1014 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 3, AUGUST 2003 ARIMA Models to Predict Next-Day Electricity Prices Javier Contreras, Member, IEEE, Rosario Espínola, Student Member, IEEE, Francisco J. Nogales, and Antonio J. Conejo, Senior Member, IEEE Abstract—Price forecasting is becoming increasingly relevant to producers and consumers in the new competitive electric power markets. Both for spot markets and long-term contracts, price forecasts are necessary to develop bidding strategies or negoti- ation skills in order to maximize benefit. This paper provides a method to predict next-day electricity prices based on the ARIMA methodology. ARIMA techniques are used to analyze time series and, in the past, have been mainly used for load forecasting, due to their accuracy and mathematical soundness. A detailed explanation of the aforementioned ARIMA models and results from mainland Spain and Californian markets are presented. Index Terms—ARIMA models, electricity markets, forecasting, market clearing price, time series analysis. I. INTRODUCTION E LECTRICITY markets are becoming more sophisticated after a few years of restructuring and market competition. They usually incorporate two instruments for trading: the pool, and bilateral contracts. In the pool, the producers submit bids, consisting of a set of quantities at certain prices, and the consumers do likewise. There is an operator that clears the market and announces the set of clearing prices for the next day. On the other hand, the companies also want to hedge against the risk of daily price volatility using bilateral contracts. For both cases, predicting the prices of electricity for to- morrow or for the next 12 months is of the foremost importance for electric companies to adjust their daily bids or monthly schedules for contracts. In the pool, market clearing prices are publicly available in the www, as it is the case of the day-ahead pool of mainland Spain (www.omel.es), the Californian pool (www.calpx.com), or the Australian national electricity market (www.nemmco.com.au). With a good next-day price forecast, a producer can develop an appropriate strategy to maximize its own benefit, or a consumer can maximize its utility [1], [2]. For the medium-term, spanning from six months up to one year, producers need to know how much of their energy can be sold via bilateral contracts. By means of a reliable daily price forecast, producers or energy service companies are able to de- lineate good bilateral contracts, or financial ones. Manuscript received October 12, 2001. This work was supported in part by the Ministry of Science and Technology (Spain) and the European Union through grant FEDER-CICYT 1FD97-1598. The authors are with the E.T.S. de Ingenieros Industriales, Univer- sidad de Castilla—La Mancha, 13071 Ciudad Real, Spain (e-mail: Javier.Contreras@uclm.es; Rosa.Espinola@uclm.es; FcoJavier.Nogales@ uclm.es; Antonio.Conejo@ uclm.es). Digital Object Identifier 10.1109/TPWRS.2002.804943 Therefore, an accurate price forecast for an electricity market has a definitive impact on the bidding strategies by producers or consumers, or on the price negotiation of a bilateral contract. Auto Regressive Integrated Moving Average (ARIMA) models have been already applied to forecast commodity prices [3], [4], such as oil [5] or natural gas [6]. In power systems, ARIMA techniques have been used for load forecasting [7], [8] with good results. Currently, with the restructuring process that is taking place in many countries, simpler Auto Regressive (AR) models are also being used to predict weekly prices, like in the Norwegian system [9]. In addition, Artificial Neural Networks (ANN) techniques, that have been widely used for load forecasting, are now used for price prediction [10]–[13]. In particular, Ramsay et al. [11] have proposed a hybrid approach based on neural networks and fuzzy logic, with examples from the England-Wales market and daily mean errors around 10%. Also, Szkuta et al. [12] have proposed a three-layered ANN with backpropagation, showing results from the Victorian electricity market, with daily mean errors around 15%. Finally, Nicolaisen et al. have presented Fourier and Hartley Transforms [13] as “filters” to the price data inputs of an ANN. Stochastic models of prices, as in [14], are also competing with traditional time series models in order to predict daily or average weekly prices [15]. This paper focuses on the day-ahead price forecast of a daily electricity market using ARIMA models. That is, this paper pro- vides ARIMA models to forecast today the 24 market clearing prices of tomorrow. These models are based on time series anal- ysis and provide reliable and accurate forecasts of prices in the electricity market of mainland Spain [16] and California [17]. The remainder of the paper is organized as follows. In Sec- tion II, a general methodology to build an ARIMA model for price forecasting and the final models for the Spanish and Cal- ifornian markets are provided. Section III presents numerical testing results, and Section IV states some conclusions. II. ARIMA TIME SERIES ANALYSIS ARIMA processes are a class of stochastic processes used to analyze time series. The application of the ARIMA method- ology for the study of time series analysis is due to Box and Jenkins [18]. In this section, the description of the proposed ARIMA model and the general statistical methodology are presented. The gen- eral scheme is as follows: Step 0) A class of models is formulated assuming certain hypotheses. 0885-8950/02$17.00 © 2003 IEEE