Forecasting U.S. domestic flight volumes
Monthly departures are one of the most seasonal series in transportation. This note walks through how two standard approaches — SARIMAX and exponential smoothing — handle that seasonality, and how to decide which one to trust.
Almost every aviation question eventually reduces to a volume question. How many flights, on what schedule, in which direction the trend is bending. Get the volume path roughly right and the rest of the analysis — capacity, revenue, utilization — has something solid to stand on. Get it wrong and every downstream number inherits the error.
So it is worth being deliberate about how those forecasts are built. This note compares two workhorses on monthly U.S. domestic flight volumes: a seasonal ARIMA with exogenous terms (SARIMAX) and an additive exponential-smoothing model, ETS(A,N,A). Both are fit and evaluated in R.
The shape of the data
Domestic departures carry a strong, stable seasonal signature — summer peaks, winter troughs, a repeatable within-year rhythm — layered on a slower-moving trend that shifts with the business cycle and, more abruptly, with shocks. Any credible model has to reproduce the seasonal shape first and the trend second.
That immediately narrows the field. A model that cannot represent a 12-month seasonal cycle is disqualified before it starts, no matter how well it fits the recent trend.
Two ways to model it
SARIMAX
Seasonal ARIMA models the series through its own autocorrelation — how this month relates to recent months and to the same month a year ago — and lets you add exogenous drivers where they help. The strength is flexibility: with the right differencing and seasonal terms it can capture both the annual cycle and the persistence in the trend. The cost is that it asks more of you. Order selection and the stationarity assumptions are decisions, not defaults.
ETS(A,N,A)
The exponential-smoothing family describes a series as a combination of level, trend, and seasonal components. The (A,N,A) specification reads as: additive errors, no trend component, additive seasonality. In plain terms — it leans hard on a steady level and a fixed seasonal pattern, and deliberately declines to extrapolate a trend. That restraint is a feature when the recent trend is noisy and you don't want the model chasing it.
The interesting result is rarely which model wins. It is what the disagreement between them tells you about the series.
Choosing between them
Two checks do most of the work:
- Out-of-sample error. Hold back the most recent stretch, forecast it, and compare against what actually happened. Accuracy on data the model never saw is worth far more than fit on data it was trained on.
- Residual diagnostics. Run a Ljung-Box test on the residuals. If meaningful autocorrelation is left behind, the model has missed structure that a better specification could still capture — and the forecast intervals will be too optimistic.
When SARIMAX passes the residual check and holds its accuracy out of sample, its added flexibility earns its keep. When it doesn't — over-fit, unstable orders, residuals that still carry signal — the disciplined ETS(A,N,A) is often the more honest forecast, precisely because it refuses to invent a trend.
The takeaway
For a strongly seasonal, moderately trending series like domestic departures, the practical answer is usually to run both and read them against each other. Where they agree, you have a robust base case. Where they diverge, the gap is a map of your uncertainty — and that gap is exactly the thing to surface for anyone making a capacity or capital decision on top of the number.
A forecast's job is not to sound confident. It is to be honest about what is known, what is seasonal, and what is genuinely uncertain.
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