjust the linear trend forecasts using the adjusted seasonal indexes computed in part (c).

Answer 1

Answer :

a.

            There appears to be a seasonal pattern in the data and perhaps a moderate upward linear trend.

B.         Four quarter moving averages beginning with

(1690 + 940 + 2625 + 2500) / 4 = 1938.75

            Other moving averages are

            1966.25                       2002.50

            1956.25                       2052.50

            2025.00                       2060.00

            1990.00                       2123.75          

C.

Quarter	Seasonal-Irregular Component Values	Seasonal Index	Adjusted Seasonal         Index
1	0.904	0.900	0.9020	0.900
2	0.448	0.526	0.4970	0.486
3	1.344	1.453	1.3985	1.396
4	1.275	1.164	1.2195	1.217
			4.0070

            Adjustment for seasonal index = 4.000 / 4.007 = 0.9983

D.        The largest seasonal effect is in the third quarter which corresponds to the back-to-school demand during July, August, and September of each year.