Anyone who's ever worked on a city budget, planned for seasonal spikes in 311 calls, or tried to guess whether sales tax revenues will dip during an economic slowdown knows the challenge of wrestling with uncertainty. Luckily, forecasting gives us tools to handle that uncertainty thoughtfully... notably, prediction intervals.

In this post, we’ll explain what prediction intervals are, why they matter for municipal forecasting, and how they may help city leaders make better decisions with clearer expectations. No equations necessary.

Prediction intervals give target zones

Most people are familiar with the idea of forecasting a single number, like "We expect $9.2 million in sales tax revenues next quarter."

However, the problem with this is that a single number implies precision that just doesn’t exist. City revenues move within a range shaped by economic shifts, policy changes, changes in development, consumer behavior, and plenty of things no model can fully predict. A prediction interval simply acknowledges this reality and provides a range of plausible values based on historical patterns and model uncertainty.

So, with a prediction interval, perhaps we’d say: "We expect our sales tax revenues to be between $8.6 million and $9.8 million next quarter."

The range is a lot more informative than the single number and a lot more honest about how the world behaves compared to the single number.

So, what really is a prediction interval?

A prediction interval (PI) is a statistical way of expressing uncertainty. If your forecast for next quarter’s sales tax is $10.2M with a 95% PI of ±$400k, you’re really saying that:

• The model’s best single guess is $10.2M;
• But based on past volatility, the most plausible range is $9.8M to $10.6M.

Here’s the subtle part: a 95% interval doesn’t promise that next quarter’s revenue will land inside the range. It says that if we produced this kind of forecast over and over, about 95% of the time reality would fall inside the interval we published. Any single forecast is one roll of the dice. The interval describes the process, not a guarantee.

No one really needs to memorize that definition (don’t worry, we’ll do it for you), but understanding the spirit of it helps avoid confusion in interpreting the interval.

Where do these ranges come from?

Prediction intervals are built from two ingredients: the historical variation your city has already lived through, and the model’s estimate of how unpredictable the future is likely to be. The more stable the history, the narrower the interval. The more volatile the system, the wider the interval. Both tell you something useful.

That second ingredient, what statisticians call "model uncertainty," captures all the ways a forecasting model can fall short of the real world. Every model makes assumptions about trends, seasonality, and what’s driving behavior. Those assumptions may be imperfect, the future values of key inputs may be unknown, and real data is naturally noisy. When we build forecasts for cities, prediction intervals help us quantify the uncertainty inside the model, but they aren’t magic. Real outcomes can still land outside the interval when something the model never saw shows up: a one-time policy change, a major new employer, or a broader economic shock.

Interpreting wide vs. narrow prediction intervals

Prediction intervals, whether narrow or wide, are very informative. Narrow intervals imply that the system is predictable, and you may be able to rely more heavily on the central estimate. However, wide intervals tell us that uncertainty is high, and we may want to plan even more cautiously.

Why prediction intervals over a single number

For city budgeting and planning, prediction intervals offer clear advantages, such as:

Better Fiscal Planning: Knowing the potential downside helps finance teams prepare reserves, adjust spending, or set expectations with council early.

Better Informed Capital Decisions: Projects that rely on stable future revenues can be tested against low-end scenarios.

Operational Preparedness: Emergency services, utilities, and transit systems can plan for both high and low demand scenarios rather than a single guess.

Increased Transparency: Elected officials and the public see the forecast and the uncertainty, rather than setting up a “gotcha” moment when reality inevitably differs from a point estimate.

Clearly, a forecast range is a more responsible tool for stewardship.

Common Misunderstandings

Forecasting intervals can be confusing. Here are some pitfalls to avoid:

Believing narrower is always better

If it is too good to be true, then it’s not true. Sometimes a narrow interval means the model is overconfident.

You can shrink the width of a prediction interval by lowering your interval coverage (say, from 95% to 80%). That being said, while the estimate will look cleaner and more precise, this shouldn’t be reassuring. Statistical conventions recommend the usage of 90, 95, and 99% prediction intervals, though you may be comfortable with more risk.

Interpreting the central estimate as “the real number”

Reality may fall anywhere in the interval.

Assuming intervals account for everything

Policy changes, economic shocks, and one-time abnormal events often lie outside historical variance that a model captures.

Thinking uncertainty undermines validity

In reality, professionals who quantify uncertainty are more trustworthy, not less!

Mixing prediction intervals up with confidence intervals

We'll discuss this more in an upcoming post!

How to visualize a prediction interval

The concept of PIs is better conveyed visually. Here are a few popular options:

• Shaded fan charts: show widening uncertainty as time moves forward
• Bands around a line: predicted value in the center, intervals as the shaded region
• Scenario ranges: Optimistic, base, and pessimistic outcomes instead of statistical language.

These visualizations make uncertainty feel more concrete and actionable.

Embracing uncertainty is embracing better decisions

Prediction intervals may make your forecasts convey less certainty, but they surely will make them more realistic. By showing the range of plausible forecasts, they help leaders prepare for the future with clearer expectations, better assumptions, and fewer surprises. In municipal work, where every dollar and every service matters, that kind of clarity is invaluable.