Electricity Price Forecasting in the Spanish Market using Cointegration Techniques

Transcription

1 1 Electricity Price Forecasting in the Spanish Market using Cointegration Techniques Antonio Bello, Javier Reneses 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 relationships 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. Furthermore, 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. Index Terms Electricity price forecasting, Price Fundamentals, Cointegration, Error Correction Model I. INTRODUCTION Electricity sector liberalization and the current financial crisis have made market stakeholders face new challenges. Specifically, trying to predict the electricity price is essential for all market agents. That is why many models have been proposed in the literature in order to analyze and forecast electricity prices with different aims and time horizons. Price formation in spot electricity markets is a complex process posing substantial modeling challenges. Note that electricity prices are dependent on a large set of factors. For this reason, price forecasting techniques must simultaneously reflect the production cost and the strategic behavior of market agents. However, this is a difficult task in electricity markets worldwide because the combination of both effects causes that the price dynamics is extremely complex. Its evolution is distinguished by seasonality, high volatility and prevalent spikes. This fact has motivated the use of explanatory variables in some of the models proposed in the literature in order to aid in the definition of price distributions [1]. Further modeling examples using exogenous variables include [2], which utilized multiple regression with nuclear available capacity, gas price, rain and temperature as regressors. Therefore, some variables to consider in forming expectations of prices are the demand, the weather, the technology mix and proxies for economic activity. Moreover, electricity prices are directly affected by The authors are with the Institute for Research in Technology [Instituto de Investigación Tecnológica (IIT)], Technical School of Engineering (ICAI). Universidad Pontificia Comillas, Madrid E-28015, Spain ( antonio.bello@iit.upcomillas.es; javier.reneses@iit.upcomillas.es). fuel (oil, gas, coal) and emissions allowances prices, especially in markets where coal and gas are used as primary energy sources for electricity generation. Notwithstanding, there are other situations that can be only attributed to malfunctions of the wholesale market. The main causes are competitive games (upwards or downwards), or wrong demand forecasting. The question is to determine to what extent the spot price follows its fundamentals. Numerous studies exist in the literature seeking long-term equilibrium relationships between a great number of economic time series [3] [4]. It can be assumed that in the short-term such relationships can be altered, but it is expected a long-term convergence towards a stable relationship. It should be mentioned that there exist many differences between the existing international electricity markets. These dissimilarities arise from, among other things, different regulatory schema, differences in generation technologies, climatological variation and differences in end-users. Such inconsistencies limit the degree to which we can extrapolate the results from one market and apply them to another. While, with careful consideration, we can perceive similarities, it can be fruitful to evaluate each market separately. Therefore, in this paper we focus on the particular case of Spain. A great deal of research has explored ways to analyze the relationship between Spanish electricity prices and other variables. For instance, [5] explore the relationship between Spanish electricity price, crude oil prices and US dollar-euro exchange rates. Recently, [6] investigates the relation between electricity prices and commodity prices. However, last years has witnessed a dramatic increase in the use of renewable energy sources (RES). Therefore, it seems necessary to take into account the effects of the deployment of these technologies in electricity prices. In [7] is precisely discussed the effect on electricity prices produced by the introduction of RES. To the best of our knowledge, the causal relationship among electricity prices and several technical, weather and economic variables (such as energy commodity prices) has not yet been simultaneously analyzed in the Spanish electricity market. The aim of this paper is firstly, to analyze the role of different variables in the characterization of electricity price and secondly, to estimate ECM models which can allows us to draw conclusions about the long-term and short-term deviations. It is also examined whether this analysis can provide useful information for making satisfactory price predictions in electricity markets. II. THE TIMES SERIES DATA SET The proposed methodology is applied to the Spanish market. Thus, the complete data set used in this paper consisted of spot

2 2 prices, the specific production for each one of the technologies and the international balance of exports-imports in a daily basis. Note that although most data are generated from an hourly basis, we will use a daily average in order to reduce undesirable noise. This data set from the Spanish day-ahead market comprises the period from 1st January 2009 to 30th November The data from 1st January 2009 to 30th April 2011 are used to adjust the proposed models and those daily data corresponding to the rest of the sample are used to validate the models. Furthermore, as no major structural or regulatory change happened during this period, it can be possible to capture the price dynamics by using a common statistical model. Notwithstanding, significant differences can be identified with regard to daily market price and demand coverage. It must be said that the data for electricity price and technology-specific productions that have been used for this work are available in databases published by the market operator and the system operator. Regarding fuels costs, publicly available sources have also been used. The ICE Futures Brent Index, which is published on a daily basis for information, is used as price benchmark for crude oil. On the other hand, API 2 index is used as a benchmarking for coal. The API 2 is published exclusively through the Argus/McCloskey s Coal Price Index service. Finally, for the purposes of this study we took daily observations of Emission allowance spot prices (price index provided by Bloomberg). variables integrated in principle of the same order. Cointegration requires that two basic requirements are verified. On the one hand, that there are two variables which are integrated of the first order. On the other hand, that there is a linear combination of both variables that is stationary of null order (i.e., an equilibrium relationship in the statistical sense). Therefore, the concept of cointegration is equivalent to the idea of stable equilibrium. When there is such relationship between economic variables, the deviations of that relationship can not be strong and grow unlimitedly. Moreover, if it is verified that a set of variables are cointegrated, it is ensured the existence of a relationship between them which is not spurious or fictitious. To carry out the cointegration analysis, the integration order of the series was firstly determined. This is particularly important because when a series is non-stationary or integrated, the values which it takes in a certain time is the buildup of all past disturbances. An illustrative example of an integrated series of order one I (1) is shown in Figure 1. It is easy to check how the series oscillates widely and not around the mean value. Moreover, the variance is time dependent. Figure 1. Daily series of Brent Crude III. METHODOLOGY NOMENCLATURE API Coal (API2) price BRT Brent oil price CHP Combined heat and power COP Carbon Dioxide price DEM Electric Demand DTH Maximum daily thermal and hydro production hole EXP Exports FEX Foreign Exchange Rate IMP Imports MHP Micro hydroelectric power NUC Nuclear energy production OTH Other Special Regime Technologies RRH Run-of-the-river hydro production SOL Solar energy production THM Minimum daily thermal production WND Wind energy production A. Estimation procedure As has already been advanced, we are interested in proposing a multivariate model to analyze the dynamic relationships between different variables. At the same time, we want to use it to predict the dynamic of electricity prices in the medium term. For this purpose, it can be very useful using cointegration techniques. The notion of cointegration was introduced by [8] and [9] as a way of considering equilibrium relationships between An analytical method was used to identify the nonstationarity and the presence of unit root 1 in the considered variables. For this, a good way is to observe the graphs and correlograms of each of the series in order to analyze their behavior as the number of lags increases. In order to determine in advance whether each of the series, which will appear in the cointegrating relationship, is stationary we can use tests such as the Dickey-Fuller, Augmented Dickey-Fuller and Phillips-Perron [10] Likewise, we used one of the classic unit roots contrasts: the Augmented Dickey-Fuller (ADF test). Next, we estimate the cointegrating relationship by Ordinary Least Squares (OLS) and validate such a relationship. To this end, we used the Johansen method, although there are other methods such as Engle and Granger or Phillips-Ouliaris. It will then proceed to further explain each of the phases that compose the methodology of Engle and Granger: a) stationarity estimation of the series, b) conducting cointegration tests and c) error correction method. 1 The existence of a unit root means that all fluctuations represent permanent changes in the long-term trend

3 3 B. Stationarity test In order to verify the data for the presence of unit roots, we use the ADF test [11]. Note that as it was stated in [12], it is recommended testing for the existence of unit roots with trend components included. Therefore, a first step is to select if in the test is included an intercept, trend and intercept or nothing. Thus, in order to carry out the ADF test, the parameters from Eq. 1,2 and 3 are estimated by OLS. In these equations, x t is the variable of interest and ξ t the errors committed. The number of lags to be included in the augmented part is p. To check whether the variable has intercept, trend or both, the variable can be plot. Therefore, the choice can be based on the temporal sequence of each variable. However, basing the election in this procedure does not cease to be somewhat arbitrary. Thus, among the three possibilities customarily it is selected the model in which the deterministic components are significant as tabulated by Dickey and Fuller. It starts with the most general model and is passed to the next if the deterministic components are not statistically significant. x t = βx t 1 + p φ i x t i + ξ t (1) i=1 x t = α 0 + βx t 1 + p φ i x t i + ξ t (2) i=1 x t = α 0 + α 1 t + βx t 1 + p φ i x t i + ξ t (3) i=1 A problem, which now arises, is the determination of the optimum number of lags p of the dependent variable. There are several different ways of selecting that number. On the one hand, the frequency of the data can be used to decide. However, when the data frequency is high (e.g. daily), it does not lead to an obvious choice. On the the other hand, the election may be based on the minimization of the information criteria usually used in the literature. Thus, for the inclusion of lags the Schwarz information criterion (SIC) was used. Finally, it is assessed the null hypothesis that the coefficient β is equal to zero, i.e. the variable x t has a unit root and, hence it does not revert to its mean value. If the null hypothesis is rejected, it means that x t is a stationary time series. The critical values for any sample size are obtained as indicated in [13]. The Tables VIII and IX (included in the Appendix) show, respectively, the ADF test results of the used variables in levels and in first differences. The results for the variables in levels mean that we cannot refuse the existence of a unit root with a significance level of 1%. However, starting from the results of the test with the first difference of the variables, it can be inferred that all variable are I (1) C. Cointegration analysis In order to verify that cointegration exists Johansen s test [14] has been used. Johansen s method is based on the maximum likelihood estimation of the VECM. Johansen s method considers the following tests to determine the number of cointegration vectors: the denoted as Trace and the named Maximum Eigenvalue. It is necessary to verify that in the selected model (with trend or not, intercept or not), appears at least one cointegrating vector for both tests. A first step is making reasonable assumptions about the trend underlying the data. In this case, we have chosen the option in which the data in levels and cointegrating equations have linear trends (note the general expression in Eq. 4). In this equation, y t is a nonstationary I(1) variable, x t is a vector of deterministic variables and is the coefficient matrix. We will not go further in the mathematical formulation, as it is with greater level of detail in [15] and [16]. An important issue to verify in the Johansen test is also to determine how many lags should take the variables. An option consists of including lags until the residues become white noise. This can also be done using criteria such as Akaike and Schwarz. Cointegration is verified by applying the Johansen s cointegration test, with an optimal lags numbers of 7, which is obtained using the Akaike information criterion [17]. yt 1 + Bx t = α (β y t 1 + ρ 0 + ρ 1 t) + α γ 0 (4) On the one hand, the Table I displays the statistic results of the trace test. The first column of this table shows the number of cointegration relationships under the null hypothesis. The second column shows the range of the ordered eigenvalues of the matrix. The third column displays the trace statistic and the fourth one shows the critical values at 5% of significance. Finally, the last column shows the probability associated with the statistic. On the other hand, the Table II shows the test of the maximum eigenvalues. It tests the null hypothesis that the cointegration rank is equal to r against the alternative hypothesis that the cointegration rank is equal to r + 1. the eigenvalues and the statistics of the trace and maximum eigenvalues for the sequence of null hypothesis consisting on the existence of several number of cointegrating vectors. Both statistics reject the null hypothesis that there are at most three cointegrating vectors, but do not reject the hypothesis that there is at most four cointegration vectors. Therefore, one can conclude that the long term relationship between the variables is defined by four cointegrating vectors. Or what is the same, it allows us to identify at most four long-term stable relationships between the variables under consideration. Table I UNRESTRICTED COINTEGRATION RANK TEST (TRACE) No. of CE(s) Eigenvalue Trace Statistic Critical Value 0.05 Prob. At most Table II UNRESTRICTED COINTEGRATION RANK TEST (MAXIMUM EIGENVALUE) No. of CE(s) Eigenvalue Max-Eig Statistic Critical Value 0.05 Prob. At most Note that, in the cointegration analysis, we used the levels of the variables instead of log levels. The reason, as stated in [18], is that if a series is cointegrated in levels, so is if it is applied the logarithmic transformation.

4 4 D. Vector Error Correction Model Using what is known as Error Correction Model we can relate the short term behavior of the stocks comprising the spread with their long-term behavior. We should note that a cointegration relationship expresses a long-run equilibrium but obviously in the short term imbalances can arise. The simplest way of expressing the error correction model is is expressed in the Eq. 5 and Eq.6. y t y t 1 = α+β (x t x t 1 )+γ (y t 1 a bx t 1 )+ε t (5) y t = α + β x t + γu t 1 + ε t (6) In Eq. 6 indicates that a difference is applied to the variables x t and y t. Regarding u t 1, this term is the residual of the cointegration relationship in the previous period. In this term, b is the cointegration coefficient between the variables. The coefficient of the error correction term γ, which is necessarily negative, is responsible for setting the short-term relationship that tends to equilibrium. A negative value of this parameter indicates that periods in which y t is high, i.e. above bx t, they will tend to come followed by relatively low growth of this variable. The parameter γ also represents the speed of convergence between the short and long term. The closer it is to 1, the more quickly the model will return to equilibrium. It should be said that the introduced model can be complicated and expanded all that is desired by introducing lags of the variables to enhance the adjustment level. Including too many lagged terms can introduce poblems of multicollinearity and will consume many degrees of freedom. Moreover, the inclusion of too few delays may lead to the occurrence of specification errors. One way to address this issue is to use a criterion such as the Akaike or Schwarz and choose the model that gives the lowest values of these criteria. The error correction model is obtained by first estimating the cointegration relationship using the Johansen procedure above described. Subsequently, the terms of the vector autoregression model (VAR) including the error correction term gauged from the first stage, are successively estimated. IV. DISCUSSION OF RESULTS In this section, the results obtained with the proposed methodology are analyzed. Therefore, it is analyzed with detail whether the model (which will henceforth be denoted by MI) is capable of reconciling the short-run behavior of daily electricity price with its long-run behavior. In addition, it will verify the degree of adjustment of this model and two simplified versions thereof in- and out- of the sample periods. The proposed model is an expansion of the general expression presented in Eq. 5 and Eq. 6. In this way, MI has constant term and trend in the cointegration equation, as well as a constant term in the dynamic model. In this work, as previously indicated, were introduced 7 lags of the explanatory variables using Akaike Information Criteria. This value obtained by a pure statistical procedure was fully expected. This is due to the presence of a weekly seasonality. Finally, for each of the lags was conducted a specific analysis to determine whether each term is significant or not from a statistical standpoint. In the case that it were not, it was removed from the final specification of the model. The estimation of one of the long-run relationship is reported in Table III. In this table can be appreciated all the estimated normalized cointegrating coefficients and corresponding standard errors. All of this will provide us long-term information. But is still needed to check that the signs of this vector are what would be expected according to theory. It is easy to check how the long-run electricity price is positively affected by coal, brent and CO2 price, as well as the demand and wind production. These results were as one would expect, with the caveat of the variable WND. However, the explanation may be due to the fact that in some instances, the agents with greater market power tend to bid more aggressively in the long-term in order to recover costs during periods of high wind. Also, it should be noted that, in the short term, the corrective mechanism of the deviations collects the price decline as was expected. Conversely, an increase in production with renewable energy sources which are legislated under what is referred to as special regime (mini-hydro, solar, combined heat and power and others), run-of-the river hydro and nuclear have, as was expected, a negative effect on electricity prices. In addition, there is a linear deterministic trend (TRN) which also contributes in a negative way to decrease the price of electricity. Foreign exchange rate (USD/Eur) has also a strong negative impact on the electricity price. This was to be expected since an increase in this ratio means that agents have an advantageous position, for example, to purchase products traded in dollars. Remember that the price of fuels in international markets is referenced in dollars. Surprisingly, the minimum daily thermal production (coal and gas) and the maximum thermal and hydro production hole have a negative impact on the price of electricity in the long run. This may be explained either because for these side effects are to a large extent picked up in the deterministic trend. On the other hand, may be due to the substitutivity that may occur with more efficient and cleaner technology in the Spanish electricity system. Furthermore, although there is no multicollinearity, part of the effects collected by these variables is included in other variables present in this analysis. It is also particularly noteworthy the variable analysis of imports and exports with other electricity markets. Logic dictates that the coefficient of exports should be negative. The reason is that in the database that was used in this work, this variable is already negative. Then we proceed to analyze in the Table IV if the equilibrium relationship in the long term is relevant in the proposed model. The estimated coefficient of the lagged error correction term γ is negative and statistically significant, indicating the importance of the error correction term in adjusting towards the equilibrium. It also reaffirms the assumption that there is a long-term relationship. The adjustment speed is low. This suggests that long time is required to return to the equilibrium in case that there are disturbances in the long term relationship. Table V summarizes some of the most significant statistics of the proposed VECM model. In it, you can appreciate

5 5 Table III NORMALIZED COINTEGRATING COEFFICIENTS API BRT COP DEM DTH WND FEX EXP RRH IMP NUC SOL THM OTH MHP TRN Coef S.E Table IV LAGGED ERROR CORRECTION TERM Coef. S.E. t-statistics p-value γ < the average of the dependent variable and the sample quasi standard deviation (SD Var.). Similarly, we have also included the standard error of the equation. Table V STATISTICAL SIGNIFICANCE OF THE MODEL Mean Dep. Var. S.D. Var. Sum Sq. Resid S.E. equation Then it will analyze whether the model is able to capture with sufficient precision the dynamics of electricity prices based on all explanatory variables which have been used. As shown in the Figure 2, the model properly reproduces the behavior of the data. It is also capable of reproducing the trend changes from the original series. Another fact to emphasize is that succeeds in capturing the maximums and minimums of the original series. Figure 2. Comparison between the actual price and the estimated price inand out- of the sample Actual Estimated-MI The question is now to determine whether it would be possible to get a sufficiently acceptable adjustment without having a model so complex. With this aim, a comparison was made with two representative models. In the first of them (called MII), the same explanatory variables as those included in the model MI have been used. However, unlike the latter, only a delay of the explanatory variables has been introduced. In the second one (denoted as MIII), only the five most representative variables were used. The variables that were the most representative are: DEM, THM, DTH, RRH and the aggregate production of all the technologies included in the special regime including wind. With the aim of analyzing the adjustment capacity of the models a comprehensive analysis in the in-sample data set is carried out. Moreover, in order to estimate the models generalization capabilities, an out-of-sample analysis is also accomplished. The Tables VI and VII provide a thorough analysis of the main statistical properties which are achieved with each model in their respective data sets. As seen, all models are capable of capturing the statistical distribution of the price fairly accurately and similarly. As it was expected, the largest differences are appreciated in the out-of-sample period. More specifically, the models failed when characterizing certain extremely low prices that occurred in a timely manner. In order to test their predictive capability the mean square error is also displayed. It is undoubtedly the case that all models have a quite acceptable predictive power. It is evident that MI is clearly superior in terms of prediction performance to the other proposed models. The Figures 3 and 4 include illustrative results of the residuals. Note that model MII showed slightly worst global performance than the other models. The results obtained in this comparison suggest that the correct specification of lagged terms of the most significant explanatory variables is a critical factor. It contributes to significantly improve the predictive capabilities of these methods in a greater extent than incorporating a higher number of variables. The errors analysis evidence that they do not behave with predictable trend. Therefore, there is no information unexplained by model variables. This leads directly to the results of the normality test of Jarque-Bera, in which the null hypothesis of normality in the residuals can not be rejected. Table VI COMPARATIVE STATISTICS BETWEEN THE ACTUAL PRICE AND THE ESTIMATED PRICE IN THE IN-SAMPLE PERIOD Actual Estimated - MI Estimated - MII Estimated - MIII Mean Median Maximum Minimum Std. Dev Skewness Kurtosis MSE V. CONCLUSIONS This paper investigates the decisive variables in the Spanish electricity price formation. Also, by using cointegration techniques has been demonstrated the existence of an equilibrium relationship in the long term between the electricity price and variables such as fuel costs, exchange rate, demand,

6 6 Table VII COMPARATIVE STATISTICS BETWEEN THE ACTUAL PRICE AND THE ESTIMATED PRICE IN THE OUT-OF-SAMPLE PERIOD Actual Estimated - MI Estimated - MII Estimated - MIII Mean Median Maximum Minimum Std. Dev Skewness Kurtosis MSE Figure Analysis of the residues in the in-sample period M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M1 M2 M3 M MI MII MIII producible of different technologies and international balance of exports-imports. It is also evident that there is a causal relationship between these technical, economical and weather variables. Through this analysis of cointegration, it can be possible to estimate the direction and magnitude of long-term relationships between all the used variables. This paper develops an error-correction model (ECM) which explains, in a flexible manner, deviations in the electricity price from the equilibrium in the long-term. By means of the ECM, Figure Analysis of the residues in the out-of-sample period M5 M6 M7 M8 M9 M10 M MI MII MIII the changes of the electricity price is effectively explained by the sum of a dynamic short-term relationship and a static longterm relationship. The paper examines different approaches for modelling the dynamic of electricity price. Model results satisfy all desirable statistical tests. Further research has been undertaken in order to evaluate the relationship between model complexity and adjustment capacity. Several statistical analysis and illustrative test results are provided. All the evidence suggest that including the optimal number of lagged terms is crucial in order to capture flexible responses in the short-term. All proposed models demonstrate to have a very high explanatory power, both, inand out-sample period. All of this makes them reliable models to carry out simulations and forecasts. VI. APPENDIX Table VIII ADF - VARIABLES IN LEVELS Variable Model t-statistic Prob. Lags PMD COP API BRT FEX DEM WND NUC RRH SOL THM IMP EXP DTH CHP OTH MHP None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend

7 7 Table IX ADF - VARIABLES IN FIRST DIFFERENCES Variable Model t-statistic Prob. Lags PMD COP API BRT FEX DEM WND NUC RRH SOL THM IMP EXP DTH CHP OTH MHP None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend None Constant Const. and Trend [7] L. Gelabert, X. Labandeira, and P. Linares, An ex-post analysis of the effect of renewables and cogeneration on spanish electricity prices, Energy Economics, vol. 33, Supplement 1, no. 0, pp. S59 S65, [8] C. W. J. Granger, Some properties of time series data and their use in econometric model specification, Journal of Econometrics, vol. 16, no. 1, pp , [9] R. F. Engle and C. W. J. Granger, Co-integration and error correction: Representation, estimation, and testing, Econometrica, vol. 55, no. 2, pp , [10] P. C. Phillips and P. Perron, Testing for a unit root in time series regression, Tech. Rep., [11] D. A. Dickey and W. A. Fuller, Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, vol. 74, no. 366, pp , [12] J. Y. Campbell and P. Perron, Pitfalls and opportunities: What macroeconomists should know about unit roots, National Bureau of Economic Research, Working Paper 100, [13] J. MacKinnon, Approximate asymptotic distribution functions for unitroot and cointegration tests, Journal of Business and Economic Statistics, vol. 12, no. 2, pp , [14] S. Johansen, Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control, vol. 12, pp , [15], Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models, Econometrica, vol. 59, no. 6, pp , [16], Likelihood based inference in cointegrated vector error correction models, Oxford University Press, [17] H. Akaike, A new look at the statistical model identification, Automatic Control, IEEE Transactions on, vol. 19, no. 6, pp , [18] D. F. Hendry and K. Juselius, Explaining cointegration analysis: Part 1, The Energy Journal, vol. 0, no. Number 1, pp. 1 42, Antonio Bello was born in Cuenca, Spain, in He received the degree of Industrial Engineer and M.Sc. in Power Systems from Universidad Pontificia Comillas, Madrid, Spain, in 2010 and 2012, respectively. Since September 2010, he is an Assistant Researcher at the Institute for Research in Technology (IIT), Universidad Pontificia Comillas. His areas of interest include operation, simulation models, forecasting, planning of electricity markets and risk management support. REFERENCES [1] N. Karakatsani and D. Bunn, Forecasting electricity prices: The impact of fundamentals and time-varying coefficients, International Journal of Forecasting, vol. 24, no. 4, pp , [2] A. Schmutz and P. Elkuch, Electricity price forecasting: Application and experience in the european power markets, Proceedings of the 6th IAEE European Conference, Zurich, [3] Causality-in-mean and causality-in-variance among electricity prices, crude oil prices, and yen-us dollar exchange rates in japan, Research in International Business and Finance, vol. 26, no. 3, pp , [4] M. Shahbaz, C. F. Tang, and M. S. Shabbir, Electricity consumption and economic growth nexus in portugal using cointegration and causality approaches, Energy Policy, vol. 39, no. 6, pp , [5] M. P. Munoz and D. A. Dickey, Are electricity prices affected by the us dollar to euro exchange rate? the spanish case, Energy Economics, vol. 31, no. 6, pp , [6] V. Moutinho, J. Vieira, and A. C. Moreira, The crucial relationship among energy commodity prices: Evidence from the spanish electricity market, Energy Policy, vol. 39, no. 10, pp , Javier Reneses was born in Madrid in He obtained his Electrical Engineering Degree (1996) and a PhD in Industrial Engineering (2004) from the Universidad Pontificia Comillas (ICAI), Madrid, Spain, and a Degree in Mathematics from the Open University in Spain [Universidad Nacional de Educación a Distancia (UNED)] in At present, he is a Research Fellow at the Institute for Research in Technology (IIT), Advanced Technical Engineering School (ICAI), Comillas Pontifical University. His areas of interest include operation and planning of energy systems and regulation of electric power systems.