Exploring dependence structures among European electricity markets: Static and dynamic copula-GARCH and dynamic state-space approaches

In this paper, we examine various characteristics of both base and peak electricity spot prices and their returns, and investigate dependence structures, extreme co-movements, risk spillovers, and integration relationships among the five major European electricity markets, including France, Germany, the Netherlands, Spain, and the UK. To do so, we propose a new perspective by applying a hybrid of ARMA-GARCH, static and dynamic copulas, and dynamic state-space models with the Kalman filter to address the issue. Based on the results of the ARMA-GJR-GARCH model, we first find that there are spillover effects in the returns of both base and peak spot prices in the five European electricity markets, and there are heteroskedastic, asymmetric, and leverage effects with negative and positive shocks, including spikes and drops during both base and peak load periods. Hence, a decrease in prices will boom the variance of the returns, and a decrease in returns can lead to a much greater increase in volatility. Second, there exist some extents of positive dependencies, tail dependencies, and extreme co-movements among the European electricity markets based on the copula models. In addition, we find that the degree of (tail) dependence and the potential state of market integration are stronger and higher during the peak period than the base period, implying that the European electricity markets could boom or crash together, especially during the peak load period. Further, the results of both the dynamic copulas and dynamic state-space models show that most pairs of the European electricity markets co-move symmetrically and have a time-varying dependence, but do not appear to grow over time. Finally, we provide an application of the copula-GARCH model in estimating and predicting risk spillovers across the five European electricity markets. We document that there are high-risk spillover effects in the European electricity markets because the values of the Conditional Value-at-Risk (CoVaR) are large. Also, we find that the more integrated the market, the more the systematic risk contribution of the market as indicated by ΔCoVaR. Our findings provide useful information regarding the dependence, integration, risk management, and asset pricing for the European electricity markets. •A hybrid of ARMA-GARCH, static and dynamic copulas and dynamic state space models are deployed.•Investigating various behaviours of European electricity base and peak spot prices and returns.•Mode