Question 1: Monthly sales ( $100,000) of the South Pole Ice Cream Company are shown in the table below:
|
Month
|
1990
|
1991
|
1992
|
|
January
|
2.3
|
2.54
|
3.3
|
|
February
|
2.6
|
2.8
|
3.31
|
|
March
|
2.75
|
3
|
3.78
|
|
April
|
2.85
|
3.43
|
4.2
|
|
May
|
3.25
|
3.85
|
4.2
|
|
June
|
3.37
|
3.9
|
5
|
|
July
|
3.25
|
3.8
|
*
|
|
August
|
3.37
|
3.9
|
*
|
|
September
|
3.2
|
3.6
|
*
|
|
October
|
3.2
|
3.55
|
*
|
|
November
|
2.75
|
3.25
|
*
|
|
December
|
2.65
|
3.2
|
*
|
(a) Plot the data on a graph with time on the horizontal axis and sales on the vertical axis.
(b) Fit a linear trend equation to the data.
(c) Introduce an appropriate number of (significant)dummy variables and regress sales on time and the dummy variables.
(d) On the basis of your model in part (c) forecast sales for the missing months in the above table, and determine an approximate 95% confidence interval for sales in December 1992.
(e) Calculate seasonally adjusted monthly sales by the ratio to trend method for the last six months of 1992. Bear in mind that you have to use the regression model of part (b) for forecasting the sales that need to be adjusted.
Question 2: A firm has experienced the demand shown in the table below over the past ten years.
|
Year
|
Demand
|
5-Year
Moving
Average
|
3-Year
Moving
Average
|
Exponential
Smoothing
to = 0.9
|
Exponential
Smoothing
w = 0.3
|
|
19X0
|
800
|
-
|
-
|
-
|
-
|
|
19X1
|
925
|
-
|
-
|
?
|
?
|
|
19X2
|
900
|
-
|
-
|
?
|
?
|
|
19X3
|
1025
|
-
|
?
|
?
|
?
|
|
19X4
|
1150
|
-
|
?
|
?
|
?
|
|
19X5
|
1160
|
?
|
?
|
?
|
?
|
|
19X6
|
1200
|
?
|
?
|
?
|
?
|
|
19X7
|
1150
|
?
|
?
|
?
|
?
|
|
19X8
|
1270
|
?
|
?
|
?
|
?
|
|
19X9
|
1290
|
?
|
?
|
?
|
?
|
|
19Y0
|
???
|
?
|
?
|
?
|
?
|
(a) Fill in the table above (at the "?") by preparing forecasts based on a five-year moving average, a three-year moving average, and exponential smoothing forecasts (with w = 0:9 and w = 0:3). Note: The exponential smoothing forecasts may be begun by assuming Yt+1^ = Yt.
(b) Using the forecasts from 19X5 to 19X9; compare the accuracy of each of the forecasting methods based on the RMSE criterion.
(c) Which forecast would you use for 19Y0? Why?