Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices

Abstract

Novel periodic extensions of dynamic long-memory regression models with autoregressive conditional heteroscedastic errors are consid- ered for the analysis of daily electricity spot prices. The parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood. The methods are implemented for time series of 1,200-4,400 daily price observations in four European power markets. Apart from persistence, heteroscedasticity, and extreme observations in prices, a novel empirical finding is the importance of day-of-the-week periodicity in the autocovariance function of electricity spot prices. In particular, the very persistent daily log prices from the Nord Pool power exchange of Norway are effectively modeled by our framework, which is also extended with explanatory variables to capture supply-and-demand effects. The daily log prices of the other three electricity markets—EEX in Germany, Powernext in France, and APX in The Netherlands—are less persistent, but periodicity is also highly significant. The dynamic behavior differs from market to market and depends primarily on the method of power generation: hydro power, power generated from fossil fuels, or nuclear power. The article improves on existing models in capturing the memory characteristics, which are important in derivative pricing and real option analysis. Electricity supply has been the responsibility of public- private companies in many OECD countries until recently. It is anticipated that the private trading of electricity will fur- ther intensify in the future and eventually move toward fully privatized electricity markets. In such markets, large volumes of electricity power will be traded in the short and long term together with future contracts and options. Although similari- ties with financial markets exist with respect to its operations, the price formation at electricity markets is more complex, be- cause it depends strongly on the short-term characteristics of the energy supply function. The instantaneous nature of elec- tricity and the availability of different plant technologies lead to atypical supply functions. On the other hand, electricity de- mand functions typically depend on weather variables, seasons in the year, day-of-week effects, and holidays. These character- istics of electricity supply-and-demand functions determine the specific behavior of electricity prices encountered in empirical work. The dynamic behavior of prices is important for deriva- tive pricing and real option analysis. Therefore, the empirical time series modeling of electricity prices is important for finan- cial traders and investors. Following the standard practice of modeling volatility in fi- nancial returns, we are interested in the conditional mean and variance of price innovations. For many efficient financial and commodity markets, log prices are assumed to behave as a ran- dom walk, and price innovations are obtained by simply taking