Case studies / Public services
Seasonal ARIMA Forecasting with Intervention Analysis for Resource Planning
Twelve years of monthly demand with seasonality, trend and structural breaks — where simple smoothing methods failed consistently.
The challenge
What the organisation came with
A public sector organisation needed accurate demand forecasts to support workforce and resource planning — the kind of forecast that determines staffing levels and budget allocation for the year ahead.
Their historical demand contained three complications at once. There was strong seasonal variation, a long-term trend, and structural changes caused by external events — step changes in the level of the series that no amount of smoothing will absorb.
Simple forecasting methods produced consistently inaccurate estimates. Not occasionally wrong: systematically wrong, because the methods being used could not represent the features actually present in the data.
The approach
How it was analysed, and why that method
Why SARIMA with intervention analysis
A seasonal ARIMA model was fitted, which represents both the seasonal cycle and the underlying trend within a single framework, and intervention analysis was used to model the structural breaks explicitly rather than letting them contaminate the trend estimate.
Moving averages and simple exponential smoothing were rejected. Neither can adequately model seasonality alongside structural breaks — a smoother treats a step change as noise to be averaged away, which is precisely why the earlier forecasts drifted.
An external event that permanently shifts the level of a series is a fact about the world. Modelling it explicitly preserves the trend estimate either side of it; smoothing over it corrupts both.
From model to operational tool
Forecast accuracy was assessed on held-out data rather than on the period the model was fitted to. The model was then packaged as automated scripts and a forecasting dashboard, so the organisation could regenerate forecasts as new months arrived without commissioning fresh analysis each time.
Delivered
What the client received
The value
What changed as a result
The organisation incorporated the forecasts into annual operational planning and budget allocation.
The dashboard and scripts mattered as much as the model: a forecast that can only be refreshed by re-engaging a consultant tends not to get refreshed.
Written from the assigned statistician's own project notes. The client is not named and no identifying detail, data or figures are published. Scale and timeframe are approximate.
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