The data in Table 7.5 (page 343) give quarterly sales of the popular game Oligopoly at the J-Mart variety store. Consider using the multiplicative decomposition method to forecast Oligopoly sales for year 4. Use of a spreadsheet is recommended for all parts except (h) and (n).

a. Compute appropriate four-period moving averages for these data.

b. Compute centered moving averages for these data.

c. Calculate sn_t x ir_t values for these data.

d. Calculate estimates of the seasonal factors for quarterly Oligopoly sales (that is, compute sn_t values for these data).

e. Compute the deseasonalized observations for these data.

f. Plot the deseasonalized observations versus time. From your data plot, what kind of trend appears to exist.

g. Assuming that a linear trend TR_t = ₀ + ₁t describes the deseasonalized observations, compute least squares point estimates of ₀ and ₁.

i. Compute cl_t x ir_t values for the Oligopoly data.

j. Compute estimates of the cyclical factors for the Oligopoly data (that is, compute cl_t values for these data).

k. Compute estimates of the irregular factors for the Oligopoly data (that is, compute ir_t values for these data).

l. Do the cl_t values determine any well-defined cycle? Explain your answer.

m. Using estimated trend and seasonal factors compute point forecasts of Oligopoly sales for each quarter of year 4.

n. Using estimated trend and seasonal factors, compute approximate 95% prediction interval forecasts of Oligopoly sales for each quarter of year 4.

Year	Quarter	Oligopoly Sales
1	1	20
	2	25
	3	35
	4	44
2	1	28
	2	29
	3	43
	4	48
3	1	24
	2	37
	3	39
	4	56