[Paper Review] Comparing the Forecasting Performances of Linear Models for Electricity Prices with High RES Penetration

Angelica Gianfreda, Francesco Ravazzolo+1 more|arXiv (Cornell University)|Jan 3, 2018

Energy Load and Power Forecasting51 references51 citations

TL;DR

This study compares univariate and multivariate linear models—frequentist and Bayesian—for forecasting hourly day-ahead electricity prices in high renewable energy (RES) penetration markets. It finds that Bayesian vector autoregressive (BVAR) models incorporating forecasted demand, wind, solar, and fossil fuel prices deliver superior point and density forecasts across Germany, Denmark, Italy, and Spain, with wind forecasts proving more informative than solar ones.

ABSTRACT

This paper compares alternative univariate versus multivariate models, frequentist versus Bayesian autoregressive and vector autoregressive specifications, for hourly day-ahead electricity prices, both with and without renewable energy sources. The accuracy of point and density forecasts are inspected in four main European markets (Germany, Denmark, Italy and Spain) characterized by different levels of renewable energy power generation. Our results show that the Bayesian VAR specifications with exogenous variables dominate other multivariate and univariate specifications, in terms of both point and density forecasting.

Motivation & Objective

• To evaluate the forecasting performance of univariate versus multivariate linear models in high RES electricity markets.
• To compare frequentist and Bayesian estimation approaches for autoregressive and vector autoregressive models.
• To assess the incremental forecasting value of including forecasted demand, wind, solar, and fossil fuel prices in day-ahead price models.
• To determine whether wind or solar power forecasts are more informative for price prediction in different European markets.
• To provide empirical guidelines for market participants and regulators on optimal model specifications for electricity price forecasting.

Proposed method

• Employs univariate autoregressive (AR) and multivariate vector autoregressive (VAR) models for hourly day-ahead electricity prices.
• Incorporates exogenous variables: forecasted demand, forecasted wind and solar power generation, and fossil fuel prices (coal, gas, CO2).
• Applies both frequentist and Bayesian estimation methods, with the latter using informative priors to improve small-sample performance.
• Uses a panel data structure across four European electricity markets: Germany, Denmark, Italy, and Spain.
• Employs standard metrics: root mean squared error (RMSE) for point forecasts and continuous ranked probability score (CRPS) for density forecasts.
• Conducts out-of-sample forecasting with rolling windows to evaluate predictive accuracy across different time periods and market conditions.

Experimental results

Research questions

• RQ1 Do multivariate models outperform univariate models in forecasting hourly day-ahead electricity prices?
• RQ2 Does the Bayesian approach improve forecasting accuracy compared to the frequentist approach in this context?
• RQ3 Which exogenous variables—demand, wind, solar, or fossil fuels—provide the most significant forecasting gains?
• RQ4 Is the inclusion of wind power forecasts more informative than solar power forecasts for price prediction in high RES markets?
• RQ5 How does the forecasting performance vary across different European electricity markets with varying RES penetration levels?

Key findings

• Bayesian VAR models with exogenous variables (demand, wind, solar, and fossil fuels) consistently dominate all other univariate and multivariate specifications in both point and density forecasting accuracy.
• The inclusion of forecasted wind power leads to better performance than including only solar power, particularly for hours 8–24 in Germany, Italy, and Spain.
• Simultaneous inclusion of both wind and solar forecasts further improves model performance beyond using either alone.
• Fossil fuel prices (coal, gas, CO2) remain important predictors even with high RES penetration, and their exclusion reduces forecast accuracy.
• Multivariate models outperform univariate models due to their ability to capture inter-hourly dependencies in electricity price dynamics.
• The forecasting gains from including RES and demand are most pronounced during peak hours, with consistent improvements across all scoring rules (RMSE and CRPS).