1. Calculate a forecast using a simple three-month moving average.
The simple three-month moving average for month ‘t’ is given by,
At  ( Dt  Dt 1  Dt 2 ) / 3 , where Dt denotes the actual demand in month ‘t’.
Now, the forecast for the next period is calculated using the formula
Ft+1 = At  ( Dt  Dt 1  Dt 2 ) / 3
Month
January
February
March
April
May
June
July
August
September
October
November
December
Total Demand
Last
Year
510
383
1403
1913
1148
893
829
638
2168
1530
701
636
12752
3 period
3 period
moving avg forecast
765.3
1233.0
1488.0
1318.0
956.7
786.7
1211.7
1445.3
1466.3
955.7
Avg Demand
1062.67
Avg Bias
Abs Dev
Mean Abs Dev
765
1233
1488
1318
957
787
1212
1445
1466
Error
1147.67
-85.00
-595.00
-489.00
-318.67
1381.33
318.33
-744.33
-830.33
Total Bias -215.00
Bias x
-23.89
5909.67
656.63
2. Calculate a forecast using a three-period weighted moving average. Use weights of
0.60, 0.25 and 0.15 for the most recent period, the second most recent period, and the
third most recent period, respectively.
The three-period weighted moving average for month ‘t’ is given by,
At  0.60Dt  0.25Dt 1  0.15Dt 2
Now, the forecast for the next period is calculated using the formula
Ft+1 = At  0.60Dt  0.25Dt 1  0.15Dt 2
Month
Last Year
3 period
3 period
Error
weighted moving avg forecast
January
February
March
April
May
June
July
August
September
October
November
December
Total Demand
Avg Demand
Avg Bias
Abs Dev
Mean Abs Dev
510
383
1403
1913
1148
893
829
638
2168
1530
701
636
1014.1
1556.0
1377.5
1109.8
892.9
724.0
1584.7
1555.7
1128.3
786.4
12752
1062.67
1014
1556
1378
1110
893
724
1585
1556
1128
899
-408
-485
-281
-255
1444
-55
-855
-492
Total Bias -486.80
Bias x
-54.09
5172.70
574.74
3. Calculate a forecast using the exponential smoothing method. Assume the forecast for
period 1 is 1,063.
The exponential smoothing forecast for month ‘t’ is given by,
Ft   Dt 1  (1   ) At 1
The forecast using the exponential smoothing method with = 0.1 is given in the
following table.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Last Year Forecast
510
1063
383
1008
1403
945
1913
991
1148
1083
893
1090
829
1070
638
1046
2168
1005
1530
1121
701
1162
636
1116
Error
-553
-625
458
922
65
-197
-241
-408
1163
409
-461
-480
Total Demand 12752
Avg Demand 1062.67 Total Bias 51.29
Avg Bias
Bias x
4.27
Abs Dev
5980.75
Mean Abs Dev
498.40
The forecast using the exponential smoothing method with = 0.2 is given in the
following table.
Month
Last Year Forecast
Error
January
510
1063
-553
February
383
952
-569
March
1403
839
564
April
1913
951
962
May
1148
1144
4
June
893
1145
-252
July
829
1094
-265
August
638
1041
-403
September
2168
961
1207
October
1530
1202
328
November
701
1268
-567
December
636
1154
-518
Total Demand 12752
Avg Demand 1062.67 Total Bias -61.73
Avg Bias
Bias x
-5.14
Abs Dev
6193.13
Mean Abs Dev
516.09
From the above two forecast table we can see that exponential forecast using = 0.1
results in a better forecast than using = 0.2 as a smoothing constant.
4. Calculate a forecast using the trend adjusted exponential smoothing method. Use 0.20
for both alpha and beta.
The trend-adjusted exponential smoothing method uses the following formula,
with two parameters, alpha () for the average and beta () for the trend.
At = *Dt + (1 – )*(At-1 + Tt-1)
Tt = *(At – At-1) + (1 –)*Tt-1
Now the forecast for next period is given by, Ft+1 = At + Tt
For the given data, the average demand was 1063 with an average increase of 11 per
week. Therefore we can let A0 = 1063 and T0 = 11. Using  = 0.2, we get the trend
adjusted exponential smoothing forecast as follows.
Smoothed
Trend
Month
Last Year Average(At) Estimate (Tt) Forecast
Error
January
510
961.2
-11.6
February
383
836.3
-34.2
950
-567
March
1403
922.3
-10.2
802
601
April
1913
1112.3
29.8
912
1001
May
1148
1143.3
30.1
1142
6
June
893
1117.3
18.9
1173
-280
July
829
1074.7
6.6
1136
-307
August
638
992.7
-11.2
1081
-443
September
2168
1218.8
36.3
982
1186
October
1530
1310.1
47.3
1255
275
November
701
1226.1
21.0
1357
-656
December
636
1124.9
-3.4
1247
-611
Total Demand 12752
Avg Demand 1062.67
Total Bias 204.06
Avg Bias
Bias x
18.55
Abs Dev
5934.16
Mean Abs Dev
539.47
5. Calculate a seasonal influenced forecast.
Month
January
February
March
Total
April
May
June
Total
July
August
September
Total
October
November
December
Total
Year 1
510
383
1403
2296
1913
1148
893
3954
829
638
2168
3635
1530
701
636
2867
Year 2
526
394
1446
2366
1972
1183
920
4075
854
657
2235
3746
1578
723
658
2959
Year 3
501
376
1377
2254
1878
1127
876
3881
814
626
2128
3568
1502
689
626
2817
Total
1537
1153
4226
6916
5763
3458
2689
11910
2497
1921
6531
10949
4610
2113
1920
8643
Total Demand
Demad per season
12752
3188.0
13146
3286.5
12520
3130.0
38418
9604.5
Determine the “seasonal index” associated with each quarter by dividing the seasonly
demand by the average demand per season for that year. Then, calculate the average
index for each season.
Season
1
2
3
4
Year 1
0.7202
1.2403
1.1402
0.8993
Year 2
0.7199
1.2399
1.1398
0.9003
Year 3
0.7201
1.2399
1.1399
0.9000
Average seasonal
Index
0.7201
1.2400
1.1400
0.8999
6. Based on the various methods used to calculate a forecast for TFY, which method
produced the best forecast? Why? How could you improve this forecast?
To assess the accuracy you can compare the "Mean Abolute Deviation"; the smaller the
value the more accurate the forecast. Based on the forecasts, we have:
Simple Moving Average MAD:
3-Month Weighted Moving Average MAD:
Exponential Smoothing MAD:
Trend adjusted exponential Smoothing MAD:
656.63
574.74
498.40
539.47
Here the MAD for Exponential smoothing forecast with smoothing constant = 0.1 is
smaller. So the Exponential smoothing method produced the best forecast.