Measuring Trend: Method of Moving Averages

The method of moving averages measures trend by smoothing out the short-term ups and downs in a series, so that the underlying long-term direction becomes visible. For an odd period (3-yearly, 5-yearly, 7-yearly, ...), a $k$-yearly moving average is computed as follows:

1. Add up the values of the first $k$ years — this is the first moving total.
2. Divide that total by $k$ to get the first moving average, and place it against the middle year of that block of $k$ years.
3. Slide the block forward by one year — drop the earliest year's value and add the next year's value — to get the next moving total, and repeat.

Worked Example — 3-yearly moving average. A firm's sales (₹ lakh) over seven years were:

3-yearly moving totals and moving averages:

Notice two structural features of the method: the trend values (16, 20, 24, 28, 32) rise smoothly and evenly even though the raw sales figures did not, and the first and last years always lose a trend value (here, 2015 and 2021) because a full block of $k$ years cannot be centred on them — a genuine, honest limitation of the method, not a computational slip.

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