BLEND persistence: a step-by-step forecast
Worked example / Exemple chiffré. All input values below are fictitious teaching values, not observations or results from the cited paper.
Result: with recent irradiance 600 W/m², yesterday’s target-phase value 400 W/m² and correlation 0.6, simplified BLEND predicts 560 W/m².
The question / La question
Should the next forecast follow the latest measurement or the recurring daily pattern? BLEND combines both. The closed form below is the simplified, tilde variant; the full cyclostationary variant has a different coefficient.
Calculate it, without using the future
- Set the forecast origin t to 12:00 today, horizon h to one hour and cycle T to 24 hours. The target is 13:00 today.
- Use I(t) = 600 and I(t + h − T) = 400, measured at 13:00 yesterday. Both are available at issue time.
- Estimate the phase-dependent correlation ρ(t,h) = 0.6 using a historical training period only.
- Compute λ = (1 + 0.6)/2 = 0.8.
- Compute Î(t+h) = λ I(t) + (1−λ) I(t+h−T) = 0.8 × 600 + 0.2 × 400 = 560 W/m².
| Reference | Forecast W/m² |
|---|---|
| Ordinary persistence | 600 |
| Previous-cycle, target-phase persistence | 400 |
| Simplified BLEND | 560 |
What this study contributes
The published study develops a family of analytical forecasting operators for periodically correlated energy signals. The calculation illustrates its simplified BLEND member; it does not reproduce the full benchmark.
Limits that matter
A convex combination stays between its two inputs; this alone says nothing about forecast accuracy. Statistics require enough past cycles. The weight changes with phase and horizon. Do not estimate it using the test period. The MATLAB function stores a forecast at its issue-time index: align it with the observation at t+h when scoring.
Source definitions, especially simplified BLEND · MATLAB implementation · Full method guide
À retenir : pondérer une mesure récente et la même phase du cycle précédent. Le coefficient simplifié ne remplace pas toutes les variantes BLEND ; la prévision et son observation doivent être alignées dans le temps.
Authors, source and citation
Cyril Voyant, Candice Banes, Luis Garcia-Gutierrez, Gilles Notton, Milan Despotovic, Zaher Mundher Yaseen. Symmetry-constrained forecasting of periodically correlated energy processes. Applied Mathematical Modelling. doi:10.1016/j.apm.2026.116988.
Cyril Voyant wrote this teaching page. The method belongs to the complete author team credited above.
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