Elsevier

Energy Economics

Volume 37, May 2013, Pages 152-166
Energy Economics

Applying ARMA–GARCH approaches to forecasting short-term electricity prices

https://doi.org/10.1016/j.eneco.2013.02.006Get rights and content

Abstract

Accurately modeling and predicting the mean and volatility of electricity prices can be of great importance to value electricity, bid or hedge against the volatility of electricity prices and manage risk. The paper applies various autoregressive moving average (ARMA) models with generalized autoregressive conditional heteroskedasticity (GARCH) processes, namely ARMA–GARCH models, along with their modified forms, ARMA–GARCH-in-mean (ARMA–GARCH-M), to model and forecast hourly ahead electricity prices. In total, 10 different model structures are adopted, and this paper thus conducts a comprehensive investigation on the ARMA–GARCH based time series forecasting of electricity prices. Multiple statistical measures are employed to evaluate the modeling sufficiency and predication accuracy of the ARMA–GARCH(-M) methods. The results show that the ARMA–GARCH-M models are in general an effective tool for modeling and forecasting the mean and volatility of electricity prices, while ARMA–SGARCH-M models are simple and robust and the ARMA–GJRGARCH-M model is very competitive. In addition, we observe that hourly electricity prices exhibit apparent daily, weekly and monthly periodicities, and have the nonlinear and asymmetric time-varying volatility together with an inverse leverage effect.

Highlights

► Apply 10 ARMA–GARCH(-M) models to forecast electricity prices. ► Show that ARMA–GARCH-M models are more effective for forecasting price mean and volatility. ► Find that ARMA–SGARCH-M models are robust and ARMA–GJRGARCH-M models are competitive. ► Illustrate that hourly electricity prices exhibit daily, weekly and monthly periodicities. ► Disclose that prices have the nonlinear and asymmetric volatility with inverse leverage effect.

Introduction

In recent years, electricity markets in many countries have been deregulated to introduce competition in supply and demand activities. In a deregulated electricity market, generators compete to sell electricity and at the same time suppliers to consumers compete to purchase electricity. The supply and demand activities of electricity force the electricity market to reach an equilibrium price so that the trades can happen. However, the demand of electricity is influenced by some social and economic activities and by weather conditions. Particularly electricity cannot be physically stored in a direct way, and thus production and consumption as well as equilibrium prices have to be continuously balanced to smooth out supply and demand shocks. It is evident that the introduction of deregulation makes electricity prices become uncertain and have a high volatility. The volatility of electricity prices is as comparable as other financial markets like stocks or other commodities (Escribano et al., 2002). To accurately value electricity, bid or hedge against the volatility of electricity prices and manage risk, generators and suppliers in deregulated electricity markets extensively use modeling and prediction techniques to characterize and understand the behavior of electricity prices and estimate electricity prices (Carolina et al., 2011, Fanone et al., 2013).

Autoregressive integrated moving average (ARIMA) models with autoregressive conditional heteroskedastic (ARCH) (Engle, 1982) or generalized autoregressive conditional heteroskedastic (GARCH) (Bollerslev, 1986) processes are the widely used approaches to modeling the mean and volatility of electricity prices. For GARCH models, one of their advantages over ARCH models is parsimony which implies that fewer model parameters are needed to conduct estimation. In the literature, the GARCH models frequently used are the general GARCH model (Garcia et al., 2005) and the exponential GARCH (EGARCH) model (Bowden and Payne, 2008). Note that GARCH models have a number of variants and several of them can model asymmetric time-varying volatility. As such, it is necessary to comprehensively evaluate and compare these models in an attempt to select an appropriate one among them. The goal of this article is to show our effort in this aspect. Specifically, we use 10 different ARMA–GARCH(-M) approaches to model the mean and volatility of electricity prices from the New England electricity market, employ various criteria to evaluate the modeling sufficiency of in-sample electricity prices, and then use the built models to perform the prediction for out-of-sample electricity prices.

The rest of the article is organized as follows. Section 2 reviews the current literature related to modeling the mean and volatility of electricity prices. Section 3 describes the general GARCH methodology and their typical variants. Section 4 presents the criteria adopted to analyze model specification and measure modeling sufficiency. Section 5 applies 10 different ARMA–GARCH(-M) approaches to model the mean and volatility of hourly electricity spot prices from the New England electricity market, and analyzes the obtained results. Section 6 uses the established ARMA–GARCH(-M) models to conduct the out-of-sample electricity price prediction, and the prediction accuracy of different models is compared. Finally, Section 7 concludes this study by summarizing the major discoveries and contributions.

Section snippets

Literature review

The methods applied to predict electricity prices are pretty diverse. Aggarwal et al. (2009) classify these methods into three groups with each divided into several subsets. The first group is based on game theory, and it includes several equilibrium models such as Nash equilibrium, Cournot model (Siriruk and Valenzuela, 2011), Bertrand model, and supply function equilibrium (Bajpai and Singh, 2004). The models in this group are able to model the strategies of market participants and identify

Conventional ARIMA–GARCH models

ARIMA approach developed by Box and Jenkins (1976) is a class of stochastic models used to analyze time series data. Consider the following autoregressive moving average model denoted as ARMA(p, q)yt=δ+i=1pϕiyti+j=1qθjεtj+εt,where δ is a constant term, ϕi the ith autoregressive coefficient, θj the jth moving average coefficient, and εt the error term at time t. p and q are called the orders of autoregressive and moving average terms, respectively. When the backshift operator B is applied,

Evaluation methods of model sufficiency

The evaluation methods of model sufficiency can give critical guidance to the appropriate choice of models. These methods can be divided into two categories. One is used to evaluate the goodness of fit of fitted models and it includes (adjusted) R2, F-test, Akaike's Information Criterion (AIC), and Schwarz's Bayesian Information Criterion (SC, BIC or SBC). Another category is the diagnostic checking of fitted models. Some methods can be used to check fitted models. In this work, ACF and PACF

Data description

The data used in this study is hourly real time location-based marginal prices (LMP) in ISO New England market from January 1, 2008 to February 28, 2010 for a total of 18,960 observations. ISO New England manages a few wholesale electric power markets in the United States that allow generators to sell their electricity to marketers who then sell the electricity to end users such as businesses and households. LMP implies the cost of supplying the next increment of electricity to a specified grid

Conclusions

In a deregulated electricity market, hourly ahead price forecasting is critical for market participants. An accurate hourly ahead price forecasting can help power suppliers to adjust their bidding strategies to achieve the maximal revenue, and meanwhile consumers can derive a plan to minimize their cost and to protect themselves against high prices. In the future, electricity markets will be further deregulated and thus become fully privatized, and the private trading of electricity along with

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