Point Forecasts

A point forecast is a single number for a future value — “demand next week is 500 units.” It is almost always a summary of something larger: most forecasting methods produce a distribution over possible futures, and “the point forecast is the mean of this distribution.”

Which makes the central question about point forecasts not how to compute one but what is lost when you report only that.

Which summary, and why it matters

The mean is not the only candidate, and the choice is made — knowingly or not — by the error measure you optimize: “a forecast method that minimizes the MAE will lead to forecasts of the median, while minimizing the RMSE will lead to forecasts of the mean.”

For a symmetric distribution the two coincide and the question is academic. For a skewed one — demand with occasional spikes, revenue with a long tail, latency — they differ, sometimes a lot, and the downstream decision usually has a preference. Skew alone does not determine the right stock or capacity choice: overage and shortage costs matter. With exponential demand of mean 1, shortage cost 9 and overage cost 1, the simple newsvendor optimum is the 0.9 quantile, about 2.303; ordering the mean is too low in that example. See forecast error, mean, and median.

Where the decision is explicitly asymmetric — the cost of being under differs from the cost of being over — the right summary is often neither, but a quantile chosen to match that ratio. See quantile forecasts and quantile level.

Reported alone, it reads as certainty

The authors of the standard text put the cost bluntly: “point forecasts can be of almost no value without the accompanying prediction intervals.” Their reasoning is that without an interval “there is no way of telling how accurate the forecasts are.”

The practical version of that: 500 units with interval [420, 580] and the same point estimate with interval [50, 950] provide different evidence, but neither width dictates an action. Compare expected losses, decision thresholds, available options, and the cost and timing of additional information. A slide with a single line on it cannot convey which of those situations you are in, and readers will assume the first. See prediction intervals and probabilistic forecasts.

Two further properties of point forecasts are worth knowing because they surprise people.

• Means add; quantiles generally do not. The mean forecast for a total is the sum of the mean forecasts for its parts. Component quantiles generally do not add to the total’s quantile. Whether the sum is too high, too low, or equal depends on the joint distribution; stock substitutability is a separate constraint.
• A forecast is not a target. A number that has been negotiated to match a plan is a commitment, and scoring it as a forecast measures the negotiation. Keeping the two separate is the precondition for any accuracy measurement meaning anything.

Where a single number genuinely is what a system needs — an input to an automated order, a field in a downstream table — the discipline is to keep the distribution available upstream and choose the summary deliberately at the point of use, rather than collapsing it at the point of production. A method that produces only a point value and no distribution is a deterministic forecast, and the accuracy of one is judged against a benchmark rather than in the abstract — see naïve baseline forecast.

References:

• Hyndman & Athanasopoulos, Forecasting: Principles and Practice (3rd ed.), §5.8 “Evaluating point forecast accuracy”
• Hyndman & Athanasopoulos, Forecasting: Principles and Practice (3rd ed.), §5.9 “Evaluating distributional forecast accuracy”
• Hyndman & Athanasopoulos, Forecasting: Principles and Practice (3rd ed.), §5.5 “Distributional forecasts and prediction intervals”