Sequence Models for Multi-Horizon Return Forecasts

Most cross-sectional return models make one prediction: what happens over the next fixed period, say five days. But a desk usually cares about several horizons at once — the 1-day move, the 5-day move, the 20-day move — and those forecasts are not independent. A stock that just jumped on an earnings beat behaves differently over the next day than over the next month. Training a separate model for each horizon throws away that structure and triples the work.

A sequence model treats the recent past — a run of daily returns, volumes, and features — as an ordered path rather than a single row of numbers, and learns to output a forecast for multiple horizons from one pass over that path.

Why order matters

A cross-sectional tree model sees "20-day momentum = 8%" as one number regardless of whether that 8% built up steadily or arrived in one gap yesterday. A sequence model — typically a recurrent network (LSTM/GRU) or a 1D convolution over time — reads the day-by-day path itself: [+0.3%, +0.1%, ..., +6%, +0.5%]. It can learn that a slow grind and a sudden jump with the same total return decay differently, because it has seen the shape, not just the summary statistic.

Worked example

A researcher builds a model that reads each stock's last 20 daily returns and volumes and outputs three numbers: predicted 1-day, 5-day, and 20-day forward return. For a stock that gapped up 6% on an earnings beat three days ago and has since drifted flat, the model outputs +0.05% (1-day), +0.20% (5-day), and -0.10% (20-day) — it has learned from history that single-day earnings jumps tend to give back a little of their gain over a month, a pattern a same-day snapshot of "20-day momentum" alone would not distinguish from a slow grind that keeps drifting up. Compare that to a stock with the same 20-day cumulative return built from a steady daily climb: the model outputs +0.15% (1-day), +0.60% (5-day), +0.90% (20-day), continuing the trend rather than fading it.

What this means in practice

Multi-horizon sequence models are attractive on desks that trade at more than one holding period from the same signal family, because a single training run produces consistent forecasts across horizons rather than several models that can quietly disagree about direction. The cost is data: sequence models need enough history per name to learn shape, not just level, and they are more prone to overfitting the idiosyncrasies of whichever market regime dominates the training window — a network trained mostly on calm markets can badly misjudge event-driven jumps it saw only a handful of times.