Decomposition: Level, Trend, Season
Splitting a series into level, trend, season and remainder makes each component inspectable and each failure attributable. What the parts mean and how to read them.
Decomposition splits a series into a level, a trend, a seasonal shape and whatever is left over. Its value is not that it forecasts better than other methods — often it does not by much — but that each part can be looked at separately, so a failure can be attributed to a part rather than to the model.
The series discussed in “Decomposition: Level, Trend, Season” is easier to interpret when changes in work capture are visible rather than silently folded into the history. Used for employee time tracking, open the current capability summary can provide consistent time and project evidence, provided corrections, category changes and missing periods remain traceable.
For a planning function that has to explain itself, that is worth more than a point of accuracy.
For an independent reference relevant to “Decomposition: Level, Trend, Season”, consult R Project for Statistical Computing. Compare the general material with the organisation’s actual horizon, data definitions and decision process.
The four parts
The level: where the series sits now. The trend: how that level is moving. The season: the repeating within-year or within-week shape. The remainder: everything the first three do not explain.
- Level — where the series sits now, with season and trend removed.
- Trend — how that level is moving.
- Season — the repeating within-year or within-week shape.
- Remainder — everything the first three do not explain.
A forecast is the first three projected forward; the remainder is what the band is measuring.
Reading the level
The deseasonalised, detrended current position. This is the number to watch for structural change, because in the raw series a change is always confounded with whichever cycle it fell in.
Most operations have never seen their own deseasonalised level, and showing it once usually starts a useful conversation.
Reading the trend component
Whether it is real, how steep, and whether it has changed direction recently. A trend component that wanders between re-fits is not a trend.
This is also where damping is applied, visibly, rather than being buried in a method.
Reading the seasonal component
The shape, and whether it is stable across years. A seasonal factor that is different in each of three years is not seasonality; it is events being absorbed into the season because they fell in the same month.
Plotting the seasonal factors by year, overlaid, settles this in a glance.
Reading the remainder
The most useful part and the least looked at. A remainder that is random noise means the three components have captured the structure. A remainder with pattern in it means something is missing.
Runs of same-signed remainder, spikes on particular dates, or a remainder that grows over time are each a specific diagnosis.
Remainder with dates on it
The most actionable finding available. Join the largest remainders to the event calendar and the change record; most of them will have a cause.
Each cause found is a driver that can be added, and the remainder shrinks by the amount it explained.
Whether the season scales with the level
Whether the seasonal swing scales with the level. In most demand series it does, which argues for multiplicative. Where it does not — a fixed-count effect like a daily batch — additive is correct.
Choosing wrongly produces seasonal errors that grow or shrink with the level, which is a recognisable pattern in the remainder.
Multiple seasons
Weekly and annual together, which most methods handle by applying one after the other. Where the two interact strongly — a bank holiday Monday — explicit event handling beats multiplied factors.
Three or four seasonal cycles is where decomposition starts to creak and an explicit regression on calendar features does better.
What decomposition does not do
Anticipate events, see structural breaks before they happen, or forecast the remainder. The remainder is, by construction, the part nobody can forecast.
Where the remainder is large relative to the components, the series is mostly noise and no method will do much.
Using it as a diagnostic rather than a forecaster
A legitimate and underused approach: forecast with something simple, and decompose in parallel to understand what is happening.
The decomposition tells you what to investigate; the simple method produces the number.
What to show a decision maker
The level with the season removed, the trend with its cause named, and the size of the remainder as a band. Three things, one chart.
It is much more informative than a forecast line and it invites the right questions.
Decomposition at two frequencies
Where both a weekly and an annual cycle exist, they are usually extracted in sequence: weekly first on daily data, annual afterwards on the weekly aggregate.
Doing it the other way round contaminates the annual estimate with weekday effects, because months contain different numbers of each weekday.
The component nobody owns
In practice the seasonal factors get set once and inherited forever, while the level and trend are re-estimated constantly.
Putting a date and an owner on the seasonal component is what stops a 2021 shape being used to staff 2026.
Re-fitting
Seasonal components annually, trend quarterly, level continuously. The seasonal component in particular should not be re-fitted every cycle: it is the most stable part and re-fitting adds noise.
A seasonal factor that changes materially at each re-fit is a sign that events are being absorbed into it, which is the one failure of this method worth watching for.