The revenues (in millions of dollars) of a chain of ice cream stores are listed for each quarter during the years 1995 – 1999:

Revenue Period

16 1

25 2

31 3

24 4

14 5

27 6

32 7

23 8

17 9

31 10

40 11

27 12

18 13

29 14

45 15

24 16

21 17

30 18

52 19

32 20

Using SPSS:

a) Plot the times series and describe the variation of the time series. Would an additive or multiplicative model be more appropriate to describe the variation of the time series?

b) Use exponential smoothing to forecast revenues for the year 2000.

c )Assuming a multiplicative model, compute the seasonal indexes for the revenues. Interpret the indexes.

d) Forecast revenues for the year 2000 using regression and seasonal indexes assuming a multiplicative model.

e) Assuming an additive model, compute the seasonal indexes of revenues. Interpret the indexes.

f) Forecast revenues for the year 2000 using regression and seasonal indexes assuming an additive model.

g) Which of the three forecasts of revenues computed in (b), (d) and (f) would you recommend using?

See the attached file.

a) Plot the times series and describe the variation of the time series. Would an additive or multiplicative model be more appropriate to describe the variation of the time series?

*see attachment for graph*

From the time series plot it is clear that within year variation is increasing year by year. Hence a multiplicative model would be appropriate to describe the variation of the time series.

b) Use exponential smoothing to forecast revenues for the year 2000.

Forecasted demand is given by

F_t = F_t-1 + α(A_t-1 – F_t-1) , where

Ft is the forecasted demand at time t

Ft-1 is the forecasted demand at time t – 1

At-1 is the actual demand at time t-1

Forecast

Model Q1 2000 Q2 2000 Q3 2000 Q4 2000

Revenue-Model_1 Forecast 29.18 29.18 29.18 29.18

UCL 49.60 49.65 49.70 49.75

LCL …

The solution discusses using revenues of ice cream stores to describe time series.