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Quantitative Decision Making 7 th ed By Lapin and Whisler. Section 7.5: Forecasting Using Seasonal indices. Recall: Classical Time Series Model. Y t = T t ·C t ·S t ·I t T t : The trend component C t : The cyclic component S t : The seasonal component I t : The irregular component. - PowerPoint PPT Presentation
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Quantitative Decision Making 7th edBy Lapin and Whisler
Yt= Tt·Ct·St·It
Tt: The trend component
Ct: The cyclic component
St: The seasonal component
It: The irregular component
1. Isolate trend and cyclical elements together.
2. Four-quarter moving averagestt
tt
ttttt ISCT
ISCT
AverageMoving
Y
1. Add up the first four values in a time series, then divide by four.
2. Repeat this computation, but the initial quarter is dropped and the fifth is added.
3. Continue this process until you run out of new quarters.
Year Quarter
Data Four Quarter Moving Average
1 1 75
2 60
=(75+60+54+59)/4 = 62
3 54
=(60+54+59+86)/4 = 64.75
4 59
=(54+59+86+65)/4 = 66
2 1 86
=(59+86+65+63)/4 = 68.25
2 65
=(86+65+63+80)/4 = 73.5
3 63
4 80
Year Quarter
Data Four Quarter Moving Average/ Centered Moving Average
1 1 75
2 60
=(75+60+54+59)/4 = 62
3 54 =(62+64.75)/2 = 63.375
=(60+54+59+86)/4 = 64.75
4 59 =(64.75+66)/2 = 65.375
=(54+59+86+65)/4 = 66
2 1 86 =(66+68.25)/2 = 67.125
=(59+86+65+63)/4 = 68.25
2 65 =(68.25+73.5)/2 = 70.875
=(86+65+63+80)/4 = 73.5
3 63
4 80
Year
Quarter
Data
Four Quarter Moving Average/ Centered Moving Average
Original as percentage of moving average
1 1 75
2 60
=(75+60+54+59)/4 = 62
3 54 =(62+64.75)/2 = 63.375 =(54/63.375) x 100 =85.21
=(60+54+59+86)/4 = 64.75
4 59 =(64.75+66)/2 = 65.375 =(59/65.375) x 100 = 90.25
=(54+59+86+65)/4 = 66
2 1 86 =(66+68.25)/2 = 67.125 =(86/67.125) x 100 = 128.12
=(59+86+65+63)/4 = 68.25
2 65 =(68.25+73.5)/2 = 70.875
=(65/70.875) x 100 = 91.71
=(86+65+63+80)/4 = 73.5
3 63
4 80
Calculating Seasonal Indices
Year Quarter
1 2 3 4
1 ---- --- 85.21 90.25
2 128.12 91.71 85.13 106.14
3 117.45 92.75 85.13 104.29
4 117.99 92.03 --- ---
Median 117.99 92.03 85.13 104.29
Sum of Medians: 399.44 Seasonal Index = Median x (400/399.44)
Seasonal Indices
118.16 92.16 85.25 104.44
Year
Quarter
Data
Four Quarter Moving Average/ Centered Moving Average
Original as percentage of moving average
Seasonal Indices
1 1 75 118.162 60 92.16
=(75+60+54+59)/4 = 62
3 54 =(62+64.75)/2 = 63.375 =(54/63.375) x 100 =85.21
85.25
=(60+54+59+86)/4 = 64.75
4 59 =(64.75+66)/2 = 65.375 =(59/65.375) x 100 = 90.25
104.44
=(54+59+86+65)/4 = 66
2 1 86 =(66+68.25)/2 = 67.125 =(86/67.125) x 100 = 128.12
118.16
=(59+86+65+63)/4 = 68.25
2 65 =(68.25+73.5)/2 = 70.875
=(65/70.875) x 100 = 91.71
92.16
=(86+65+63+80)/4 = 73.5
3 63 85.254 80 104.44
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