Asymmetric Intervals

Overview

The EPF confidence intervals are asymmetric — the upper bound may extend further from the point prediction than the lower bound. This reflects the inherent asymmetry in electricity price forecast errors, where large positive surprises (price spikes) are more common than large negative surprises.

Why Asymmetric?

Price Distribution Asymmetry

Electricity prices are bounded below (rarely go below -20 EUR/MWh) but unbounded above (can spike to 200+ EUR/MWh during scarcity events). This creates an asymmetric error profile:

Typical error distribution:

         ▃▆█████▆▃▂▁▁
    ─────┼───────────────→
   -20  -10   0   +10  +20  +30  +40
        (overprediction)  (underprediction)

The right tail (underprediction) extends further than the left tail (overprediction).

Symmetric Intervals Fail

A symmetric interval (±15 EUR/MWh) would:

Overcover on the downside: Prices rarely fall 15 EUR below predictions
Undercover on the upside: Prices occasionally spike 15+ EUR above predictions
Waste interval width: Width allocated to the downside is wasted; width needed on the upside is insufficient

How Asymmetry Arises Naturally

The conformal prediction method produces asymmetric intervals automatically through signed residuals:

residual = actual_price - predicted_price

Positive residual → model underpredicted (price higher than expected)
Negative residual → model overpredicted (price lower than expected)

If the distribution of positive residuals (underprediction) extends further than negative residuals (overprediction), the quantile-based bounds will be asymmetric:

Example

Calibration residuals for DA1 bucket:

5th percentile:  -8.2 EUR/MWh  (lower bound shift)
95th percentile: +15.7 EUR/MWh (upper bound shift)

For a point prediction of 55.0 EUR/MWh:

90% CI lower: 55.0 + (-8.2) = 46.8 EUR/MWh  (8.2 below point)
90% CI upper: 55.0 + 15.7   = 70.7 EUR/MWh  (15.7 above point)

The upper band is nearly twice as wide as the lower band, correctly reflecting the greater upside risk.

Asymmetry by Condition

The degree of asymmetry varies with market conditions:

By Hour of Day

Period	Typical Asymmetry	Reason
Night (0–6)	Nearly symmetric	Stable, predictable prices
Morning ramp (7–9)	Moderate upside	Demand uncertainty
Solar peak (10–14)	Strong downside	Solar oversupply possible
Evening peak (18–21)	Strong upside	Demand spikes, solar dropout

By Horizon

Horizon	Asymmetry	Reason
D+1	Moderate	Short-term, less extreme errors
D+3	Growing	More room for conditions to change
D+7	Largest	Maximum uncertainty, rare events more likely

By Season

Season	Asymmetry	Reason
Summer	Upside heavy	Cooling demand spikes, low wind
Winter	Upside heavy	Heating demand, cold snaps
Spring/Fall	More balanced	Moderate conditions, fewer extremes

Visualization

On the forecast chart, asymmetric intervals appear as:

                    ┌─── Upper 90% (wider)
                   ╱
        ┌─── Upper 50%
       ╱
──────●────── Point prediction
       ╲
        └─── Lower 50%
                   ╲
                    └─── Lower 90% (narrower)

The visual asymmetry immediately communicates the direction of risk: when the upper bands are wider, prices are more likely to surprise on the upside.

Practical Value

Asymmetric intervals are more useful for decision-making than symmetric ones:

Traders: Can see that upside risk is larger, informing hedging strategy
Grid operators: Can assess worst-case cost scenarios (upper bound)
Renewable developers: Can evaluate downside price risk (lower bound)
Risk managers: Asymmetry directly maps to Value-at-Risk concepts