Why Direct over Recursive

The Decision

The EPF system uses a direct multi-horizon forecasting strategy: separate models are trained for each horizon group, each predicting target prices directly from origin-time features. The alternative — recursive prediction, where each step’s output feeds as input to the next step — was evaluated and rejected.

Direct vs Recursive: How They Work

Recursive (Rejected)

Origin → Model → Predict hour 1 → Use as input → Predict hour 2 → ... → hour 168

A single model is trained, and predictions are made sequentially. Each prediction becomes a feature for the next time step. This mirrors the autoregressive structure of time series.

Direct (Chosen)

Origin → Model_DA1 → Predict hours 14-25 (D+1 morning)
Origin → Model_DA2 → Predict hours 26-37 (D+1 afternoon)
Origin → Model_S1  → Predict hours 33-56 (D+2)
...
Origin → Model_S5  → Predict hours 129-176 (D+6-D+7)

Each horizon group has its own model, trained specifically for that range. All models use only features known at origin time — no predicted values are ever used as inputs.

Why Direct Wins for EPF

1. No Error Propagation

The fundamental problem with recursive prediction is error compounding:

Hour 1 error: ±2 EUR/MWh
Hour 2 input includes hour 1's error → Hour 2 error: ±3 EUR/MWh
Hour 3 input includes hour 2's error → Hour 3 error: ±5 EUR/MWh
...
Hour 168: errors have compounded across 168 steps

By day 7, recursive errors can grow to the point where forecasts are no better than naive baselines. Direct prediction eliminates this entirely — each model’s error is independent.

2. Horizon-Specific Patterns

Different horizons have fundamentally different predictability:

D+1 morning (DA1): Highly predictable from overnight conditions, demand forecasts
D+1 afternoon (DA2): Solar generation creates volatility, but D+1 demand forecast is strong
D+2 (S1): D+1 published prices are a powerful feature
D+6-D+7 (S5): Weather forecast skill degrades; weekly seasonality dominates

A single recursive model must handle all these regimes. Direct models specialize, learning different feature importances for each horizon.

3. Parallelizable Prediction

Direct models are independent and can predict in parallel:

Sequential (recursive): ~168 model calls, each waiting for the previous
Parallel (direct):      7 model calls, all simultaneous

This is critical for production latency — the 10:00 UTC day-ahead forecast must complete quickly to be useful for trading decisions.

4. Independent Retraining

If day-ahead accuracy degrades but strategic accuracy is fine, only the DA1/DA2 models need retraining. Recursive models cannot be retrained at specific horizons without affecting all downstream predictions.

The Trade-off

Direct prediction has real costs:

Aspect	Direct	Recursive
Number of models	7 (DA1, DA2, S1–S5)	1
Model storage	~7× more artifacts	Minimal
Training time	~7× more (but parallelizable)	Less
Feature engineering	Must pre-compute all features at origin	Can use rolling features
Boundary effects	Potential discontinuities between groups	Smooth transitions

Boundary Discontinuities

Adjacent horizon groups may predict slightly different prices at their boundary. For example, DA2’s prediction for D+1 23:00 and S1’s prediction for D+2 00:00 are generated by different models and may not transition smoothly. In practice, this is rarely noticeable because:

The hours are 1 hour apart in real time
Both models see similar features at the origin
The ensemble averaging across three model types further smooths transitions

Horizon Group Design

The groups are designed to balance specialization with training sample efficiency:

Group	Hours	Size	Rationale
DA1	14–25	12h	D+1 morning — distinct demand profile
DA2	26–37	12h	D+1 afternoon — solar peak, demand peak
S1	33–56	24h	D+2 — D+1 prices as features
S2	57–80	24h	D+3
S3	81–104	24h	D+4
S4	105–128	24h	D+5
S5	129–176	48h	D+6–D+7 — merged for sample efficiency

S5 combines two days because forecast skill at 6–7 day horizons is similar, and merging them doubles the training samples available to the model.