Elsevier

Energy Economics

Volume 59, September 2016, Pages 435-454
Energy Economics

Electricity price forecasting using sale and purchase curves: The X-Model

https://doi.org/10.1016/j.eneco.2016.08.008Get rights and content

Highlights

  • Real auction data is used for probabilistic electricity price forecasting.

  • Full supply and demand curves are modeled and forecasted.

  • The new stylized fact of price clustering is elaborated.

  • The X-Model provided great prediction performance, especially for price spikes.

  • Bridges the gap between fundamental/structural and econometric models.

Abstract

Our paper aims to model and forecast the electricity price by taking a completely new perspective on the data. It will be the first approach which is able to combine the insights of market structure models with extensive and modern econometric analysis. Instead of directly modeling the electricity price as it is usually done in time series or data mining approaches, we model and utilize its true source: the sale and purchase curves of the electricity exchange. We will refer to this new model as X-Model, as almost every deregulated electricity price is simply the result of the intersection of the electricity supply and demand curve at a certain auction. Therefore we show an approach to deal with a tremendous amount of auction data, using a subtle data processing technique as well as dimension reduction and lasso based estimation methods. We incorporate not only several known features, such as seasonal behavior or the impact of other processes like renewable energy, but also completely new elaborated stylized facts of the bidding structure. Our model is able to capture the non-linear behavior of the electricity price, which is especially useful for predicting huge price spikes. Using simulation methods we show how to derive prediction intervals for probabilistic forecasting. We describe and show the proposed methods for the day-ahead EPEX spot price of Germany and Austria.

Introduction

In the recent decades modeling electricity prices have become a complex and broad field of research. Due to the liberalization of markets and increasing disclosure of data, new insights concerning the structure and behavior of the prices were gained. Researchers pointed out that there are typical characteristics of electricity prices regardless where it has been traded. These are summarized as the stylized facts of electricity prices, see e.g. Weron (2006). One of these stylized facts concerns tremendous deviations of the price pattern from its mean, called price spikes. This specific feature of electricity prices has huge impacts for research as well as politics and companies. Many electricity companies, e.g. in Germany, are obliged to market some of their electricity at an exchange, which makes their earnings prone to heavy price spikes and creates a complex task for their risk management department. Moreover, many financial contracts such as futures or options are dependent on the variance of the price process and therefore demand eligible estimation techniques. Also long-term cost calculation for investment projects or political programs like the development of renewable energy are dependent on stable and reliable methods for calculation of electricity prices, which can account for the likelihood of price spikes.

Therefore, a great variety of models for estimating the electricity price occurred during the past decades. Those models are often related to well-known models of the finance literature but can originate from many other fields of research. Weron (2014) for instance divides electricity price models into five different groups, multi-agent, fundamental, reduced-form, statistical and computational intelligence models. Besides the multi-agent and fundamental approaches all models have in common that they focus on the price itself or related time series like renewable energy or electricity demand. Multi-agent models usually focus on the supply and demand of electricity to obtain prices by equilibrium, optimization or simulation (Ventosa et al., 2005, Liu et al., 2012), but hence often do not incorporate the time-series of electricity bids and asks of a real exchange into their approaches. Fundamental approaches cover a great variety of models but mainly emphasize the basic economic and physical relationships of the market (Weron, 2014).

Concerning price spikes, the distinction between different model approaches can be refined when the explicit or implicit incorporation of price spikes is considered. In the area of time series models the usage of specific heteroscedastic models for the variance of the process are typical (e.g. Bowden and Payne, 2008, Liu and Shi, 2013). But standard GARCH-type models cannot account for all of the extreme price events within the data (Swider and Weber, 2007). Hence, many researchers developed extended models which can account for severe price movements. These models commonly fall into two main categories. First, there are regime-switching models, which introduce different regimes, usually a base and a spike regime, with different probabilities for a price spike to occur (see, for instance Karakatsani and Bunn, 2008, Janczura and Weron, 2012, Eichler and Tuerk, 2013). Second, there are diffusion models, which add a jump component, e.g. a Poisson process, to allow for price spikes (see, for instance Weron, 2008, Escribano et al., 2011). Rarely there are approaches which focus solely on the price spike itself and try to forecast the event without modeling the whole price time series, e.g. in Christensen et al. (2012).

However, all of these approaches for modeling price spikes have in common that they are focused mainly on the price time series and not of the underlying mechanic which determines the price process. The electricity price can also be seen as the intersection between the part of the electricity supply and demand which was traded at an exchange. The resulting sale and purchase curves, which are also referred to as ask and bid curves or market supply and market demand curves, contain all the information which is needed to determine the market price but provide even further information on all the other prices for other market volumes. This information can be necessary especially for the estimation of the likelihood of extreme price events, as the elasticity of the price, which can be obtained from the shape of the sale and purchase curves, vastly accounts for price movements.

But even though a time-series approach for modeling and especially forecasting auction data is relatively new and has not been applied for electricity price data in a comprehensible manner, modeling the structure of the supply and demand curves in general has been done by some authors, even if very little of them do utilize real auction data. Most of these models belong to the field of fundamental models, but are also often referred to as structural models, as they try to capture the structure of the market. Many of them originate from the field of derivative pricing and do not focus on forecasting the electricity price itself and therefore avoid the uncertainties which come along with it. Barlow (2002) is one of the first authors in electricity price research who formulates a model motivated by real auction data of an electricity market. In his paper he uses a non-linear Ornstein–Uhlenbeck process to obtain a realistic image of the true underlying price process and is also able to capture extreme price events. In the book of Eydeland and Wolyniec (2003) in Chapter 7 a basic market model approach which maps the energy supply to the price of electricity is introduced. They make use of the structure of the market by constructing the so called bid stack, which refers to the marketed aggregated supply of energy for different prices and should, in theory, be equivalent to the sale curve at the investigated auction market.1 Given the specific cost functions of energy generators they are able to determine the bid stack function and afterwards the system price of electricity. Another promising approach arose in the working paper of Buzoianu et al. (2005), who model the marketed supply and demand curves. They assume a linear demand function and a nonlinear supply function to construct a price–quantity model, where the intersection of both curves equals the market clearing price. To approximate the market curves they use external factors like temperature, gas energy supply and gas price. Boogert and Dupont (2008) use a market structure approach which includes the relationship of electricity demand to available capacity to forecast electricity prices and the probability of spikes for the Dutch electricity market. Another structural approach can be found in Howison and Coulon, 2009, Carmona et al., 2013 who perform an analysis of the sale and purchase structure and integrate some of its aspects by incorporating the bid stack model. Extensions to basic structural models are often done via the introduction of market specific determinants, as for instance the solar and wind power feed-in as done by Wagner et al. (2014) or CO2-emissions as done by Hendricks and Ehrhardt (2013).

Some of the recent approaches try to capitalize the increasing amount of available data, especially the hourly auction data of the EPEX, which allows for a deep analysis of the real offered volumes for selling and purchasing electricity. As this results usually in a large amount of data and therefore complexity, some researchers tried to simplify the resulting market curves by merging them into a new curve with desirable properties. For instance, Eichler et al. (2012) illustrate in an extended abstract an idea for modeling the German/Austrian EPEX price using the supply/demand curves. They utilize the curves to model a scaled supply and demand spread using an autoregressive time series model with weekday effects. Coulon et al. (2014) try to overcome the common issue of the assumption of inelastic demands by constructing a “price curve” out of the marketed supply and demand curve for the same hour. The resulting curve exhibits many well-known typical behavioral attributes, e.g. weekday effects. The price curve is then matched with a pseudo-demand curve, which is again a vertical line, where the intersection of both results in the market clearing price. A related approach is used by Aneiros et al. (2013) for the Spanish electricity market. They consider a functional modelling approach for a similar price curve as defined in Coulon et al. (2014), but call it “residual demand curve”. However, in electricity price research the term residual demand curve is usually more common in the framework of market and bidding behavior (as in Hortacsu and Puller, 2008, Vázquez et al., 2014 or Portela et al., 2016). Hildmann et al. (2015) analyze empirically the impact of renewables to the real auction data of the EPEX, if they were not subsidized by the government. For instance, by manipulating the marketed supply curve accordingly they show that negative prices diminish completely when the wind power feed-in is marketed at its true marginal costs. A more detailed survey on structural models can be found in Carmona and Coulon (2014).

All of these papers have in common, that they exhibit at least one of the following major drawbacks. They do not incorporate real auction data (e.g. Boogert and Dupont, 2008), they assume, that the demand is inelastic and therefore focus only on the bid stack (e.g. Eydeland and Wolyniec, 2003, Howison and Coulon, 2009, Carmona et al., 2013)2, they use simplifications or modulations which skip the important correlation structure between bids (e.g. Buzoianu et al., 2005, Coulon et al., 2014) or they are not properly adjusted for forecasting real electricity prices (e.g. Barlow, 2002). Besides electricity price research an econometric time-series approach which actually covers the contemporaneous nature of functionally related and time-dependent auction data can be found in Bowsher (2004), who applies a functional signal plus noise time series model to a security of the FTSE100.

Our idea aims to fill the gap between research done in time-series analysis, where the structure of the market is usually left out and the research done in structural analysis, where empirical data is utilized very rarely and even less thoroughly. It is especially new in the sense that it gets the best of both ends, it will provide deep inside on the bidding behavior of market participants, while still remaining a high accuracy in probabilistic forecasting of the market price. We will therefore use the true data generating process, e.g. the sale and purchase curves of the electricity price, to provide better probabilistic forecasts for extreme price movements while still modeling the time series of electricity prices by an autoregressive approach. We will use the hourly day-ahead electricity price auction data of Germany and Austria provided by the EPEX Spot, also known as Phelix. It will be shown that incorporating the sale and purchase data yields promising results for forecasting the likelihood of extreme price events. Within our approach we will be able to estimate the full prediction density of electricity prices.

Our paper is organized as follows. The next section focuses on our idea and will describe the data and our observations for the EPEX Spot day-ahead auctions. We will follow up with a detailed description of our model and its specific setup for the auction data. Afterwards we show the empirical results of our approach. Our last section discusses our findings and will provide insights for possible improvements and future research. During the paper we will use the phrase “price curves” for both, the sale and purchase curve. Every price will be provided in EUR/MWh and every volume in MW, if not specified otherwise. Note that the market clearing volume is reported by the EPEX as energy in MWh. As we will only consider hourly data we denote the volume in MW.

Section snippets

Price formation process and price curves structure

The electricity price of exchanges is the result of competitive bidding and offering. Focusing merely on the time series of prices therefore neglects their true source. If the true sale and purchase curves were known, the price could be solely determined by the intersection of both curves — regardless of any time dependencies between different prices. Many authors point out that the price is driven by external factors, e.g. wind and solar or electricity demand, see for instance Weron (2014).

Model for the supply and demand curve

Modeling the supply and demand curve of electricity prices is a very complex task. Researcher who try to analyze the complex bidding structure of the supply and demand at electricity exchange usually utilize multi-agent models or fundamental models (Weron, 2014). But those approaches do rarely take into account the real time series of auction data and are therefore unsuitable for giving practical information on short-term forecasts of the electricity price time series. This is especially

Empirical results

In order to show the results of our X-Model under real world conditions, we performed an rolling window out-of-sample study for the time period from 01.11.2014 to 19.04.2015. To evaluate our results, we compare our model with the results of standard models and models used frequently in the literature. Additionally, we show a detailed forecasting analysis for three days namely the 19.12.2014, 24.03.2015 and 12.04.2015. We chose those days for the following reasons. The first day is suitable to

Summary and conclusion

We present a model for the day-ahead electricity spot price by directly modeling the supply and demand curves. We call our model the X-Model, as we estimate the market clearing price as the intersection of the sale and purchase curve of the German-Austrian day-ahead electricity market of the EPEX. Simple dimension reduction techniques and high-dimensional statistical methods allow us to deal with the huge amount of bid data. We group the possible bid prices to price classes and assume a linear

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