## Identifying the seasonal variation

If we used our original sales series there would not be enough data to allow us to identify seasonal variations, so we are going to use the sales figures from our worked example above.

Looking at the original sales figures we can see not only an upward trend in sales, but also a consistent seasonal pattern. Sales in quarter 1 and quarter 4 are higher than the trend sales, and sales in quarter 2 and quarter 3 are lower than the trend sales. We can calculate an average variation from the trend for each of these quarters, which will allow us to adjust the extrapolated trend sales for each quarter to take account of the recognised seasonal pattern of the past. In other words, the trend line and the extrapolated trend smooth out seasonal variations - what we need to do to forecast future actual sales per quarter is to recreate these variations around the extended trend..

 Quarter Sales (\$000s) Moving average trend (\$000s) Sales - trend = seasonal variation (\$000s) 1 240 2 224 3 204 227.5 - 23.5 4 240 229.5 + 10.5 1 244 233.0 + 11 2 236 237.75 - 1.75 3 220 242.5 - 22.5 4 262 246.75 + 15.25 1 260 250.25 + 9.75 2 254 254.4 - 0.4 3 230 4 286

The figures in the last column show the seasonal variation for each quarter and confirm that sales in quarters 1 and 4 are higher than trend sales and sales in quarters 2 and 3 are lower than trend sales. We can use these seasonal variations to calculate the average seasonal variations, but it is important to note than from the limited sales data available these variations are based on such a small number of observations that they are unlikely to be very accurate and, therefore, should be used with caution. Firms that have been operating for many years are likely to have

 Quarter Calculation Average seasonal variation 1 (11 + 9.75) / 2 10.375 2 ( - 1.75 + - 0.4) / 2 - 1.075 3 (- 23.5 + - 22.5) / 2 - 23 4 (10.5 + 15.25) / 2 12.875

The average seasonal variations can be used with the extrapolated trend to produce a more accurate forecast. Where there is negative result the actual forecast sales can be established by taking the sales variation away from the trend sales figures. So for quarters 2 and 3, the predicted actual sales will be below the trend sales, although quarter 2 is very close to the trend sales. The average seasonal variations for quarters 1 and 4 should be added to the trend sales figure to produce more accurate sales figures.

In other words if the projected sales for the first quarter of year 4 is \$140,000, this figure would need to be increased by \$10.375 to provide a more accurate prediction.

### Trend Analysis Summary Method

• Plot the actual sales
• Work out the trend by using 8 quarter moving averages
• Add the trend to the original graph
• Extend (extrapolate) the trend (using other data for its angle)
• Calculate average seasonal variations for each quarter
• Predict actual future by recreating the shape of the seasonal variations around the extrapolated trend
• Read off the predicted actual sales for the future period required.