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Smoothing with moving averages

How can smoothing with moving averages support strategic choice or positioning?

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Contents

A simple way to reduce short-term volatility in historical demand data so that the underlying growth trend becomes easier to estimate.

When a volatile demand series is difficult to interpret visually—particularly on a logarithmic chart—a moving average offers a straightforward numerical way to expose the trend.

When to use it

Apply moving-average smoothing when historical market size rises and falls irregularly and the underlying direction is obscured.

Origins

Moving averages developed within time-series statistics as a family of filters for separating a persistent trend from short-term variation. The centred simple moving average used here averages observations on either side of the focal period. It is a descriptive smoothing technique, not the same as the moving-average error models used in more advanced forecasting.

What it is

Markets can behave like a roller-coaster: annual movement may be real, yet the individual peaks and troughs can hide the direction that matters for planning.

Where a market has no consistent year-to-year pattern, take particular care with the H stage—estimating historical growth—in the HOOF approach to demand forecasting.

A logarithmic plot with a reasoned line of best fit is one way to reduce the visual effect of volatility. A centred moving average provides a simpler non-graphical alternative by replacing each observation with the average of a window around it.

How to use it

Work through the historical series as follows:

Choose the window. Examine the apparent cycle and select a smoothing period that reflects it; a three-year window is common for annual data.

Calculate centred averages. For each eligible year, average the value for that year with the values immediately before and after it. A centred window cannot produce an estimate for the first or last observation without an additional assumption.

Estimate the trend. Compare suitable smoothed start and end points and calculate the compound rate of change.

Figure A.1 illustrates the method with market-demand data from a consulting assignment.

Figure A.1 Smoothing with moving averages: an example

	2000	2001	2002	2003	2004	2005	2006	2007
Actual demand (£m)	1426	1223	1150	1201	1387	1452	1582	1555
Actual change/year (%)	n/a	–17%	–6%	4%	15%	5%	9%	–2%
Smoothed demand (£m)	n/a	1283	1191	1246	1347	1474	1530	n/a
Implied change/year (%)	n/a	n/a	–7%	5%	8%	9%	4%	n/a

Looking only at the endpoints—2000 and 2007—suggests a total increase of 5.4 per cent, equivalent to compound growth of just 0.75 per cent a year.

That result is misleading because 2000 coincided with the peak of the dot-com boom. Starting there suppresses the apparent trend; choosing the trough in 2002 would exaggerate it. A three-year moving average reduces this sensitivity by adding the previous, current and following observations and dividing the sum by three.

The smoothed series reveals a clearer pattern. Comparing 2001 with 2006 produces a total increase of 19 per cent and an average of 3.6 per cent a year across five smoothed years rather than seven raw observations. Reporting one decimal place implies more precision than the method supports. A planning estimate of 3.5 per cent a year, with a range of plus or minus 0.5 per cent—or approximately 3 to 4 per cent—better represents the evidence.

Top practical tip

Choose the averaging window from the business cycle and data frequency, then test whether a different reasonable window changes the conclusion.

Top pitfall

Do not calculate mechanically and ignore context. A boom, recession, supply shock or reporting change can explain an irregular value that smoothing would otherwise conceal.