wenmin-wu/timeseries-ratio-target-for-smape

Ratio Target for SMAPE

Overview

When the evaluation metric is SMAPE, predicting absolute values penalizes errors asymmetrically. Transforming the target to y_{t+1}/y_t - 1 (the relative change) aligns standard regression losses with SMAPE's symmetric percentage nature. The model learns relative changes, then predictions are converted back via pred * last_known_value + last_known_value.

Quick Start

import pandas as pd

df = df.sort_values(["entity_id", "date"])
df["target_ratio"] = df.groupby("entity_id")["value"].transform(
    lambda s: s.shift(-1) / s - 1
)

# Train model on target_ratio with standard MAE/MSE loss
# At inference:
last_known = df.groupby("entity_id")["value"].last()
df["prediction"] = last_known * (1 + predicted_ratio)

Workflow

1. Sort by entity and time, compute value_{t+1} / value_t - 1 as the training target
2. Clip extreme ratios (e.g., to [-0.005, 0.005]) to limit outlier influence
3. Train any regression model (XGBoost, LightGBM, linear) on the ratio target
4. At inference, multiply predicted ratio by the last known value to recover the forecast
5. For multi-step horizons, chain predictions or use the last known value for all steps

Key Decisions

• Clip bounds: [-0.005, 0.005] works for slowly-changing density metrics; widen for volatile series
• Division by zero: replace zero denominators with a small epsilon or carry forward the last nonzero value
• Multi-step: chaining introduces compounding error — for short horizons (1-3 steps), direct last-value scaling is more stable
• vs log-differencing: ratio target is simpler and avoids log(0) issues; log-diff is better when changes span orders of magnitude

References

• Better XGB Baseline
• GoDaddy: Tune Stacking