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Forecast Accuracy Interview Questions: MAPE, WAPE, MASE, and Zero Demand
Practice forecast accuracy interview questions with hand-calculated MAPE, WAPE, and MASE, zero-demand caveats, and a defensible metric scorecard.
A forecast can be numerically close on a high-volume product and disastrously wrong on an intermittent one. In an interview, the hard question is rarely “What does MAPE stand for?” It is whether your accuracy measure still has a meaning when demand is zero, when products have different scales, and when a planner must act on the result. This guide gives you a calculation you can do by hand, a decision rule you can defend, and the caveats that distinguish a useful metric from a dashboard number.
Research fact: Hyndman and Athanasopoulos define forecast error on held-out observations and explain why MAPE is undefined at a zero actual; Hyndman’s later WAPE analysis gives the separate all-zero test-set limitation. Candidate reports: none are used to claim a particular employer asks these questions. Inference: an interviewer who asks about zero demand is testing denominator discipline and business judgment, not acronym recall.
What exactly is being scored?
Start by defining the unit of one forecast: item, location, target period, forecast origin, and horizon. A prediction made Monday for Friday demand is a different task from one made Thursday for Friday, even if both are labeled “Friday forecast.” If one model sees a promotion calendar after it was finalized and another does not, their scores are not comparable. Align each forecast with the actual value it was intended to predict, using only information available at its origin.
Let actual demand be A and the prediction be F. The signed error A minus F shows direction; absolute error |A minus F| shows magnitude. A forecast of zero against actual ten has signed error ten. A forecast of twenty against actual ten has signed error minus ten. Both have absolute error ten, but the operating consequences may differ: stockouts and waste have different costs. A single absolute-error score hides that distinction, so keep a bias measure and business-cost view alongside the headline accuracy measure.
Original interview exercise, not a reported company question: a store has actual daily unit demand [100, 0, 50] and forecasts [90, 10, 40]. The three absolute errors are [10, 10, 10]. Their mean absolute error is ten units. This miniature case intentionally includes a zero; it lets you explain exactly which denominators survive. Before computing, ask whether zero is a real no-sale day, a closed store, a stockout that censored observed sales, or a missing record incorrectly filled with zero. A metric cannot repair a bad target definition.
The Forecasting: Principles and Practice accuracy chapter distinguishes errors on new observations from fitted residuals. Your answer should too. Training fit is useful for debugging, but the score used for model choice should come from a genuine holdout or time-series backtest. State how promotions, holidays, new products, and changes in assortment affect the split; random row shuffling can leak future regimes into training.
MAPE: intuitive percentage, fragile denominator
Mean absolute percentage error averages |A minus F| divided by |A| over scored observations, usually multiplied by 100. In the exercise, day one contributes 10/100 = 10%; day three contributes 10/50 = 20%. Day two requires 10/0, so the three-day MAPE is undefined. It is not zero, not infinity as a usable KPI, and not the average of only the other two percentages unless the reporting contract explicitly excludes zero-actual periods.
That exclusion can reverse a decision. Imagine Model X always predicts a modest positive amount on zero-demand days while Model Y predicts zero there. If you silently drop zero-actual rows, the score ignores a real operational difference. Adding an arbitrary epsilon to the denominator merely changes the weighting scheme and can make the result highly sensitive to a chosen constant. If a tool returns a huge finite number instead of an exception, inspect its denominator policy rather than quoting the number as business truth.
MAPE also gives near-zero actuals enormous influence. Missing one unit when actual demand is one creates 100% error; missing ten units when demand is one hundred creates 10%, even though the latter consumes more inventory. That may be right for an equal-item percentage question but wrong for an inventory-cost question. Ask whose errors the metric is intended to weight and whether each SKU-day should count equally. Do not claim that a percentage metric automatically makes unlike products comparable; the behavior at small denominators matters.
A concise interview answer is: “MAPE is easy to communicate when actuals are strictly positive and materially away from zero. I would disclose the zero policy, report coverage, and pair it with unit error and a baseline. For sparse demand I would not use raw MAPE as the sole selection metric.” That answer sets a decision boundary rather than memorizing a formula.
WAPE: an aggregate denominator with a different failure mode
Weighted absolute percentage error divides the sum of absolute errors by the sum of absolute actuals over the same evaluation set. For the three-day case, numerator = 30 and denominator = 150, so WAPE = 20%. The zero-demand day still contributes its ten-unit miss to the numerator, while the nonzero days provide the denominator. This is why WAPE can be defined when some actuals are zero, unlike MAPE.
But if every actual in a test slice is zero, WAPE becomes numerator/0 and is undefined. Saying “WAPE handles zeros” without that qualification is an interview trap. Even with nonzero total demand, the aggregate score gives higher-volume observations greater implicit weight. That can make sense for total units missed, yet it may hide the failures of small but important items. Report both aggregate WAPE and segmented results when the business cares about long-tail SKUs, locations, or critical parts.
Hyndman’s 2025 discussion of WAPE also argues that a test-set denominator can make comparisons unstable for trending or seasonal series: the same absolute-error process can appear to improve when actual volume grows. That is an analytical caveat, not a reason to ban WAPE from every operational dashboard. Be precise about the estimand and time window. A monthly WAPE for a business with rising demand does not isolate model quality from the denominator’s growth; compare an unchanged baseline on the same periods before crediting the model.
The word “weighted” can invite an additional ambiguity. Some teams use “WMAPE” for sum absolute error divided by sum actual, while others apply external item weights. Ask for the exact formula and grain. If the dashboard first computes a WAPE per store and then averages stores, that result differs from pooling numerators and denominators across stores. Your answer should show which entity gets equal voice.
MASE: scale error by a training-period baseline
Mean absolute scaled error takes mean absolute test error and divides by the mean absolute error of a simple training forecast. For nonseasonal data, the common scale is the average absolute difference between consecutive training observations. For seasonal data with period m, use the average absolute difference between an observation and the one m periods earlier. The Forecasting: Principles and Practice definition makes this training-versus-test distinction explicit.
Suppose the exercise’s training sequence was [70, 80, 100]. The nonseasonal naïve differences are |80−70| = 10 and |100−80| = 20, averaging 15. The test MAE is 10, so MASE = 10/15, or about 0.67. The interpretation is that the model’s mean absolute test error is 0.67 times this training naïve scale. It does not prove the model beat an actual naïve forecast on the same test days. To claim that, calculate both models on the same holdout.
MASE can remain defined when a few test actuals are zero because those test actuals are not individual denominators. It is not guaranteed to be defined: if the training series is constant under the chosen naïve or seasonal-naïve comparison, its scale is zero. A very short history may also be insufficient for the chosen seasonal lag. Say what you would do: flag the series, use unit error and an explicit baseline on the evaluation window, or use a carefully defined pooled scale if the business question justifies it. Never hide a zero training denominator behind a default value.
MASE is especially helpful when comparing methods across series with different unit scales, but define the aggregation. An unweighted mean of per-series MASE gives each series equal weight; a sales-weighted aggregate answers another question. Neither is universally correct. For inventory planning, present at least one customer-impact or cost metric beside MASE. A model can reduce typical absolute error while increasing expensive stockouts.
How would you choose among these metrics in an interview?
Do not answer “always MASE.” First ask what decision the forecast drives. If the task is a single stable, positive-demand series and stakeholders understand percentage errors, MAPE may be a useful descriptive number with its assumptions stated. If they want total missed units relative to total units across an evaluation pool, WAPE communicates that ratio, provided the pool’s actual total is nonzero and time-window effects are visible. If they compare many scales or sparse series, MASE is a strong candidate when a meaningful, nonzero training baseline exists.
Then write a scorecard with at least three lanes: a primary metric, a failure guard, and a business outcome. For a store-replenishment forecast, that might be MASE, the count of all-zero or undefined series, and measured stockout plus waste cost. For capacity planning, it might be WAPE on a fixed region-month panel, a per-region tail-error report, and the cost of underprovisioning. The choice must follow the loss the organization can tolerate, not the neatness of a formula.
| Situation | First check | Defensible response |
|---|---|---|
| One zero actual among many | Is it real demand? | MAPE undefined; WAPE may be defined; inspect the process |
| Entire evaluation slice has zero actual | Does a positive forecast cost anything? | WAPE undefined; report unit error and false-positive volume |
| Constant training history | Is naïve scale zero? | MASE undefined; use another explicit comparison |
| Strong trend or seasonality | Does the denominator change with time? | Compare on matched windows and keep a baseline |
| High-value sparse item | Does aggregate volume drown it out? | Segment score and add business cost |
What does a convincing calculation answer look like?
A clear answer has four moves. First specify the forecast contract and validate actuals. Second compute absolute errors before percentages. Third inspect every denominator and state which metrics are undefined. Fourth map scores back to the decision. In the food-stocking practice question, the fourth move matters most: equal absolute errors can imply different waste and shortage costs.
If an interviewer changes the case to [0, 0, 0] actual demand and [1, 0, 2] forecasts, MAE is one unit, MAPE is undefined, WAPE is undefined, and MASE depends on the separate training baseline. If that baseline is nonzero, MASE can still be calculated; if it is zero, it cannot. This is a better answer than forcing a percentage onto a no-demand period. The operational discussion then asks whether those three forecast units caused excess stock, staffing, or harmless capacity reservation.
If the case changes to actuals [100, 200, 300] with the same ten-unit error each day, MAPE averages roughly 6.1% while WAPE is 30/600 = 5%. Neither number alone says the forecasts improved from the sparse-demand case; the target mix and denominators changed. Put both models on the same held-out observations, show item-level distribution and bias, and keep uncertainty ranges or scenario forecasts when decisions require them.
Finally, rehearse the explanation without formulas on a whiteboard: “MAPE asks for an average percentage per observation; WAPE asks what fraction of the total actual volume we missed; MASE asks how our error compares with a training naïve scale.” Immediately add the denominator caveat to each sentence. That short explanation is usually more persuasive than reciting three equations and ignoring zero demand.
Start with Build a time-series forecasting model, then use the three-day exercise above to challenge the metric you would report. A defensible forecast-accuracy answer makes its denominator, baseline, and business cost visible.