Choosing the Forecast Horizon

Two teams build volatility forecasting models on the same data. One predicts tomorrow's volatility; the other predicts volatility 20 trading days out. Both are legitimate forecasting problems, but they're not comparable, and treating them as interchangeable is a common mistake — a model that's excellent at 1-day-ahead prediction can be nearly worthless at 20 days out, and vice versa. The forecast horizon — how far into the future the target sits relative to the features — is one of the first and most consequential choices in building any forecasting model, and it should be driven by what the forecast will actually be used for, not by whatever the data happens to make convenient.

The trade-off: predictability versus usefulness

As the horizon $h$ grows, most financial time series get harder to predict — the signal-to-noise ratio typically decays, often close to something like $1/\sqrt{h}$ for a mean-reverting quantity, because more unpredictable events have time to occur between "now" and the forecast target. But a longer horizon is often more useful operationally: a 1-day volatility forecast may be too accurate-but-late to act on if it takes two days to actually rebalance a hedge, while a 20-day forecast gives enough lead time to execute a plan before the predicted change happens.

$$\text{Usable horizon} = \max\big(\text{execution lag},\; \text{decision lead time needed}\big)$$

In plain English: the shortest horizon actually worth forecasting is set by how long it takes to act on the forecast — there's no point forecasting one day ahead if executing the resulting trade takes three days, because the forecast will already be stale by the time anyone can use it.

Worked example: matching horizon to a hedging decision

A desk needs to decide how much collateral to post against a derivatives book, a decision that takes about 3 business days to fully execute once made (approvals, counterparty confirmation, funding transfer). A 1-day-ahead volatility forecast, however accurate, arrives too late to act on before conditions have already moved past it — by the time the collateral adjustment clears, three more days of information have arrived that the 1-day forecast never saw. A 5-day-ahead forecast, even though its raw accuracy (say, R² of 0.15 versus 0.35 at 1 day) is lower, is the one that's actually operationally useful, because it gives enough lead time to complete the adjustment process before the predicted volatility change occurs. Choosing the "more accurate" 1-day model here would be optimizing the wrong thing entirely.

Sketching predictive R² (or correlation) against horizon length, as the explorer's decaying curve illustrates, is a good habit before committing to one horizon — it shows both how fast accuracy decays and where a workable trade-off between accuracy and lead time actually sits.

What this means in practice

Before choosing a forecast horizon, write down explicitly how the forecast will be used and how long that use takes to execute — the horizon should be at least that long, even if a shorter one would score better on a pure accuracy metric. It's also worth evaluating a range of horizons rather than one, since the R²-versus-horizon curve itself is useful information: a curve that decays very fast suggests a fundamentally short-memory process, while a slowly decaying one suggests real forecastable structure exists further out.