|
Time Series Analysis Example
Refer to the historical demand for Product 4 in "Data Analysis
Exercise #2," available from the Handouts page of the course web
site. Four different forecasting techniques were used to analyze the
data. For each, the optimal model parameters (i.e., b0
and b1 for trend, SI for seasonal index, and a
for exponential smoothing) were determined, and the resulting models were
used to predict past demand, as well as demand for time period 13.
The table below summarizes the results of the analyses. Note that a
number of a values were used with the
exponential smoothing approach, and the value of 0.95 resulted in the
lowest MAD.
Clearly, simple exponential smoothing is not
an appropriate forecasting approach for this product. (Exponential
smoothing should be used only when no trend or seasonality are exhibited,
and this example demonstrates what would happen if this advice were
ignored.) It should also be
clear that the best approach to use for forecasting future demand for
Product 4 is the pure trend approach, since it resulted in the lowest MAD
when used to predict the past. Hence, our best forecast of demand
for first quarter next year (i.e., Period 13) is 41,800 units, and we
expect this to be wrong by somewhere around 1900 units (the trend model's
MAD).
| Period |
Demand |
Trend |
Seasonal |
Combined |
Exponential |
| t |
At |
Ft |
|et| |
Ft |
|et| |
Ft |
|et| |
Ft |
|et| |
1
2
3
4
5
6
7
8
9
10
11
12 |
15
17
24
28
24
29
31
30
31
37
37
40 |
17.4
19.4
21.5
23.5
25.5
27.6
29.6
31.6
33.7
35.7
37.7
39.8 |
2.41
2.44
2.53
4.50
1.54
1.43
1.40
1.63
2.66
1.31
0.72
0.24 |
23.0
27.1
31.0
33.3
23.0
27.1
31.0
33.3
23.0
27.1
31.0
33.3 |
7.98
10.13
6.98
5.25
1.02
1.87
0.02
3.25
8.02
9.87
6.02
6.75 |
15.4
19.8
24.5
28.3
20.9
26.4
32.0
36.3
26.5
32.9
39.5
44.4 |
0.37
2.79
0.47
0.28
3.07
2.64
0.98
6.33
4.50
4.06
2.48
4.39 |
15.0
15.2
16.1
17.3
17.9
19.1
20.3
21.2
22.2
23.7
25.0 |
2.00
8.80
11.92
6.73
11.06
11.95
9.75
9.78
14.80
13.32
14.99 |
| 13 |
n/a |
41.8 |
n/a |
23.0 |
n/a |
32.1 |
n/a |
26.5 |
n/a |
| Best method: Pure
Trend |
b0 =
15.38
b1 = 2.03
R2 = 91%
Syx = 2.39 |
SI1 =
0.804
SI2 = 0.949
SI3 = 1.084
SI4 = 1.163 |
b0 =
17.38
b1 = 1.73
R2 = 77%
Syx = 3.62 |
Alpha = 0.95 |
| MAD = 1.90 |
MAD = 5.60 |
MAD = 2.69 |
MAD = 3.23 |
|
