Matching Forward-Return Horizon to Signal Decay

A short-term order-flow imbalance signal genuinely predicts something about the next few minutes of price movement — and almost nothing about where price will be next month. If you label your training data with next-month returns and train a model on that order-flow feature, you're asking the model to find a relationship in the data that simply isn't there over that horizon, and it will either learn nothing useful or, worse, latch onto spurious noise that happens to correlate over the sample period. The forward-return horizon used to build training labels has to roughly match the timescale over which the underlying signal actually carries information — its decay.

What signal decay means

Every predictive signal has a half-life: the length of time before its predictive edge meaningfully fades. A momentum factor built from 12-month past returns might carry useful predictive information for the next one to three months. A microstructure signal like order-book imbalance might only be informative for the next few seconds to minutes. Signal decay can be measured empirically by computing the correlation (or information coefficient) between the signal and forward returns at a range of horizons, and observing where that correlation peaks and where it fades back toward zero.

Why mismatched horizons hurt training

If the true signal decays over roughly a week and you label training examples with 1-day forward returns, you're forcing the model to predict a horizon shorter than where the signal's edge is strongest — the labels are dominated by short-horizon noise the signal barely touches, and the model under-learns the real relationship. If instead you label with 60-day forward returns, the label window stretches far past where the signal has any real information left; the true short-lived predictive relationship gets diluted and swamped by everything else that happens to a stock's price over two months, and the model again fails to find the real signal, or finds a spurious substitute that happens to fit the noise in that particular sample.

Worked example: measuring decay before labeling

Suppose you compute the information coefficient (a rank correlation between a signal and forward returns) for a signal at several horizons: 1 day, 0.02; 5 days, 0.06; 10 days, 0.05; 20 days, 0.02; 60 days, 0.00. The correlation peaks around the 5–10 day mark and has essentially vanished by 60 days. This tells you the signal's real decay window is roughly one to two weeks — a training label built from 5-day or 10-day forward returns will capture the bulk of the signal's genuine predictive content, while a 1-day label captures too little of it (the signal hasn't fully "played out" yet) and a 60-day label captures none of it (by then the signal's edge is long gone and the label is dominated by unrelated later events).

Adjust the decay rate above — a signal's information coefficient across horizons traces a similar shape, rising then fading, and the forward-return label horizon should be chosen near where that curve peaks, not arbitrarily.

What this means in practice

Horizon matching is one of the most common and most avoidable mistakes in quantitative signal research: many "broken" models are actually fine signals labeled with the wrong horizon. Measuring empirical decay before committing to a training label — rather than defaulting to whatever horizon a data pipeline already produces — is a cheap diagnostic that should come before any model-building.