Short- to Mid-term Day-Ahead Electricity Price Forecasting Using Futures.

• Author: Steinert, Rick
• Position: Report - Statistical table

1. INTRODUCTION

   Modeling and forecasting electricity prices have become an important and broad part of economic research during the last decades. The specifics of electricity prices, also known as stylized facts as well as the due to new laws rapidly changing market conditions especially in Europe and Germany have promoted this development. Moreover, the data transparency has tremendously increased during the last years, either by law or by negotiated agreement data for e.g. electricity consumption, production, prices and even planned capacities can be downloaded via different sources like ENTSO-E or the exchanges themselves. The electricity exchanges also expanded their product portfolio by launching new electricity related products like new block products, derivatives or complete new spot auctions as e.g. the EXAA GreenPower auction. Even though these changes will provide the informed decision maker with more valid options, it also increases the complexity of the decision making process.

   One of the research approaches which tries to incorporate the changing market conditions is the econometric perspective, which in general constructs models which aim to capture the underlying behavior of the electricity price time series and can provide forecasts afterwards. These forecasts can help market participants in their decision making for e.g. investment decisions. Moreover, forecasts offer different utility dependent on their forecasting horizon. Forecasts of only a few days in advance can help electricity companies to adjust their production planning. For instance, if an owner of a pumped-storage hydroelectricity plant has information on extremely low prices in the future they can easily schedule their generation of electricity by releasing their water reservoir now and refill it later when the electricity price is low. Medium- or long-term forecasts can help market participants to identify investment opportunities in the long-run, e.g. when the decision of the construction of a new wind power plant is considered, as they need to have reliable information on future cash-flows for their product. This is especially important in Germany, as the market premium which producers of renewable energy receive is calculated according to the attachment 1 of [section]23a EEG ("Erneuerbare-Energien-Gesetz") by using, among others, the average monthly spot prices of the EPEX SE.

   Econometric models usually use the intertemporal correlation structure of day-ahead electricity prices and combine them with external fundamental or stylized facts related regressors to provide good forecasts, see for instance Weron (2014) for an extensive review of different models. However, these models usually struggle when it comes to mid- or even long-term horizon forecasting. The reason for that is mainly, that every non-deterministic regressor like electricity load, wind- and solar power production, water reservoir levels or fuel prices have to be forecasted as well. This means that the forecaster has not only the task to come up with a good model for the electricity price but also for the regressors, even though both time series may come from very different disciplines of research. Moreover, due to their autoregressive structure every error in forecasting of one of the series will have an impact on any consecutive forecasting time point, depending on the magnitude of the intertemporal correlation of the time series itself and especially the residuals. Some authors therefore try to either use already forecasted regressors or only lags of external regressors (e.g. Bunn et al. (2016) or Hagfors et al. (2016)). This in turn leads to a situation where the forecasting horizon is restricted to the lowest used lag of the external regressors. When the day-ahead price of electricity is concerned, this means that due to the usual hourly resolution, forecasting e.g. four weeks leads to 4 X 7 X 24 = 672 points in time which have to be forecasted. Simple autoregressive models also converge quickly to their mean, which make them incapable of forecasting longer forecasting horizons (Keles et al., 2012).

   Therefore, we want to setup a model, which is capable of generating reliable short to midterm forecasts of up to four weeks by using regressors, which provide a preferably long deterministic structure, which means that we do not have to forecast them for as long as possible. For this we have decided to use the EPEX day-ahead electricity spot price of Germany and Austria and combine it with the EEX Phelix futures which have a cash settlement based on the average EPEX spot price for different time horizons. As the literature is not consentaneous on the distinction between shortterm, mid-term and long-term, we decided to declare the forecasting horizon we use as short- to mid-term. Our forecasting horizon comprises 1 to 28 days. In the next paragraphs, whenever we list a paper according to their forecasting horizon, we follow their own definition of the term.

   The literature on mid- to long-term electricity price forecasting is very scarce (Yan and Chowdhury, 2013). This holds especially true for econometric modeling. Maciejowska and Weron (2016) for instance utilize an autoregressive modeling approach to forecast the UK electricity price for up to 45 days. The authors compare the difference in forecasting accuracy of, among others, AR-models with hourly precision and AR-models which only use the daily average. They find that in the mid-term simpler models without hourly resolution seem to be superior against more complex models which keep the complex hourly structure, while in the short-term this the relation is the other way round. Moreover, they also find that including regressors did not always lead to better forecasts, the inclusion of C[O.sub.2] prices for instance weakened the accuracy in general due to problems with forecasting this time series.

   In the study of Ziel and Steinert (2018) the authors apply an econometric autoregressive approach towards the sale and purchase curves of the EPEX day-ahead electricity price. By a simulation study they can replicate the market situation and provide mid- to long-term probabilistic forecasts for the electricity price as well as all other related components. For their study they use the auction bids as well as external regressors like wind and solar power. By evaluating coverage probabilities they are able to compare their probabilistic forecasting values with the real electricity price time series and state that given the long horizon the models tends to have promising results.

   Other approaches for mid- and long-term forecasting originate from other fields of electricity price research, e.g. heuristics as in Yan and Chowdhury (2015) or fundamental models like in Bello et al. (2016, 2017).

   Nevertheless the relationship between spot and future products is an extensive field of research in finance and in energy economics as well. However, the typical relationship of futures can be described by the difference in expectation about spot prices and the price of a future, which in commodities research is due to the participants necessity of getting a premium for storing a specific asset (Weron and Zator, 2014). But as electricity prices cannot be stored easily, this relationship tends to be more complex. The basic relationship is typically described as follows: (see e.g. Benth et al. (2008))

   [mathematical expression not reproducible] (1)

   where E[P.sub.T] | [I.sub.t]] is the expected electricity price of delivery period T based on the information set [I.sub.t] at time t

   To display the direct relationship of future products to expected prices, it helps to rearrange equation (1) to E[P.sub.T] | [I.sub.t]]:

   E[[P.sub.T] |[1.sub.t]] = R[P.sub.t,T] + [F.sub.t,T](2)

   It can be seen that there is a direct theoretical link between the expectation for electricity prices in the future, which can be e.g. generated by econometric modeling, and the price of the corresponding future product. Assuming that the risk premium is 0, we could easily obtain future electricity prices by taking a look at the future products. However, several authors have found various results concerning the risk premium, usually stating that there is a negative or positive risk premium present, usually determined by a complex set of variables see e.g. Redl and Bunn (2013) or Aoude et al. (2016). Given historical information on day-ahead electricity prices and futures as well as other relevant information concerning the risk premia it is possible to construct and forecast the hourly price forward curve. This was done with real data for the German and Austrian electricity market for instance by Caldana et al. (2017). Even though the authors had to forecast electricity spot prices as well, the focus of their study was to get realistic approximations for the hourly price forward curve. Paraschiv et al. (2015) utilized the estimated hourly price forward curves to simulate realistic hourly day-ahead spot price behavior for the German/Austrian market. They also conduct a forecasting study with two different time points with two different forecasting horizons each. They show that their combined regime-switching approach yielded better results than a combined ARIMA benchmark when the mean absolute percentage error (MAPE) is considered. Due to the nature of their approach and the fact that they have a similar forecasting horizon as we do, we will compare our models later on in detail. However, our model will differ in the sense that we focus on capturing the day-ahead price movements only by using the observable historic futures, for which we do not necessarily need the full hourly price forward curve. Nevertheless, the possible dependency of day-ahead electricity prices on future products is rather complex and needs a specific modeling approach.

   We will therefore setup a model which will use future products observable at a time point t to forecast hourly...