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Double moving average

Definition

A double moving average is a moving average applied to a series that has already been smoothed by a moving average. The second pass smooths the first-pass values further. In time-series work, it can support trend analysis and, with additional calculations, a forecasting method that estimates level and slope.

What it means

An ordinary moving average reduces short-term fluctuations by averaging neighboring observations. A double moving average repeats that operation on the resulting averages, rather than returning to the original observations for an unrelated second calculation.

The extra smoothing can make a persistent pattern easier to see, but it also changes how quickly the series responds to new information. Here the term refers to repeated averaging in forecasting and time-series analysis. It should not be confused with a trading strategy that merely compares two moving averages of different lengths.

How it works

Choose the averaging window and its alignment. For a trailing three-period calculation, average the latest three observations to produce each first-pass value. Once three first-pass values are available, average those to obtain the second-pass value. Continue as new observations arrive.

If both passes use complete trailing windows of length n, the first second-pass value requires 2n minus 1 original observations. The combined weights on those observations are not equal: middle observations participate in more of the overlapping windows.

Forecasting procedures can use the difference between the first and second averages to estimate a trend. Simply treating the twice-smoothed value as a forecast is a different choice and does not automatically correct the lag introduced by smoothing.

Three practical examples

1. An operations analyst smooths daily workload observations twice to inspect an underlying pattern before investigating unusual days.

2. A service team compares a simple trend-forecasting baseline based on double moving averages with other methods on withheld historical periods.

3. A personal activity dashboard displays a twice-smoothed history to reduce visual noise, while retaining the raw observations so that sudden changes remain visible.

Think of it this way

Think of making a rough line easier to follow by smoothing it once and then smoothing the softened line again. The result is calmer, but sharp corners become less obvious. This can help reveal a broad direction while also hiding or delaying evidence of a sudden turn. The smoother line is a transformed view of the measurements, not a more accurate record of what happened on each day.

Worked example

Suppose an invented daily series is 10, 12, 14, 16 and 18. Use complete trailing windows of three observations for both passes.

The first moving averages are (10 + 12 + 14)/3 = 12 at day three, (12 + 14 + 16)/3 = 14 at day four, and (14 + 16 + 18)/3 = 16 at day five.

The first double moving average, available at day five, is (12 + 14 + 16)/3 = 14. Expanding the overlapping calculations gives the same answer as (10 + 2 times 12 + 3 times 14 + 2 times 16 + 18)/9 = 126/9 = 14.

The combined weights are therefore 1, 2, 3, 2 and 1, divided by nine. This is not the same weighting rule as an ordinary five-period moving average, even though both happen to equal 14 for this perfectly linear example.

At day five the actual observation is 18, the first average is 16 and the second average is 14. Their gaps illustrate lag on an increasing series. No future observation was used, and no forecast-accuracy claim follows from this constructed example.

Illustrative case study

Fictional case: Aspen Operations reviews a noisy daily series of service requests. A twice-smoothed plot helps managers see a gradual rise that is difficult to notice in the raw chart. However, a sudden jump after a product launch appears only gradually in the smoother.

The team keeps both plots visible and uses the raw series for immediate investigation. When testing forecasts, analysts reproduce each historical forecast using only observations available on that date. They compare errors across ordinary weeks and launch periods rather than assuming that a smoother-looking line must predict better.

Common misconceptions and mistakes

Double smoothing is not the same as doubling the window length, and it does not give every original observation an equal weight. The worked example's triangular weights explain why.

Do not confuse this method with double exponential smoothing or with the moving-average error component of an ARIMA model. A centered smoother may use observations from both sides of a date, which makes it unsuitable as a real-time calculation at that date without delay. Additional smoothing also does not automatically remove seasonality, outliers or structural changes.

Business use

Use a double moving average as a transparent exploratory tool or a clearly specified forecasting baseline. Document window lengths, alignment, missing-data handling and whether partial windows are allowed. These choices affect both the numbers and when they become available.

Evaluate forecasts at the horizons that matter operationally, using a time-respecting backtest. Consider whether reduced noise is worth slower response to change. For a dashboard, distinguish observed values from smoothed estimates; for planning, assess forecast errors and uncertainty rather than selecting the visually smoothest line.

People also ask

Is the result always better than a single moving average?

No. It smooths more, but the extra lag may be undesirable.

Does double mean two different window lengths?

In this sense it means applying a moving average to moving-average values; any window choices should be stated.

Can it forecast a trend?

A forecasting procedure can derive level and slope from the averages, but the second average alone is not automatically a trend-adjusted forecast.

Check your understanding

With complete trailing windows of length four for both passes, how many original observations are needed for the first second-pass value?

Answer: Seven. The first-pass values become available at observations four, five, six and seven; averaging those four values gives the first double moving average.

Related terms

• Moving average
• Smoothing
• Forecast horizon
• Exponential smoothing
• trend
• lag
• rolling window and time-series validation

Learn next

apply one-pass and two-pass averages to a short series containing a sudden jump. Compare response speed and the effective weights. Then evaluate any forecasting extension on future observations that were excluded from its calculation.

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Sources

Primary sources: Hyndman, Glossary of Forecasting Terms, double moving average and moving average entries: https://robjhyndman.com/mwh3/FG4.pdf

NIST/SEMATECH e-Handbook, Centered Moving Average, including its discussion of double moving averages for trending series: https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc422.htm

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