Combining Forecasts Across Horizons

A trend-following signal built from the last 60 days of price action and a mean-reversion signal built from the last 2 days are both, in some sense, "predicting tomorrow's return." Trading them as separate strategies works, but so does something less obvious: blending them into a single forecast that captures the fast-moving edge of one and the persistent edge of the other, rebalanced at whatever pace suits the mix. Doing this well is a horizon problem before it is a weighting problem.

Why horizon mismatch matters

If a short-horizon signal is measured in units of "expected return over the next day" and a long-horizon signal is measured in "expected return over the next month," adding them raw compares apples to oranges — the short-horizon number needs to be scaled up (or the long-horizon one scaled down) to a common horizon before combination makes sense. The usual approach converts each signal into an expected return per unit time, then re-aggregates to the horizon actually being traded.

$$w_i = \frac{IC_i / \tau_i}{\sum_j IC_j / \tau_j}$$

In words: give each signal a weight proportional to its information coefficient (how well it predicts) divided by its characteristic horizon, so that a signal predicting well over a short window contributes proportionally more per unit time than a slower one with the same raw predictive power.

Worked example

A desk has two signals on the same stock: Signal A (short-term) has an information coefficient of 0.08 measured at a 5-day horizon; Signal B (long-term) has an information coefficient of 0.12 measured at a 60-day horizon. Converting to a common "per 5 days" basis: Signal A stays at 0.08. Signal B's edge, spread across twelve 5-day periods, scales down by roughly $\sqrt{5/60} \approx 0.29$ under a typical square-root time-scaling assumption, giving an effective 5-day IC of about $0.12 \times 0.29 = 0.035$. Combining with equal-confidence weighting (proportional to each IC), Signal A gets weight $0.08/(0.08+0.035) \approx 0.70$ and Signal B gets $0.30$ — most of the near-term forecast should lean on the fast signal, with the slow signal contributing a smaller, steadier tilt.

Picture two decay curves like the one above, one falling fast and one falling slowly — combining forecasts across horizons means weighting each curve by how much signal it still has left at the horizon you actually care about, not by its peak.

What this means in practice

Multi-horizon combination is how many production signals are actually built: a slow factor (say, value) sets the long-run direction, and a fast factor (say, short-term reversal) times the entry and exit around it. Treated as one blended forecast rather than two separate strategies, the combination can trade less than the fast signal alone (because the slow signal keeps it from flip-flopping) while capturing more return than the slow signal alone.