# Ratio to trend values year quarters i ii iii iv 2000

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Ratio to-Trend Values Year Quarters I II III IV 2000 2001 2002 2003 2004 109.09 86.08 77.67 85.04 105.96 131.15 122.35 106.42 114.29 117.20 107.46 109.89 93.91 97.84 105.52 93.15 90.72 79.34 85.52 97.04 Total Average Adjusted Seasonal index 463.84 92.77 92.02 591.41 118.28 117.33 514.62 102.92 102.09 445.77 89.15 88.43

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207 The total of average of seasonal indexes is 403.12 (>400). Thus we apply the correction factor (400/403.12) = 0.992. Now each quarterly average is multiplied by 0.992 to get the adjusted seasonal index as shown in table. The seasonal index 92.02 in the first quarter means that on average sales trend to be depressed by the presence of seasonal forces to the extent of approx. (100-92.02) == 7.98 %. Alternatively, values of time series would be approx. (7.98/92.02) 100 = 8.67 % higher had seasonal influences not been present. 20.3.1.3. Ratio-to-Moving Average Method This method is also called the percentage moving average method. In this method, the original values in the time-series data are expressed as percentage of moving averages instead of percentages of trend values in the ratio-to-trend method. The steps of the method are summarized as follows: i. Find the centered 12 monthly (or 4 quarterly) moving averages of the original data values in the time-series. ii. Express each original data value of the time-series as a percentage of the corresponding centered moving average values obtained in Step (i). In other words, in a multiplicative time-series model, we get iii. Original data values . . . 100 100 ( . ) 100% Trend values . T C S I S I T C iv. This implies that the ratio-to-moving average represents the seasonal and irregular components. v. Arrange these percentages according to months or quarter of given years. Find the averages over all months or quarters of the given years. vi. If the sum of these indexes is not 1200 (or 400 for quarterly figures), multiply them by a correlation factor = 1200/ (sum of monthly indexes). Otherwise, the 12 monthly averages will be considered as seasonal indexes. Example - 3 Calculate the seasonal index by the ratio-to-moving method from the following data: Year Quarters I II III IV 2001 2002 2003 2004 75 86 90 100 60 65 72 78 53 63 66 72 59 80 85 93
208 Solution Calculations for 4 quarterly moving averages and ratio-to-moving averages are shown in table. Year Quarter Original Values Y=T.C.S.I 4- Quarter Moving Total 4- Quarter Moving Average 2 4- Quarter Moving Average T.C Rati-to- Moving Average (percent) =(S.I)100% 2001 2002 2003 2004 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 75 60 54 59 86 65 62 80 90 72 66 85 100 78 72 93 - 248 259 264 273 294 298 305 308 313 323 329 335 343 - - 507 523 537 567 592 603 613 521 636 652 664 678 - - - - 63.375 65.375 67.125 70.875 74.000 75.375 76.625 77.625 79.500 81.500 84.750 84.750 - - - - 85.20 90.25 128.12 91.71 85.13 106.14 117.43 92.75 83.02 104.29 92.03 92.03 - - Calculation of Seasonal Index Year Quarters I II III IV 2001 2002 2003 2004 - 128.12 117.45 120.48 - 91.71 92.75 92.03 85.21 85.13 85.13 - 90.25 106.14 104.29 - Total Seasonal Average Adjusted Seasonal Average 366.05 91.51 122.07 276.49 69.13 92.22 255.47 63.87 85.20 300.68 75.17=299.66 100.30=400 The total of seasonal averages is 299.66. therefore the corresponding correlation factor would be 400/299.68 = 1.334. Each seasonal average is multiplied by the correlation factor 1.334 to get the adjusted seasonal indexes shown in table.

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209 20.3.1.4. Link Relative Method This method is also known as Pearson’s method. The percentages obtained by this method are called link relatives as these link each month to the preceding one.
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