Demand Forecast with a Regime Break
A utility forecasts monthly electricity demand for a service area. It has 96 months of data. A seasonal ARIMA model fitted to the first 72 months performs well in-sample, with a mean absolute percentage error of 3.1%. When the model is used to forecast the last 24 months, errors jump: the forecast consistently under-predicts, with a mean error of +4.8% and a MAPE of 9.6%. A new industrial customer began operations around month 70, and the utility also changed its metering system around month 78, which may have altered recorded consumption. The regulator requires a 12-month-ahead forecast with a stated uncertainty band, and the utility must submit within three weeks.
1. Diagnose why the forecast deteriorated and distinguish the two candidate explanations.
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Two explanations are on the table and they have different consequences. The first is a structural break in demand: a large industrial customer starting around month 70 raises the level of the series, so a model fitted to pre-break data will systematically under-predict, which matches the positive mean error. The second is a measurement artefact: a metering change around month 78 could shift recorded consumption without any change in true demand, producing a level shift in the data that is not a demand shift.
The timing helps discriminate. The under-prediction begins before month 78 if the industrial customer is the cause, and should be concentrated after month 78 if metering is the cause. The utility should plot the forecast errors month by month and look for the step. A further check is to compare recorded consumption against an independent series - billing records, substation load, or the customer's own meter - across the metering change. If the two series diverge only after month 78, the metering explanation gains weight.
A seasonal ARIMA fitted to 72 months simply cannot know about a level shift at month 70; its forecasts revert to the old mean. That is a model failure, not a data failure, and the fix is to model the break rather than to discard the model.
2. Recommend a forecasting approach and an uncertainty band that the regulator can accept.
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Rebuild the model on the full 96 months with an explicit intervention term. Include a step or ramp dummy for the industrial customer beginning at month 70, and a separate dummy for the metering change at month 78 if the evidence supports an artefact. Estimate the metering effect and, if it is an artefact, adjust the series before modelling so the forecast refers to true demand. Re-select the seasonal ARIMA order on the adjusted series and check residuals for remaining autocorrelation and for any further break.
For the uncertainty band, do not rely on the model's analytic prediction intervals alone. Backtest: refit on data up to month 84 and forecast months 85–96, then compute empirical error quantiles. Combine the analytic interval with the backtest error distribution, taking the wider of the two. Because the industrial customer is a single large load, add a scenario band that reflects plausible variation in its consumption.
Present the forecast as a central path with an 80% and a 95% band, state the assumptions about the industrial customer and the metering adjustment, and note that the band widens with horizon. Three weeks is sufficient for this; the work is re-estimation and backtesting, not new data collection.