ARTU — Statistical Reference Forecasting Methods for Solar Radiation

Reference implementation and technical documentation for ARTU, a second-order autoregressive naive benchmark introduced for solar irradiance forecasting, together with four classical reference methods it is built alongside: Persistence, Climatology, CLIPER, and Exponential Smoothing. Companion resource for:

C. Voyant, G. Notton, J.-L. Duchaud, L. A. Garcia-Gutierrez, J. M. Bright, D. Yang, "Benchmarks for solar radiation time series forecasting," Renewable Energy, vol. 191, pp. 747-762, 2022. https://doi.org/10.1016/j.renene.2022.04.065 (arXiv:2203.14959)

Contents

• ARTU.pdf — "Statistical Reference Method" technical note (algorithmic pseudo-code for all five reference methods below).
• K_alpha.zip — MATLAB implementation of the ARTU-specific interpolation step: K_alpha.m plus four precomputed lookup tables R0.mat, R0.01.mat, R0.05.mat, R0.1.mat (one per measurement-reliability level $R$).
• LICENSE — MIT.

The methods (from ARTU.pdf)

All five operate on the clear-sky index $\kappa(t)=I_{GH}(t)/I_{CS}(t)$ (global horizontal irradiance normalized by a clear-sky model), with $\kappa=1$ substituted whenever $I_{CS}(t)$ falls below a solar-elevation threshold $\varepsilon$ (night/twilight):

• PER (Persistence): propagates the last valid clear-sky index forward, $\widehat{I}{GH}(t+h)=\min\big(I{GH}(t-n)\cdot I_{CS}(t+h)/I_{CS}(t-n),\ \gamma\cdot I_{CS}(t+h)\big)$, clipped by an over-irradiance factor $\gamma\in[1,2]$.
• CLIM (Climatology): forecasts using the mean clear-sky index over the whole training sample, $\widehat\kappa=\overline\kappa$ — a naive floor that any useful model should beat.
• CLIPER (Climatology-Persistence): blends the two above via $\rho=\mathrm{ACF}(\kappa(n),\kappa(n-h))$, $\widehat\kappa=\rho,\kappa(t-h)+(1-\rho),\overline\kappa$.
• ES (Exponential Smoothing): like CLIPER, but averages the last $h_{\max}\in[10,48]$ clear-sky index values with exponentially decaying weights $(1-\rho)^i$ instead of just the lag-$h$ value.
• ARTU: a second-order extension of CLIPER/ES. It uses both the lag-$h$ and lag-$2h$ autocorrelations, $\rho_1=\mathrm{ACF}(\kappa(n),\kappa(n-h))$ and $\rho_2=\mathrm{ACF}(\kappa(n),\kappa(n-2h))$, and looks up the coefficients $(\alpha,K)$ solving the corresponding second-order AR system by bilinear interpolation over a precomputed grid $M(R)$ indexed by $(\rho_1,\rho_2)$, at a measurement-reliability level $R\in{0,0.01,0.05,0.1}$ (K_alpha.m + the R0*.mat tables in K_alpha.zip). With $S=\alpha+K$ and $P=\alpha K$:

$$\widehat\kappa(t)=S\cdot\kappa(t)-P\cdot\kappa(t-h)+(1+P-S)\cdot\overline\kappa,\qquad \widehat I_{GH}(t+h)=\widehat\kappa(t)\cdot I_{CS}(t+h)$$

This ARTU update rule (and the K_alpha lookup table interpolation it depends on) is also used as-is by the GHI reference forecasters in Make_Stationary.

Usage

% Unzip K_alpha.zip into your MATLAB path, then given the lag-h and lag-2h
% clear-sky-index autocorrelations (corrh, corr2h) and a reliability level Q:
[K, alpha] = K_alpha(corrh, corr2h, Q);   % Q in {0,1,2,3} -> R in {0, 0.01, 0.05, 0.1}

See ARTU.pdf, Algorithm 5, for the full ARTU update using K/alpha.

Citation

If you use this code or method, please cite the paper above (see citation.cff).

License

MIT. See LICENSE.