Question

Following are the number of victories for the Blue Sox and the hotel occupancy rate for the past eight years. You have been asked to test three forecasting methods to see which method provides a better forecast for the Number of Blue Sox Wins.

Year	Number of Blue Sox Wins	Occupancy Rate
1	70	78%
2	67	83
3	75	86
4	87	85
5	87	89
6	91	92
7	89	91
8	85	94

For the following, you are to provide all forecasts to one decimal place (example, 93.2)

You are asked to forecast the Number of Blue Sox Wins for Year 9. Although you believe there might be a linear regression relationship, your boss has told you to only consider the following three forecasting methods:

• 3-period moving average
• 3-period weighted moving average given the weights of 0.7 for the most recent period and 0.2 for the next most recent period, and the remaining weight (s) consistent with this method as we have used in class, and
• exponential smoothing with α = 0.25 and the best forecast available for the Number of Blue Sox Wins is for Year 2 which is 66.0.

a) What is the forecast from each of these methods for Year 9?

b) Which forecasting method provides the better forecast for Year 9? Why? Your selection criteria must be based on one of the numerical evaluation methods we have used on the homework this term using the forecast results for Year 5 through Year 8.

Answer 1

a)

3-period moving average:

Forecast for Number of Blue Sox Wins for Year 9 = ( Number of Blue Sox Wins for Year 6 + Number of Blue Sox Wins for Year 7+ Number of Blue Sox Wins for Year 8) / 3 = ( 91 + 89 + 85) / 3 = 265 / 3 = 88.33

The forecasts for Year 4 to Year 9 can be calculated using this method:

Year	Number of Blue Sox Wins	Forecast
1	70
2	67
3	75
4	87	70.67
5	87	76.33
6	91	83.00
7	89	88.33
8	85	89.00
9		88.33

3-period weighted moving average:

Forecast for Number of Blue Sox Wins for Year 9 = ( (Number of Blue Sox Wins for Year 8 x 0.7 ) + ( Number of Blue Sox Wins for Year 7 x 0.2) + (Number of Blue Sox Wins for Year 6 x 0.1) / (0.1 + 0.2 + 0.7)  

= ( ( 85 x 0.7) + ( 89 x 0.2 ) + (91 x 0.1) ) / 1

= (59.5 + 17.8 + 9.1)

= 86.4

The forecasts for Year 4 to Year 9 can be calculated using this method:

Year	Number of Blue Sox Wins	Forecast
1	70
2	67
3	75
4	87	72.90
5	87	82.60
6	91	85.80
7	89	89.80
8	85	89.20
9		86.40

Exponential Smoothing forecast:

α = 0.25

Forecast for Year (X+1) = α ( Number of Blue Sox Wins for Year X) + (1 - α) ( Forecast for Year X)

This formula has to be applied for calculating the forecasts for Year 3 to Year 8.

Forecast for Year 2 = 66

Year	Number of Blue Sox Wins	Forecast
1	70
2	67	66
3	75	66.25
4	87	68.44
5	87	73.08
6	91	76.56
7	89	80.17
8	85	82.38
9		83.03

So, the Exponential Smoothing Forecast for Number of Blue Sox Wins for Year 9 = 83.03

b)

For comparing the forecasts of all the 3 methods, we shall calculate Mean Absolute Deviation for each method:

3-period moving Average:

Year	Number of Blue Sox Wins	Forecast	Error (The number of Blue Sox Wins - Forecast)	Absolute Error
1	70
2	67
3	75
4	87	70.67	16.33	16.33
5	87	76.33	10.67	10.67
6	91	83.00	8.00	8.00
7	89	88.33	0.67	0.67
8	85	89.00	-4.00	4.00
9		88.33

Mean Absolute Deviation= Average value of Absolute Errors=  ( 16.33 + 10.67 + 8.00 + 0.67 + 4) / 5

= 39.67 / 5 = 7.93

3-period Weighted moving Average:

Year	Number of Blue Sox Wins	Forecast	Error (The number of Blue Sox Wins - Forecast)	Absolute Error
1	70
2	67
3	75
4	87	72.90	14.10	14.1
5	87	82.60	4.40	4.4
6	91	85.80	5.20	5.2
7	89	89.80	-0.80	0.8
8	85	89.20	-4.20	4.2
9		86.40

Mean Absolute Deviation= Average value of Absolute Errors= ( 14.1 + 4.4 + 5.2 + 0.8 + 4.2) / 5

= 28.7 / 5 = 5.74

Exponential Smoothing method:

Year	Number of Blue Sox Wins	Forecast	Error (The number of Blue Sox Wins - Forecast)	Absolute Error
1	70
2	67	66	1.00	1.00
3	75	66.25	8.75	8.75
4	87	68.44	18.56	18.56
5	87	73.08	13.92	13.92
6	91	76.56	14.44	14.44
7	89	80.17	8.83	8.83
8	85	82.38	2.62	2.62
9		83.03

Mean Absolute Deviation= Average value of Absolute Errors = ( 1 + 8.75 + 18.56 + 13.92+ 14.44 + 8.83 + 2.62) / 7

= 68.13 / 7 = 9.73

Mean Absolute Deviation is lowest (ie 5.74) for 3-period Weighted Moving Average.

Therefore, the 3-period Weighted Moving Average method provides the best forecasts.