Realized Volatility Forecasting in the Spanish Electricity Market During the 2021–2025 Energy Crisis

This paper analyzes volatility forecasting in the Spanish electricity spot market over the period 2021–2025, characterized by uncertainty, frequent price jumps, and the increasing occurrence of zero and negative prices. To accommodate these features, electricity prices are shifted to ensure welldefined logreturns, and predictable intraday and seasonal patterns are removed using the Ullrich demeaning procedure. Daily realized volatility measures are constructed from highfrequency data, including jumprobust and noiserobust estimators such as Median Realized Volatility and Realized Kernel. A broad set of volatility models, comprising GARCHtype specifications and multiple extensions of the Heterogeneous Autoregressive (HAR) framework, is evaluated using a coherent outofsample forecasting procedure. Model comparison is conducted through the Model Confidence Set methodology based on the QLIKE loss function, which identifies a Superior Set of Models with equal predictive ability. Conditional diagnostics, including OutofSample ROOS2measures and Mincer–Zarnowitz regressions, are subsequently used to characterize forecast accuracy, unbiasedness, and efficiency. The empirical results show that all GARCH models are systematically excluded from the superior set, while HARtype specifications based on realized volatility dominate. Within this set, a HAR model incorporating Median Realized Volatility, jump components, and dayoftheweek effects delivers the strongest economic performance, achieving an OutofSample ROOS 2close to 0.5 with unbiased forecasts. Overall, the findings highlight the importance of longmemory dynamics, discontinuous price movements, and residual weekly seasonality for volatility forecasting in modern electricity markets.