Transcript Document

T18-06 Seasonal Relatives
Purpose
Allows the analyst to create and analyze the "Seasonal
Relatives" for a time series. A graphical display of the
seasonal relationship is shown.
Inputs
Historical Time Series
Seasonality Labels
Outputs
Adjusted Seasonal Relatives
Graph showing Adjusted Seasonal Relatives
Limitations
60 Time Series Observations
12 Seasonality Labels
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Time Series Techniques
Seasonal Relatives – develops factors based on seasonality. These
factors are used to adjust future forecasts
Horizon: Intermediate range
Method:
Complicated Formula involving moving averages, and
centered moving averages. Depends on whether an even
or an odd number of periods are in the seasonality.
Strength: Ability to determine a seasonality factors to adjust
future forecasts.
Weakness: Lot of effort when no seasonality exists. Good idea
to look at data to determine if seasonality should be
considered.
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Forecast Accuracy
Given that a forecast is rarely correct, the methodology you choose
should be the one which provides the least error from the actual
historical demand. Forecast error is defined as the difference between
actual historical demand and the forecast.
  Forecast Error  A t  Ft
where A t  Actual historical demand at time t
Ft  Forecast at time t
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Forecast Error
24
23
22
21
2
20
19
11
18
17
16
15
14
0
1
2
3
4
5
6
7
8
9
10 11
12
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Monitoring the Forecast
There are two measures used to monitor the accuracy of a forecast. The
Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE).
The MAD is the average of the absolute value of the forecast errors.
The MSE is the average of the squared forecast errors.
MAD  average abs( )

MSE  average ( )
2

Note: The formula for the MSE shown above may vary slightly. Some
textbooks divide the sum of the squared errors by n-1 rather than n.
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Trend Adjusted Exponential Smoothing Example
Label Time
Q1
1
Q2
2
Q3
3
Q4
4
Q1
5
Q2
6
Q3
7
Q4
8
Q1
9
Q2
10
Q3
11
Q4
12
Time
Series
14.00
18.00
35.00
46.00
28.00
36.00
60.00
71.00
45.00
54.00
84.00
88.00
A company has looked at its quarterly
sales over the last three years, and
believes that in addition to a linear trend a
seasonal pattern is present.
Determine the adjusted seasonal relatives.
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Input the Seasonality Label and Time Series in the light green cells.
The adjusted seasonal
relatives are automatically
calculated.
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A graph showing the Adjusted Seasonal Relatives is
automatically produced.
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