Prediction Intervals vs. Point Forecasts

When most people think of forecasting, they imagine a single number: tomorrow's temperature will be 72 degrees, next quarter's revenue will be $4.2 million, the server will need 340 GB of storage by March. These are point forecasts, and while they are useful as summaries, they hide something critical: how confident the model actually is.

A point forecast of 340 GB is very different if the model thinks it could plausibly be anywhere from 320 to 360 GB versus anywhere from 200 to 500 GB. The action you take depends entirely on that uncertainty. Prediction intervals make it explicit.

What Are Prediction Intervals?

A prediction interval is a range that is expected to contain the future value with a specified probability. A 90% prediction interval, for example, is constructed so that the true future value falls within it approximately 90% of the time. The interval has a lower bound (the 5th percentile forecast) and an upper bound (the 95th percentile), with the point forecast typically sitting somewhere near the center.

It is worth noting the distinction from confidence intervals, which quantify uncertainty about a parameter estimate. Prediction intervals are wider because they account for both model uncertainty and the inherent randomness of future observations.

Why Point Forecasts Are Not Enough

Point forecasts fail in any decision context where the cost of being wrong is asymmetric or where you need to plan for a range of scenarios.

Inventory planning. A retailer forecasting demand for a perishable product needs to know the upside risk. Ordering to the median forecast means stockouts roughly half the time. Ordering to the 95th percentile protects against lost sales but increases waste. The right order quantity depends on the relative cost of overstocking versus understocking, and you cannot compute it without a prediction interval.

Energy trading. A wind farm operator selling power into a day-ahead market commits to delivering a specific volume. If actual generation falls short, they buy the shortfall at spot prices, which can spike dramatically. The operator needs to know the lower tail of the generation forecast to size their commitment conservatively enough to avoid catastrophic spot market exposure.

Capacity planning. A cloud platform forecasting compute demand must provision enough capacity to handle peak load, and intervals also help identify anomalous spikes. Under-provisioning causes outages; over-provisioning wastes money. The right provisioning target is a high quantile (say the 99th percentile) of the demand forecast, not the median.

In each case, the decision framework requires not just the expected value but the shape of the uncertainty around it.

How TSFMs Generate Prediction Intervals

Modern time series foundation models produce prediction intervals through several mechanisms:

Sampling-based approaches. Chronos tokenizes time series values into discrete bins and generates forecasts autoregressively, sampling from the categorical distribution at each step. By running multiple forward passes with different samples, you obtain a set of forecast trajectories. The empirical quantiles of these trajectories form prediction intervals. This approach naturally captures complex, multimodal uncertainty shapes. See our Chronos deep dive for more on how this works.

Parametric distribution heads. Moirai outputs a mixture of location-scale distributions at each forecast step. You can compute quantiles analytically from the mixture parameters without sampling, which is faster and produces smoother intervals. The trade-off is that the distributional family constrains what uncertainty shapes can be represented. Learn more in our Moirai overview.

Quantile regression. Some models directly output specific quantiles (e.g., the 10th, 50th, and 90th percentiles) by optimizing a pinball loss during training. This avoids distributional assumptions entirely but only gives you the specific quantiles you trained for.

Calibration: Do the Intervals Actually Work?

Producing prediction intervals is one thing. Producing intervals that are correctly calibrated is another. A 90% interval should contain the true value 90% of the time, not 75% or 99%.

In practice, many models produce intervals that are too narrow (overconfident) or too wide (underconfident). Calibration is measured empirically: take a large set of historical forecasts, compute the fraction of actuals that fell within the stated intervals, and compare to the nominal coverage level.

If a model's 90% intervals only cover 82% of observations, you can apply conformal calibration as a post-processing step. The idea is simple: compute residuals on a held-out calibration set, find the empirical quantile of the absolute residuals that achieves the desired coverage, and widen the intervals accordingly. This is distribution-free and provides finite-sample coverage guarantees under mild assumptions (exchangeability of the calibration and test data).

Communicating Uncertainty to Stakeholders

Prediction intervals are only valuable if decision-makers understand and trust them. A few practical approaches help:

Fan charts show the forecast median with shaded bands of increasing width for wider intervals (e.g., 50%, 80%, 95%). The visual metaphor of a widening cone communicates intuitively that uncertainty grows with the forecast horizon.

Scenario tables translate intervals into concrete outcomes: "We are 90% confident demand will be between 1,200 and 1,800 units. At the high end, we need $X of inventory; at the low end, $Y." This grounds abstract statistics in business terms.

Avoid false precision. Reporting a forecast as "1,547.3 units" implies a level of accuracy that almost certainly does not exist. Round to meaningful precision and always pair the number with its interval.

Prediction Intervals on TSFM.ai

The TSFM.ai API supports quantile-based forecasts natively. When you submit a forecast request, you can specify the quantile levels you need (e.g., 0.05, 0.25, 0.5, 0.75, 0.95), and the response includes the forecast value at each quantile for every step of the prediction horizon. All supported models, whether they use sampling, distributional heads, or quantile regression internally, present a consistent quantile interface. This means you can switch between Chronos, Moirai, TimesFM, and other models without changing your downstream decision logic. Try it in the playground.