Combine financial forecasts only after checking how their errors move

Finance may have a statistical revenue forecast and a commercial forecast for the same month. Choosing whichever performed best last month is not the only option. A combination can be useful when the methods capture different information and their mistakes do not consistently reinforce each other.

Hyndman and Athanasopoulos discuss averaging forecasts as a practical forecasting method and explain the importance of error correlation when constructing a combined distribution. That is a reason to test a combination, not a guarantee that adding another model will improve a particular business forecast.

Begin with comparable forecasts. They need the same revenue definition, customer population, currency, target period and information cutoff. Averaging recognized revenue with bookings, or a current forecast with last month's version, produces a number without a clear analytical meaning.

Consider four invented completed periods. Define error as forecast minus actual and express amounts in thousands of dollars. Method A has errors of positive 20, negative 20, positive 20 and negative 20. Method B has errors of negative 10, positive 10, negative 10 and positive 10.

A simple average of the two forecasts has errors of positive five, negative five, positive five and negative five. Its root mean squared error is five, compared with 20 for method A and ten for method B. The combination is more accurate in this constructed example because the errors partly offset.

Now reverse the signs of method B's errors so they move with method A. The equal-weight average then has errors of positive 15, negative 15, positive 15 and negative 15. Its root mean squared error is 15, worse than method B alone. The same component error sizes lead to a different combination result because their relationship changed.

For an equal-weight average, error variance equals one quarter of each component's error variance plus one half of their error covariance. Positive covariance limits the reduction from averaging. Negative covariance can provide a larger reduction. The practical question is whether the historical relationship is credible for the future decision.

Variance alone does not describe systematic bias. If both methods repeatedly overstate revenue, averaging can retain that overstatement even when the combined forecast looks less volatile. Review the mean error and the reasons behind it alongside measures of dispersion.

Different model names do not establish different information. Two methods may both rely on the same incomplete sales feed, or both assume that delayed launches start next month. Trace common inputs and judgment calls. A shared omission can survive an elaborate combination unchanged.

Examine the disagreement on material individual periods, not only its historical correlation coefficient. An apparent offset can arise because one method systematically reports an invoice a month earlier. Correcting that timing mismatch may be preferable to relying on an average that hides it.

An equal-weight average is an understandable candidate. If one method forecasts $120,000 and another $100,000 for the same defined target, the combination is $110,000. Record that rule before evaluating the period's actual result.

Weights estimated from historical errors can be useful, but they add another fitted component. A small sample can produce extreme weights that exploit accidental patterns. Compare any estimated-weight method with the simple average on outcomes that were not used to select those weights.

Avoid changing weights because the resulting number sits closer to a sales target. That turns a forecasting method into a target negotiation. If management chooses a different operating plan, preserve that plan separately from the forecast and explain the actions required to achieve it.

Retain forecasts as they were issued and compare them on common historical origins. A model may help at a one-month horizon and add little at six months. Review the combination for the actual planning horizon rather than assuming one weighting works for every decision.

Check several completed periods and relevant operating conditions. Four alternating errors make the arithmetic easy to inspect but say nothing reliable about an actual revenue process. A method whose useful information only appears during renewals may need a different interpretation outside that period.

Where the business has changed, determine whether old evaluation periods remain informative. A new billing model or acquisition can alter the target being forecast. Preserve the historical record, but do not treat an old error covariance estimate as permanent simply because it fills a required spreadsheet cell.

A combined point forecast does not automatically come with a valid uncertainty interval. Averaging the endpoints of two intervals generally does not establish the claimed coverage for the combined forecast. Dependence between errors and the way the distributions are represented matter.

Use a method that handles the combination's uncertainty coherently, then evaluate its subsequent coverage and width. If the available analysis supports only a point average, say so. A visually narrow shaded band should not be added merely because it makes the combination appear more sophisticated.

Keep model disagreement visible. A $110,000 average can conceal components at $109,000 and $111,000 or at $60,000 and $160,000. Those situations call for different investigation, even when the arithmetic midpoint is identical. Ask what information explains a material divergence before approving the operating response.

Specify the required inputs, weights, missing-model fallback and review cadence. If one contributor fails to deliver a forecast, the business should know whether to use the remaining method, a baseline or an explicitly labeled judgment. Quietly carrying forward a stale component changes the method.

Track the combination beside its components after implementation. Retain it while the evidence supports its value and the maintenance effort remains proportionate. The useful result is a more dependable forecast for a defined decision, with a clear explanation of what each method contributes.