Density forecasting for electricity prices under tail heterogeneity with the t-Riesz distribution

We introduce the vector-valued t-Riesz distribution for time series models of electricity prices. The t-Riesz distribution extends the well-known Multivariate Student's t distribution by allowing for tail heterogeneity via a vector of degrees of freedom (DoF) parameters. The closed-form density expression allows for straightforward maximum likelihood estimation. A clustering approach for the DoF parameters is provided to reduce the number of parameters in higher dimensions. We apply the tRiesz distribution to a 24-dimensional panel of Danish daily electricity prices over the period 2017-2024, considering each hour of the day as a separate coordinate. Results show that multivariate t-Riesz-based density forecasts improve significantly upon the standard Student's t distribution and the t-copula. Further, the t-Riesz distribution produces superior implied univariate density forecasts during the afternoon for the distribution as a whole and during 8 a.m.- 8 p.m. in its left tail. Moreover, during crisis periods, this effect is even stronger and holds for almost every hour of the day. Finally, portfolio Value-at-Risk forecasts during the central hours of the day improve during crisis periods compared to the classical Student's t distribution and the tcopula.