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