Moving averages are used to find the trend and seasonal variations in a set of sales figures which can then be used to forecast sales figures:

Moving averages are used in time series analysis where there are various factors which can affect how sales occur: Seasonal variations, long-term trend, cyclical variations and random variations.

To see the underlying trend, the mean average of several periods (eg 4 quarters) is used, The moving average is calculated as the mean average of the set of periods. Then the next moving average is the mean average calculated by dropping the value of the first period and using the value of the next period after the last one previously used; and so on.

If there is an odd number of periods in each of these moving averages, the moving average will align with the middle value used and is the trend value for those periods.

If there is an even number of periods in each moving average, the moving averages will occur between two periods and so the mean average of each pair of moving average must be taken to find the trend values, which will then align with the figure after the middle of the periods.

For example, using a moving average with 4 quarters:

Year 1 qtr 1

Year 1 qtr 2

____________ moving average 1 of y1q1 to y1q4

Year 1 qtr 3 _____________________________________ mean average of ma1 and ma2

____________ moving average 2 of y1q2 to y2q1

Year 1 qtr 4 _____________________________________ mean average of ma2 and ma3

____________ moving average 3 of y1q3 to y2q2

Year 2 qtr 1 _____________________________________ mean average of ma3 and ma4

____________ moving average 4 of y1q4 to y2q3

Year 2 qtr 2 _____________________________________ mean average of ma4 and ma5

____________ moving average 5 of y2q1 to y2q4

Year 2 qtr 3 _____________________________________ mean average of ma5 and ma6

____________ moving average 6 of y2q2 to y3q1

Year 2 qtr 4

with:

moving average 1 of y1q1 to y1q4: ma1 = (y1q1 + y1q2 + y1q3 + y1q4) ÷ 4

moving average 2 of y1q2 to y2q1: ma2 = (y1q2 + y1q3 + y1q4 + y2q1) ÷ 4

etc.

mean average of ma1 and ma2 : trend1 = (ma1 + ma2) ÷ 2

mean average of ma2 and ma3 : trend2 = (ma2 + ma3) ÷ 2

etc.

Using regression the line of best fit is found for the trend figures calculated from the moving averages above.

By subtracting the trend values from the actual values (with which they align) the seasonal variation for each period can be calculated.

With the trend line and the seasonal variations forecasts can now be made by extrapolating the trend line and adding on the relevant seasonal variation.

In the above example, the year 3 quarter 1 sales can be forecast by using the trend line to find the trend value for y3q1 and then adding in the seasonal variation for q1 (which can be found at year 2 quarter 1 in value trend3). Note that seasonal variations can be negative so adding in a negative value will reduce the forecast figure.

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