Introduction

Forecast accuracy decays with horizon. Predicting tomorrow's stock price achieves 2% RMSE; predicting 20 days ahead achieves 4% RMSE. This degradation is fundamental but not insurmountable. Understanding its causes and countermeasures is critical for long-horizon trading strategies.

Sources of Forecast Decay

1. Error accumulation: short-term forecast errors compound over long horizons. 2% error per day becomes ~5% over 20 days. 2. Regime non-stationarity: market structure changes unpredictably. A model trained on calm periods fails during volatility spikes. 3. Model misspecification: all models are simplifications. Long horizons expose these simplifications.

Theoretical Decay Rates

For a mean-reverting process with half-life h (days), long-horizon forecast error decays at rate sqrt(h). For mean reversion half-life of 5 days, 20-day forecast has uncertainty sqrt(20/5) = 2x the 1-day uncertainty. This sets a fundamental limit on accuracy.

For random walk processes (no mean reversion), forecast error grows without bound: σ_horizon = σ_1day * sqrt(horizon). This explains why long-term trend predictions are unreliable.

Strategies to Combat Decay

1. Ensemble models: different models decay differently. Combining them smooths decay. 2. Shrinkage: revert forecasts to mean over long horizons. This reduces variance at cost of bias. 3. Regime awareness: condition forecasts on current regime. Quiet-regime forecasts are more accurate than stress-regime forecasts.

Non-Linear Decay and Cliff Effects

In most cases, decay is smooth: RMSE increases gradually with horizon. However, at critical horizons (market event dates, earnings releases), decay accelerates. Before earnings, forecasts are highly uncertain due to unpredictable announcements.

Mitigate by using higher uncertainty estimates before key events. Update event calendars regularly and adjust forecast horizons accordingly.

Empirical Decay Curves

On S&P 500 daily returns with LSTM models: 1-day RMSE 0.9%, 5-day RMSE 1.4%, 10-day RMSE 1.8%, 20-day RMSE 2.2%. Decay is approximately sqrt(horizon). Beyond 30 days, decay flattens (uncertainty becomes dominated by long-term volatility).

Feature Staleness

Long-horizon forecasts rely on features that become stale: yesterday's volatility is relevant for tomorrow; last month's volatility is less relevant for 20-day forecasts. Use time-decayed features: weight recent observations more heavily.

Alternative Approaches

Instead of predicting prices, predict volatility or returns distribution. Distributional forecasts (quantiles) are more stable than point forecasts. Use for portfolio construction: long-horizon volatility estimates guide position sizing better than point returns.

Practical Recommendations

For trading horizons >10 days, use ensemble methods with regime conditioning. Combine multiple models with different decay characteristics. Monitor actual out-of-sample performance: if decay is faster than theoretical prediction, investigate model misspecification. Retrain monthly to adapt to changing regimes.