Does your forecast beat persistence?

1. Samples. At each issue time t, the inputs are the last values of the series, centred and scaled with the learning series (optionally reduced by PCA), plus sin/cos clock inputs of the target time when the series has a period. The target is the value h steps later. All models are scored on the same issue times.
2. Fit and choice of settings. Only the learning series is used. Settings are chosen by expanding-window cross-validation: fit on the beginning, validate on what follows, four times with a longer fitting window. The best setting is then refitted on the whole learning series.
3. Intervals. The residuals of the four validation blocks are out of sample. Their quantiles (conformal) or their mean and standard deviation (Gaussian) give the lower and upper limits. The complex-valued AR scales them by its own forecast volatility, as in its paper.
4. Scores. Each forecast uses data available at its issue time. The target supplies the observed value for scoring. With Clip forecasts at 0, forecasts below zero are clipped when the learning series is nonnegative. For solar series, keep the regular grid and select the targets to score.

• The series to forecast must follow the learning series directly, with the same time step and no gap. Missing values are not accepted: fill or remove them first.
• Models written for solar irradiance use a clear-sky model in their papers; here the series itself (or its mean profile per phase) takes that place, so they apply to any series.
• The intervals assume that the errors seen in validation stay representative of the errors on the series to forecast.
• Trending series (prices, indices): models fitted on levels cannot extrapolate beyond the range of the learning series; the ELM fails there and persistence is hard to beat (NICE ≈ 1 is the expected answer). Forecasting returns or differences is often the right question.
• A learning and comparison tool: it gives no investment, trading or operational advice.

If FrugalCast helps your work, please cite the tool and the papers of the models and metrics you use. Tick what you used, then download one .bib file.

1. Benchmarks (PER, CLIM, CLIPER, ES, ARTU). Voyant C., Notton G., Duchaud J.-L., García Gutiérrez L. A., Bright J. M., Yang D. (2022). Benchmarks for solar radiation time series forecasting. Renewable Energy 191, 747–762. doi
2. NICE^k metrics. Voyant C., Despotovic M., Garcia-Gutierrez L., Amaro e Silva R., Lauret P., Soubdhan T., Bailek N. (2025). NICE^k metrics: unified and multidimensional framework for evaluating deterministic solar forecasting accuracy. Sustainable Energy Technologies and Assessments 83, 104588. doi
3. BLEND, cyclostationary operators, Holt-Winters, Theta, PAR. Voyant C., Banes C., Garcia-Gutierrez L., Notton G., Despotovic M., Yaseen Z. M. (2026). Symmetry-constrained forecasting of periodically correlated energy processes. Applied Mathematical Modelling 157, 116988. doi
4. Extreme learning machines for energy. Voyant C., Despotovic M., Garcia-Gutierrez L., Asloune M., Saint-Drenan Y.-M., Duchaud J.-L., Faggianelli G. A., Magliaro E. (2026). Short-term forecasting of energy production and consumption using extreme learning machine: a comprehensive MIMO based ELM approach. Applied Energy 410, 127599. doi
5. AR and ELM. Despotovic M., Voyant C., Garcia-Gutierrez L., Almorox J., Notton G. (2024). Solar irradiance time series forecasting using auto-regressive and extreme learning methods: influence of transfer learning and clustering. Applied Energy 365, 123215. doi
6. Complex-valued AR and its intervals. Voyant C., Lauret P., Notton G., Duchaud J.-L., Garcia-Gutierrez L., Faggianelli G. A. (2022). Complex-valued time series based solar irradiance forecast. Journal of Renewable and Sustainable Energy 14, 066502. doi
7. Periodic AR (PAR). Voyant C., De Gooijer J. G., Notton G. (2018). Periodic autoregressive forecasting of global solar irradiation without knowledge-based model implementation. Solar Energy 174, 121–129. doi · HAL
8. Stochastic and smart persistence. Voyant C., Notton G. (2018). Solar irradiation nowcasting by stochastic persistence: a new parsimonious, simple and efficient forecasting tool. Renewable and Sustainable Energy Reviews 92, 343–352. doi
9. Forecastability. Voyant C., Julien A., Despotovic M., Notton G., Garcia-Gutierrez L. A., Nicolosi C. F., Blanc P., Bright J. (2026). Stochastic coefficient of variation: assessing the variability and forecastability of solar irradiance. Renewable Energy 256, 123913. doi
10. Verification of deterministic forecasts. Yang D., Alessandrini S., Antonanzas J., et al., Voyant C., Zhang J. (2020). Verification of deterministic solar forecasts. Solar Energy 210, 20–37. doi
11. Expected errors. Lauret P., David M., Le Gal La Salle J., Lorenz E., Perez R., Voyant C. (2025). A simple method for quickly estimating solar irradiance forecast errors. Solar Energy 301, 113821. doi
12. A priori accuracy. Voyant C., Soubdhan T., Lauret P., David M., Muselli M. (2015). Statistical parameters as a means to a priori assess the accuracy of solar forecasting models. Energy 90, 671–679. doi
13. Spatio-temporal validation. Voyant C. (2026). A tolerance-based framework for spatiotemporal forecast validation using the γ-index. International Journal of Forecasting 42, 1207–1214. doi
14. Clear sky and normalization. Voyant C., Despotovic M., Notton G., Saint-Drenan Y.-M., Asloune M., Garcia-Gutierrez L. (2025). On the importance of clearsky model in short-term solar radiation forecasting. Solar Energy 294, 113490. doi
15. Input selection. Benkaciali S., Notton G., Voyant C. (2025). Comparative study of feature selection techniques for machine learning-based solar irradiation forecasting. Sustainability 17, 6400. doi
16. Transfer to scarce data. Despotovic M., Notton G., Voyant C. (2025). Transfer learning for wind speed forecasting: a scalable approach for data-scarce environments. International Journal of Green Energy 23, 669–684. doi
17. Review. Voyant C., Notton G., Kalogirou S., Nivet M.-L., Paoli C., Motte F., Fouilloy A. (2017). Machine learning methods for solar radiation forecasting: a review. Renewable Energy 105, 569–582. doi
18. ARMA and hybrids. Voyant C., Muselli M., Paoli C., Nivet M.-L. (2012). Numerical weather prediction (NWP) and hybrid ARMA/ANN model to predict global radiation. Energy 39, 341–355. doi
19. Hybrid methodology. Voyant C., Muselli M., Paoli C., Nivet M.-L. (2013). Hybrid methodology for hourly global radiation forecasting in Mediterranean area. Renewable Energy 53, 1–11. doi
20. PV_ELM_pred: the ELM variants (code).
21. cyclostationary-forecasting-matlab: BLEND, CLIPER, Holt-Winters, Theta, PAR (code).
22. Make_Stationary: frugal deseasonalization (code).
23. nice-metrics: NICE^k (code).

All of Cyril Voyant's papers: bibliography (BibTeX, RIS, CSL-JSON).

A notebook or a script can prepare a JSON job (series and settings) for this page, in two ways: a link ending in #job=… (button Share settings), or a .json file opened with Open settings or dropped on the page. The page fills in, and computes in the reader's browser when they click Run. A job may hold up to 50,000 values in each series. The format and examples are in API.md. To automate forecasts (scheduled runs, saved models, several horizons, forecasts of the future), use FrugalCast Local, the Windows kit.

{ "learn": [/* values */], "forecast": [/* values */], "period": 24, "horizon": 1,
  "models": ["cliper", "artu", "arma", "elm"], "interval": { "kind": "conformal", "coverage": 80 } }

Every model and every horizon in one run, on your own computer, with nothing sent anywhere. FrugalCast Local is the same engine as this page, packaged as a Windows kit run from PowerShell. It is built for data that cannot leave the premises, and for computers close to where the data are measured (edge computing): a plant, a substation, a lab server, a laptop in the field.

• Data sovereignty. No cloud, no account, no network connection: the series, the fitted models and the forecasts stay on your disk. Suited to confidential, personal or critical-infrastructure data.
• Edge and frugal. Thirty light models, from persistence to extreme learning machines, that run on an ordinary PC without a GPU.
• One run, everything. All 30 models and all horizons (for example 1 to 24 steps) in a single command, with every configuration tested, its validation error, and 20 metrics on the test period.
• Operational forecasting. Fitted models are saved and reloaded without refitting: forecasts of the future, with intervals, from your latest data, run by the Windows Task Scheduler. Refit when you choose.
• Traceable. Each model follows its paper or manual exactly; a reloaded model gives the same forecasts, bit for bit, as the session that fitted it.
• Free. Free for research, teaching and other non-commercial use, with a personal key: 30-day trial, then free 3-month keys from the Collaborate page. Please cite it.

Not available yet. The local kit and any programmatic access (API) are not available for now. To be told when it is, or to test it with your data, write through the Collaborate page.