Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution
31.07.2024
Anne Opschoor (Vrije Universiteit Amsterdam and Tinbergen Institute), Dewi Peerlings (Vrije Universiteit Amsterdam and Tinbergen Institute), Luca Rossini (University of Milan and Fondazione Eni Enrico Mattei), Andre Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute)
multivariate distributions, (fat)-tail heterogeneity, (inverse) Riesz distribution, electricity prices
Tinbergen Institute
Tinbergen Institute Discussion Papers
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 t-Riesz 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 t-copula.