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Fan chart (time series)

Definition

A fan chart is a time-series visualization that displays a central forecast together with nested probability bands for future outcomes. The bands often widen with the forecast horizon, creating a fan-like appearance. Darker shading commonly marks a central region and lighter shading extends toward less central outcomes, but the legend must explain the convention. A fan chart communicates a forecast distribution rather than only a single line. Its probabilities are meaningful only to the extent that the underlying forecasting assumptions and calibration are credible.

What it means

A point forecast can hide the range of plausible outcomes relevant to planning. A fan chart makes that range visible at each future date. Some charts use equal-tail intervals around a median; others use regions organized around a mode or a skewed distribution. These choices are not interchangeable, so a central line should be labeled as a mean, median, mode or other summary. The picture does not turn uncertainty into certainty, and the outermost shaded boundary is usually a selected probability limit rather than the most extreme possible outcome.

How it works

Obtain a predictive distribution for each forecast horizon from a model, simulation or explicitly documented judgmental procedure. Choose probability levels, calculate the corresponding bounds and display them as nested bands along the time axis. Keep intervals and central summaries consistent with the selected definition. Label the variable, units, forecast origin and probability levels. Explain conditioning assumptions and distinguish uncertainty about future observations from uncertainty about an estimated mean. Evaluate interval coverage across suitable historical forecasts. Ordinary horizon-by-horizon bands generally describe marginal coverage at each date, not a simultaneous probability that the entire future trajectory stays inside the fan.

Three practical examples

• Demand planning: show a central sales forecast alongside ranges that help assess capacity needs.
• Service staffing: communicate how uncertainty changes over future scheduling periods instead of presenting one guaranteed workload path.
• Forecast review: compare stated probability bands with realized outcomes over many comparable forecast origins.

Think of it this way

Think of a forecast as a corridor of possible destinations whose width and shape can change with distance into the future. The corridor's labels explain how much probability it contains. Its edges are not walls that prevent reality from passing outside them.

Worked example

Suppose hypothetical demand forecasts are normal with mean 100 and standard deviation ten for next month, and mean 110 and standard deviation 20 for the following month. Equal-tail 80% intervals use approximately 1.28155 standard deviations: [87.18, 112.82] and [84.37, 135.63]. The 95% intervals use approximately 1.95996 standard deviations: [80.40, 119.60] and [70.80, 149.20]. Plotting both levels produces a wider second-month fan despite its higher central forecast. Each 80% interval concerns its own month. If the two future outcomes were independent, the probability that both fall within their respective 80% intervals would be 0.8 squared = 0.64, not 0.80. Real forecast errors are often dependent, so this product is an illustrative assumption rather than a general path-coverage formula.

Illustrative case study

Fictional case: Fern Capacity Planning replaces a single quarterly demand line with clearly labeled predictive bands. Managers compare capacity choices against several portions of the distribution and discuss the costs of shortages and unused capacity. Analysts retain the assumptions behind the fan and check historical coverage as new outcomes arrive. When a major operating change occurs, they explain that earlier calibration may no longer be reliable. This invented case illustrates transparent uncertainty communication and does not claim that a particular band corresponds to an optimal business decision.

Common misconceptions and mistakes

Do not call a 90% band a guaranteed range or assume outcomes outside it are impossible. Do not mistake pointwise bands for simultaneous coverage of every future date. Shading alone does not establish whether a chart uses equal-tail, highest-density or other intervals. A skewed distribution can have different mean, median and mode, so its visual center may be ambiguous. Wider horizons often have more uncertainty, but widening is not a universal mathematical requirement. An attractive fan can still be badly calibrated or omit important sources of uncertainty.

Business use

Businesses should connect the chart to decisions involving asymmetric consequences, such as excess capacity versus unmet demand. State which uncertainty sources are represented and which assumptions condition the forecast. Preserve a record of past issued forecasts so apparent accuracy is not assessed using revised predictions. Evaluate both coverage and informativeness: excessively wide bands may cover many outcomes while offering little guidance. Accessibility also matters; labeled boundaries and clear contrast help readers interpret the probabilities without depending solely on subtle color differences.

People also ask

Is the center always the expected value?

No. It may be a mean, median, mode or another chosen summary.

Does an 80% fan contain the whole future path with probability 80%?

Not generally; typical bands provide coverage separately by horizon.

Must the fan be symmetric?

No. Skewed predictive distributions can produce asymmetric bands.

Check your understanding

In the worked example, why is the second 80% interval wider?

Answer: Its forecast standard deviation is 20 rather than ten, doubling the interval's half-width under the same normal-distribution probability level.

Related terms

• Prediction interval
• Quantile
• Forecast horizon
• Calibration
• predictive distribution
• point forecast
• scenario analysis

Learn next

compare equal-tail intervals with other probability regions, then distinguish marginal forecast coverage from simultaneous path coverage using simulated forecast trajectories.

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Sources

Sources: Bank of England, The Inflation Report projections: understanding the fan chart, historical construction and skew: https://www.bankofengland.co.uk/-/media/boe/files/quarterly-bulletin/1998/the-inflation-report-projections-understanding-the-fan-chart.pdf ; Hyndman and Athanasopoulos, Forecasting: Principles and Practice, prediction intervals: https://otexts.com/fpp3/prediction-intervals.html ; Bank of England, 2024 forecasting review, discussion of fan-chart construction and limitations: https://www.bankofengland.co.uk/independent-evaluation-office/forecasting-for-monetary-policy-making-and-communication-at-the-bank-of-england-a-review/forecasting-for-monetary-policy-making-and-communication-at-the-bank-of-england-a-review .

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