In this paper an efficient method is proposed for **electricity** **price** **forecasting**. This paper focuses on Locational Marginal **Price** (LMP) that efficiently maintains power markets by alleviating transmission network congestion. There are complicated behaviors of the time series due to uncertain factors in the power markets. From a standpoint of market players, a sophisticated method is required to forecast LMP effectively. The proposed method makes use of the hybridization of GP (Gaussian Process) of hierarchical Bayesian estimation, EPSO (Evolutionary Particle Swarm Optimization) of evolutionary computation and fuzzy c-means of allowing data to belong to two or more clusters. EPSO is used to improve the accuracy of parameters in MAP (Maximum a Posteriori) estimation for GP. The use of fuzzy c-mean is useful for increasing the number of learning data for GP to deal with spikes. The effectiveness of the proposed method is demonstrated for real LMP data.

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ABSTRACT: The Iberian Market for **Electricity** resulted from a cooperation process developed by the Portuguese and Spanish administrations, aiming to promote the integration of the electrical systems of both countries. This common market consists of organised markets or power exchanges, and non-organised markets where bilateral over-the-counter trading takes place with or without brokers. Within this scenario, **electricity** **price** forecasts have become fundamental to the process of decision-making and strategy development by market participants. The unique characteristics of **electricity** prices such as non-stationarity, non-linearity and high volatility make this task very difﬁcult. For this reason, instead of a simple time forecast, market participants are more interested in a causal forecast that is essential to estimate the uncertainty involved in the **price**. This work focuses on modelling the impact of various explanatory variables on the **electricity** **price** through a multiple linear regression analysis. The quality of the estimated models obtained validates the use of statistical or causal methods, such as the Multiple Linear Regression Model, as a plausible strategy to achieve causal forecasts of **electricity** prices in medium and long-term **electricity** **price** **forecasting**. From the evaluation of the **electricity** **price** **forecasting** for Portugal and Spain, in the year of 2017, the mean absolute percentage errors (MAPE) were 9.02% and 12.02%, respectively. In 2018, the MAPE, evaluated for 9 months, for Portugal and Spain equals 7.12% and 6.45%, respectively.

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Abstract—**Electricity** **price** **forecasting** is considered as an important tool for energy-related utilities and power generation industries. The deregulation of power market, as well as the competitive financial environment, which have introduced new market players in this field, makes the **electricity** **price** **forecasting** problem a demanding mission. The main focus of this paper is to investigate the performance of asymmetric neuro-fuzzy network models for day-ahead **electricity** **price** **forecasting**. The proposed model has been developed from existing Takagi–Sugeno–Kang fuzzy systems by substituting the IF part of fuzzy rules with an asymmetric Gaussian function. In addition, a clustering method is utilised as a pre-processing scheme to identify the initial set and adequate number of clusters and eventually the number of rules in the proposed model. The results corresponding to the minimum and maximum **electricity** **price** have indicated that the proposed **forecasting** scheme could be considered as an improved tool for the **forecasting** accuracy.

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The problem of **electricity** **price** **forecasting** is related yet distinct from that of **electricity** load (demand) **forecasting** [2–5]. Although the load and the **price** are correlated, their relation is non-linear. The load is influenced by various factors such as non-storability of **electricity**, consumers’ behavioral patterns, and seasonal changes in demand. The **price**, on the other hand, is affected by those aforesaid factors as well as additional aspects such as financial regulations, competitors’ pricing, dynamic market factors, and various other macro- and micro-economic conditions. As a result, the **price** of **electricity** is a lot more volatile than the **electricity** load. Interestingly, when dynamic pricing strategies are introduced, prices become even more volatile, where the daily average **price** changes by up to 50% while other commodities generally exhibit only about 5% of change in maximum [6]. A number of research works have been performed on **electricity** **price** **forecasting** [7–10]. However, to our best knowledge, none of them is able to provide adequately accurate results consistently for all the cases for the respective experimental data of their target market. Thus, a more accurate **price** **forecasting** system is necessary to facilitate all the stakeholders, where the consumers’ consumption patterns will depend on the future **electricity** prices, and so are the businesses of the wholesalers, the traders, and the retailers.

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Since the liberalization of the **electricity** markets, **electricity** **price** **forecasting** has become an essential task for all the players of the **electricity** markets due to several reasons. Energy supply companies, especially dam-type hydroelectric, natural gas, and fuel oil power plants could optimize their procurement strategies according to the **electricity** **price** forecasts. As the share of the regulated **electricity** markets, such as day-ahead and balancing markets, increase day by day; bilateral contracts also take the regulated-market prices as a benchmark [1]. Moreover, prices of the energy derivatives are also based on **electricity** **price** forecasts [2]. From the demand side, some of the companies can schedule their operations according to the low-**price** zones and operate in these hours or months. Zareipour et al. [3] stress the importance of the short-term **electricity** **forecasting** accuracy. A 1% improvement in the mean absolute percentage error (MAPE) would result in about 0.1% - 0.35% cost reductions from short term **electricity** **price** **forecasting**, which results to circa $1.5 million per year for a medium-size utility with a 5-GW peak load [4], [5].

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The BFOA was found to search food quicker than other optimization methods (Prabaakaran, Jaisiva, Selvakumar, & Kumar, 2013) and shows a great performance rather than other meta-heuristic optimization approaches like GA (A.V.S.Sreedhar Kumar, V.Veeranna, 2013; Hoo & Han, 2012; Jhankal & Adhyaru, 2011; Majhi, Panda, Majhi, & Sahoo, 2009; Sakthivel, Bhuvaneswari, & Subramanian, 2010), PSO (Hoo & Han, 2012; Karnan & Krishnaraj, 2012; Majhi et al. 2009; Sakthivel et al. 2010), ACO (Karnan & Krishnaraj, 2012), and SA (Hoo & Han, 2012) in many fields. In fact, the application of BFOA in **electricity** **price** **forecasting** is not reported yet. Thus, the hybrid method of LSSVM and BFOA is proposed in this paper to improve **forecasting** performance for short term **electricity** **price** **forecasting**. The inclusion of BFOA as feature selection and LSSVM’s parameter selection gives more efficient and accurate result with lesser complexity than other optimization methods. The developed models are also applicable for Malaysia when the deregulated **electricity** market exists in future..

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Many **electricity** **price** **forecasting** methods have been proposed, and they generally can be divided into market simulation and the method centred on history data. Market simulation predicts the market clearing prices by simulating the competition operation. The second kind of method based on time series analysis of history data to build ma- thematical model and make the prices **forecasting** [4]. Box-Jenkins method belongs to the time-series model. Box-Jenkins Analysis refers to a systematic method of identify- ing, fitting, checking, and using autoregressive integrated moving average (ARIMA) time series models.

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16- Razak, A.W.A., Abidin, I. Z., Yap, K. S., Abidin, A. A. Z., Rahman, T. K. A., & Nasir, M. N. M. (2016). A novel hybrid method of LSSVM-GA with multiple stage optimization for **electricity** **price** **forecasting**. IEEE International Conference on Power and Energy (PECon), Melaka (2016), 390–395.

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16- Razak, A.W.A., Abidin, I. Z., Yap, K. S., Abidin, A. A. Z., Rahman, T. K. A., & Nasir, M. N. M. (2016). A novel hybrid method of LSSVM-GA with multiple stage optimization for **electricity** **price** **forecasting**. IEEE International Conference on Power and Energy (PECon), Melaka (2016), 390 – 395.

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POKORA JINDŘICH. 2017. Hybrid ARIMA and Support Vector Regression in Short‑term **Electricity** **Price** **Forecasting**. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 65(2): 699–708. The literature suggests that, in short‑term **electricity**‑**price** **forecasting**, a combination of ARIMA and support vector regression (SVR) yields performance improvement over separate use of each method. The objective of the research is to investigate the circumstances under which these hybrid models are superior for day‑ahead hourly **price** **forecasting**. Analysis of the Nord Pool market with 16 interconnected areas and 6 investigated monthly periods allows not only for a considerable level of generalizability but also for assessment of the effect of transmission congestion since this causes differences in prices between the Nord Pool areas. The paper finds that SVR, SVRARIMA and ARIMASVR provide similar performance, at the same time, hybrid methods outperform single models in terms of RMSE in 98 % of investigated time series. Furthermore, it seems that higher flexibility of hybrid models improves modeling of **price** spikes at a slight cost of imprecision during steady periods. Lastly, superiority of hybrid models is pronounced under transmission congestions, measured as first and second moments of the **electricity** **price**.

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Abstract—This paper proposes a medium-term equilibrium model which aims to explain the variation of **electricity** **price** as a function of several explanatory variables. This analysis uses the cointegration methodology to model stationarity rela- tionships while preserving the long-run relationship lost through differencing. We should note that a cointegration relationship expresses a long-run equilibrium, but obviously in the short term can befall imbalances. Using what is known as Error Correction Model (ECM), we can relate short-term behavior of the different variables with their long-term behavior. Fur- thermore, this multivariate model enables both predict and analyze the dynamic relationships between the used variables. The methodology is comprehensively tested in a case study based on the Spanish market. Examination of the model goodness of fit and interpretability is done by means of statistical and graphical tools. This approach can achieve satisfactory results in capturing the dynamics of the **price** of **electricity** and could provide companies with valuable information when facing their decision making and risk-management process.

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Figure 8 shows an increase in the ( + ) error as k increased, that is, the performance of the forecast for the day D + k worsens as the considered day D + k is farther away from day D. The forecasts provided at day D for day D + k with k = 2 to 5 can be important for a forecast user when no new forecasts are available at the days following day D due to (for example) fails in technology supporting the communications between such forecast user and the forecast provider, or due to any kind of energy storage, which might need to know prices over the next few days to decide operation now. Figure 8 proves that forecast performances up to k = 5 have an acceptable quality and, therefore, the forecasts for k = 2 to 5 (at day D) could be considered for practical strategic decisions, especially when they are the only information available (i.e., due to fails in technology, as specified above). Furthermore, the **price** forecast for k = 2 to 5 can be useful for some decisions associated with short- term bidding strategies in **electricity** markets, as for example bidding in week-ahead future **electricity** derivative products.

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Statistical analysis was used to find the dominant fac- tors that decide the present **electricity** cost. An overview of **price** and demand variation for a week, shown in Fig- ure 1 below, shows that the **price** variation is a complex trend that requires detailed analysis to establish the influ- encing factors. The figure also shows that demand varies with some readily observable repetitive pattern yet in the same period the **price** shows spikes of varying magnitude and duration.

Specifically, in [15], the authors proposed methods including hybrid networks of self-organized map (SOM) and support-vector machine (SVM) to predict short-term **electricity** **price**. With the trained network, one can predict the future hourly elec- tricity prices in one day ahead. To confirm its feasibility, the proposed model had been trained and tested on the data of historical energy prices from the New Eng- land **electricity** market. In addition, in [16], a sensitivity analysis of similar days (SD) parameters to rise the accuracy of ANN model and SD-based short-term **price** fore- casting model were presented. In order to train the network, a large sum of data were used. The model had been tested in Pennsylvania-New Jersey-Maryland (PJM) elec- tricity market. The results showed that the mean absolute percentage error (MAPE) was around 11%. Furthermore, in [17], the authors introduced a method to predict next-day **electricity** prices based on the ARIMA methodology which was used to analyze the time series problem. The ARIMA model was tested in California elec- tricity market. More than 30-day historical data samples were required to train the model.

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Support vector machine is another technique which has been reported as a better method than time series [20] and neural network [1]–[4], [21]– [31] in terms of model complexity, accuracy and efficiency. In [32], Chaotic Least Squares Support Vector Machine (CLSSVM) was combined with Wavelet Transform (WT) and Exponential Generalized Autoregressive Conditional Heteroskedastic (EGARCH) model to handle high volatility **price** series with the average error of 2.7% for PJM market and 2.58% for Spanish market. The hybrid method of rolling time series and LSSVM yielded MAPE of 2.26%; outperforming BPNN (4.11%) and ARMAX-AR-GARCH (2.72%) in [3]. Same goes for GA-LSSVM method in [26] method which produced MAPE of 4.2-9.7%; surpassing other techniques for all seasons.

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A neural network approach for **forecasting** short-term **electricity** prices. Almost Until the end of last century, **electricity** supply was considered a public service and any **price** **forecasting** which was undertaken tended to be over the longer term, concerning future fuel prices and technical improvements. Short-term forecasts have become increasingly important since the rise of the competitive **electricity** markets. In this new competitive framework, short-term **price** **forecasting** is required by producers and consumers to derive their bidding strategies to the **electricity** market. **Price** **forecasting** in competitive **electricity** markets is critical for consumers and producers in planning their Operations and managing their **price** risk and it also plays a key role in the economic optimization of the electric energy industry. Accurate, short-term **price** **forecasting** is an essential instrument which provides crucial information for power producers and consumers to develop accurate bidding strategies in order to maximize their profit.

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conditional heteroskedastic (GARCH) models and ARMA has been successfully demonstrated for predicting the **electricity** **price** in ISO New England market [12]. Alternatively, the combination of ARIMA models and signal processing techniques, such as wavelets, has been explored for the Singapore **electricity** market [13]. Although some promising results have been achieved using these linear techniques, they cannot model adequately the non‐linear characteristics of the **electricity** **price**. In cases where high‐frequency changes of the **electricity** **price** occur, the application of these methods could be considered as problematic [14]. In recent years, alternative methodologies based on computational intelligent techniques, including neural networks (NN) have been investigated by researchers for EPF. Multilayer perceptrons (MLP) and radial basis function (RBF) NNs have been successfully used in **forecasting** the **electricity** **price** volatility in PJM market, the United States [15]. **Electricity** **price** signal characteristics, such as non‐stationarity and time variance, have been addressed with the aid of appropriate feature selection techniques [16]. Similarly, MLP‐based models have been explored to predict next‐week prices in California as well as Spanish **electricity** markets [17]. These NN approaches outperformed the ARIMA as well as the naïve methods used in all cases. This reveals the superiority of NN‐based systems over methods which have been traditionally used in energy **forecasting** systems. An Elman recurrent NN has been also utilized to EPF for the mainland Spain market, using samples captured during winter and summer weeks, achieving a superior to MLP‐based NNs performance [18]. The further development of NNs has led to the evolution of deep learning (DL)‐based systems. Long‐short term memory (LSTM) and convolutional neural network (CNN) based models have been applied and compared against ARIMA and single hidden‐layer MLP models for the day‐ahead **price** market in Belgium. Results revealed a clear advantage of DL models over traditional approaches; however their performance against MLP networks was rather comparable [19].

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Abstract – In a competitive **electricity** market, short-term **electricity** **price** **forecasting** are very important for market participants.Electricity **price** is a very complex signal as a result of its non-linearity, non-stationary and time-variant behavior. This studypresents a new approach to short-term **electricity** **price** **forecasting**. The proposed method is derived by integrating the kernelprincipal component analysis (KPCA) method with the local Gaussian Process (GP), which can be derived bycombining the GP with the local regression method. Local prediction makes use of similar historical data patterns in the reconstructed space to train the regressionalgorithm. In the proposed method, KPCA is used to extract features of the inputs and obtain kernel principal components forconstructing the phase space of the time series of the inputs. Then local GP is employed to solve the **price** forecastingproblem. The proposed method is evaluated using real-world dataset. The results show that the proposed method can improvethe **price** **forecasting** accuracy and provides a much better prediction performance in comparison with other recentlypublished approaches.

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