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Quantitative Decision Making 7 th ed By Lapin and Whisler
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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
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1. Isolate trend and cyclical elements together. 2. Four-quarter moving averages
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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.
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YearQuarterDataFour Quarter Moving Average 1175 260 =(75+60+54+59)/4 = 62 354 =(60+54+59+86)/4 = 64.75 459 =(54+59+86+65)/4 = 66 2186 =(59+86+65+63)/4 = 68.25 265 =(86+65+63+80)/4 = 73.5 363 480
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YearQuarterDataFour Quarter Moving Average/ Centered Moving Average 1175 260 =(75+60+54+59)/4 = 62 354=(62+64.75)/2 = 63.375 =(60+54+59+86)/4 = 64.75 459=(64.75+66)/2 = 65.375 =(54+59+86+65)/4 = 66 2186=(66+68.25)/2 = 67.125 =(59+86+65+63)/4 = 68.25 265=(68.25+73.5)/2 = 70.875 =(86+65+63+80)/4 = 73.5 363 480
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YearQuarterData Four Quarter Moving Average/ Centered Moving Average Original as percentage of moving average 1175 260 =(75+60+54+59)/4 = 62 354=(62+64.75)/2 = 63.375=(54/63.375) x 100 =85.21 =(60+54+59+86)/4 = 64.75 459=(64.75+66)/2 = 65.375=(59/65.375) x 100 = 90.25 =(54+59+86+65)/4 = 66 2186=(66+68.25)/2 = 67.125=(86/67.125) x 100 = 128.12 =(59+86+65+63)/4 = 68.25 265=(68.25+73.5)/2 = 70.875=(65/70.875) x 100 = 91.71 =(86+65+63+80)/4 = 73.5 363 480
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Calculating Seasonal Indices YearQuarter 1234 1-------85.2190.25 2128.1291.7185.13106.14 3117.4592.7585.13104.29 4117.9992.03--- Median117.9992.0385.13104.29 Sum of Medians: 399.44 Seasonal Index = Median x (400/399.44) Seasonal Indices 118.1692.1685.25104.44
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YearQuarterDataFour Quarter Moving Average/ Centered Moving Average Original as percentage of moving average Seasonal Indices 1175 118.16 260 92.16 =(75+60+54+59)/4 = 62 354=(62+64.75)/2 = 63.375=(54/63.375) x 100 =85.21 85.25 =(60+54+59+86)/4 = 64.75 459=(64.75+66)/2 = 65.375=(59/65.375) x 100 = 90.25 104.44 =(54+59+86+65)/4 = 66 2186=(66+68.25)/2 = 67.125=(86/67.125) x 100 = 128.12 118.16 =(59+86+65+63)/4 = 68.25 265=(68.25+73.5)/2 = 70.875=(65/70.875) x 100 = 91.71 92.16 =(86+65+63+80)/4 = 73.5 363 85.25 480 104.44
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