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Price and volatility dynamics between natural gas and electricity markets: some evidence for Spain

Dolores Furió* Department of Financial Economics University of Valencia (Spain) Avenida de los Naranjos, s/n, 46022 Valencia (Spain) [email protected]

Helena Chuliá Department of Economics and Business Universitat Oberta de Catalunya Av. Tibidabo, 39-43, 08035 Barcelona (Spain) [email protected]

(*)

Corresponding author.

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Price and volatility dynamics between natural gas and electricity markets: some evidence for Spain

Abstract

The purpose of this study is to investigate the causal linkages between the Spanish electricity 1-month-ahead forward price and the Zeebrugge (Belgium) natural gas 1month-ahead forward price. To do so, we use the Johansen cointegration test and a vector error correction model (VECM). Additionally, a multivariate GARCH model is applied to analyse volatility interactions between both markets. Our findings reveal that Zeebrugge natural gas prices play a prominent role in the Spanish electricity price formation process. Furthermore, causation, both in price and volatility, runs from the natural gas market to the electricity market. These results are of practical importance for Spanish market participants.

JEL classification: C10, C32, G14, L97. Key words: natural gas, electricity, cointegration, volatility transmission

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Price and volatility dynamics between natural gas and electricity markets: some evidence for Spain

1. Introduction

Starting in the first half of the 1990s and being supported by Electricity and Gas Directives1, there has been a generalised trend towards the deregulation of energy markets at the EU level. However, the rhythm of liberalization is differentiated in Europe. Movements towards liberalized electricity and gas markets started earlier in the United Kingdom. In Continental Europe, interestingly, electricity market reforms have generally been taken further in most of the countries, whereas the opening of gas markets is still currently ongoing in many cases. The changing regulatory framework is expected to cause a structural change in the trading patterns and price formation of the electricity and natural gas industries that should be taken into account by traders and regulators. An important element of this transformation is the development of physical or virtual natural gas trading hubs, which are marketplaces that enable companies to trade spot and forward deliveries of natural gas. There are two main wholesale trading gas hubs in Western Europe, Zeebrugge (Belgium) and the National Balancing Point (NBP) in the United Kingdom. Since 1998, they have been linked through the so-called Interconnector, whose ownership is shared among some of the largest players in the industry. Both the NBP and Zeebrugge hubs provide open access to spot (and forward) markets with assumingly competitive pricing of natural gas. Over the last years an increasing volume of natural gas trading has been observed all around Europe. In fact, natural gas is becoming widely considered as a true alternative

EU Directive 96/92/EC and EU Directive 98/30/EC on common rules for the internal electricity and gas market, respectively. They were revoked by EU Directive 2003/54/EC on the internal market in electricity and EU Directive 2003/55/EC on the internal market in natural gas.

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source to oil. On the one hand, the new combined-cycle gas turbine (CCGT) plants, as opposed to the old gas plants, have short construction times and require small investments which could contribute to allowing the entry of new producers and enhance the degree of competition of the generation segments. On the other hand, its emissions of greenhouse gases are much more reduced and its reserves are more diversified and less exposed to geopolitical risk2. Since natural gas is an input in electricity generation, it is expected that natural gas price changes would be (at least partially) reflected in electricity price changes. Moreover, natural gas prices may also affect electricity prices to the extent that they serve as substitutes on the demand-side of the energy market. In this regard, as Mohammadi (2009) has pointed out, under market-based pricing, electricity prices should partly reflect fuel costs at least in the long run, while under cost-based pricing, electricity prices should reflect a mark-up over average or marginal costs. The relationship between electricity prices and fuel costs, as well as price convergence between electricity (or natural gas) prices from different markets or locations, have been extensively studied in the literature. Emery and Liu (2002) analyse the relationship between electricity and natural gas futures prices of New York Mercantile Exchange (NYMEX), California-Oregon Border (COB) and Palo Verde (PV) and find that electricity and natural gas futures prices are cointegrated. Mjelde and Bessler (2009) examine the interrelationships among electricity prices from the markets of Pennsylvania, New Jersey, Maryland Interconnection and Mid-Columbia, and four fuel sources: natural gas, crude oil, coal and uranium. Their results, among others, state that peak electricity prices react to shocks in natural gas prices. Seletis and Shahmoradi (2006) test for causal relationships between natural gas and electricity price (and volatility) changes using data over the period from 1996 to 2004 from Alberta's spot power and natural gas markets. Their results indicate that there is bidirectional (linear and nonlinear) causality between both series of prices. Surprisingly, Asche et al. (2006) report an integrated energy market when testing for that hypothesis between natural gas, electricity and crude oil prices in

The largest natural gas reserves are located in the Middle East and Eurasia. Russia, Iran and Qatar together accounted for about 57 percent of the world´s natural gas reserves as of January 1, 2009 (U.S. Energy Information Administration, EIA, 2009).

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the UK only during the period when the natural gas market was deregulated but not yet physically linked to the continental European natural gas market through the Interconnector. Mohammadi (2009) examines the long-run relations and short-run dynamics among retail electricity prices and fossil fuels (coal, natural gas and crude oil) from 1960 to 2007 in the U.S. market. Using annual data, they find evidence of significant long-run relations only between electricity and coal prices and some evidence of unidirectional short-run causality from coal and natural gas prices to electricity prices. Bosco et al. (2007) carry out an analysis to test the interdependencies of six European electricity markets and conclude that APX, EEX, EXAA and Powernext are cointegrated. They also find strong evidence of common long-term dynamics between electricity prices from the mentioned power markets and natural gas Zeebrugge midday price index. Muñoz and Dickey (2009) investigate the relationships between Spanish electricity spot prices, USD/Euro exchange rates, and oil prices and find that the three variables are cointegrated as well as there being a transmission of volatility between USD/Euro exchange rates and oil prices to electricity prices. Asche et al. (2002) examine Norwegian, Dutch and Russian natural gas export prices to Germany in 1990-1998 and use cointegration tests to conclude that the German natural gas market is integrated. Siliverstovs et al. (2005) investigate the degree of integration of natural gas markets in Europe, North America and Japan over the period from 1990 to 2004 and find that the European and Japanese natural gas markets are integrated whereas the European (Japanese) and American natural gas markets are not. In contrast, using a higher frequency of data, Kao and Wan (2009) find that the price series on the futures and spot markets in the U.S. and U.K. are cointegrated. Neumann et al. (2006) analyse convergence of spot market prices for natural gas in Europe. Applying the Kalman filter, they find perfect price convergence between the NPB (UK) and Zeebrugge (Belgium) hubs, whereas the relation of continental spot prices related to the Bunde/Oude (Germany) and Zeebrugge hubs is rather weak. In line with many other European countries, in Spain, natural gas is more and more being used for power generation. CCGT plants have experienced a huge increase in the Spanish generation park from 2002 onwards. In particular, in the Spanish day-ahead spot market,

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electricity production using natural gas with CCGT increased from 0.15% in 2002 to 5% in 2003 and to 9% in 2004. Following that growing trend, the relative share of CCGT to generation was 18% in 20053. Last but not least, CCGT plants usually set marginal prices at the Spanish electricity day-ahead market, thereby becoming strategic technology units. In fact, as stated by Muñoz and Dickey (2009), natural gas is the main component of Spanish electricity generation and of electricity prices as well. The Spanish Electricity Market, which was liberalised in 1998, is mainly organised into a (day-ahead) spot market where participants submit offers to sell or to purchase electricity for delivery at any specified hour during the subsequent day and an intra-day market in which agents can rectify their previously assumed positions. Over the counter physical and pure financial (cash-settled) bilateral contracting is also allowed. Moreover, agents can trade futures contracts on electricity at the Iberian Power Futures Market which started to work in July 2006. In contrast, despite the market for natural gas being open for competition, currently there is no Spanish natural gas market from which a price for natural gas can be set and made public. The issue of the benchmark price for natural gas that could drive the Spanish electricity price, taking into account the important role this fuel plays in the formation of the electricity price, thus remains unclear. In this sense, it is important to note that, according to a report by CNE, electricity prices in mainland Spain showed particularly high correlation with Zeebrugge natural gas prices over the period 2005-2007 (CNE, 2008)4. The aim of this paper is to go into that question in depth by examining the long-run relations and short-run dynamics between Spanish electricity forward prices and forward prices for natural gas traded at the most liquid hub in Continental Europe, namely the Zeebrugge hub. Moreover, the volatility interactions between both markets are additionally analysed. In the literature, the issue of spillovers between returns in several

These figures have been obtained from the Spanish Electricity Spot Market (OMEL) web page (www.omel.es) 4 Furthermore, with the aim to analyse the presence of forward risk premium in the Spanish Electricity Market, Furió and Meneu (2010) include the Zeebrugge natural gas one-month-forward price as an explanatory variable in their model to obtain the Spanish expected electricity price and the coefficient on such a variable turns out to be significant.

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energy markets has been analysed by Ewing et al. (2002), focusing in the oil and natural gas sectors, among others. To examine the dynamics between these forward contracts we make use of two approaches. First, we use the Johansen cointegration test and a vector error correction model (VECM) to test for causal relationships between natural gas and electricity price changes. Second, we apply a multivariate GARCH model to analyse volatility interactions between both markets. Results show that causation, both in price and volatility, runs from the natural gas market to the electricity market.

The remainder of the paper is organized as follows: section 2 describes the data used, section 3 lays out the methodology and the results and, finally, section 4 concludes.

2. Data

For the purposes of this work, forward price data are preferably used instead of spot price data because the former are much less depending on typically regional technical issues (for instance, congestion concerns). On the one hand, we use daily base-load one-month-ahead pure financial forward quotations from the Spanish Electricity OTC Market. The forward data set includes the business day prices for power to be delivered during 24 hours a day over the next month. These forward contracts do not entail physical settlement of electricity but are settled in cash against the arithmetic average of hourly prices in the spot market over the delivery period. Thus, dealing in a one-month-ahead forward contract in January means trading the electricity to be delivered over the 24 hours of every day in February. A subsequent maturity monthly forward contract is traded from the first day of each month, so it is not possible to simultaneously negotiate more than one contract maturity in the same day. On the other hand, the corresponding daily series of one-month-ahead cash settled forward natural gas prices at the Zeebrugge Hub is selected. Our sample covers the time period 01/04/2005 to 05/29/2009 and both series have been taken from the Reuters database. Although Spanish forward price data is available from 2003, our sample initiates/begins

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in January 2005 since, as previously stated, it is from that point on that natural gas arises as an important source of fuel in the Spanish electricity generation process. Prices at Zeebrugge are reported in pence sterling per therm whereas prices at OMEL are reported in euro cents per kilowatt hour (kWh). For the analysis in this paper both series of prices are converted into euros per megawatt hour (euro/MWh). Following APX Group, a conversion factor of 29.3071 kilowatt hour per therm is used. The currency conversion is made by using the exchange rates from the Reuters database. Missing data are replaced by the last available price5. Returns are computed as the log-difference in daily prices. As observed in Figure 1, both prices display rather similar overall patterns, following an increasing trend in 2005, and from the second half of 2007 to September 2008 and a declining trend in 2006, early 2007 and from October 2008 to the end of the sample. At this stage, it is evident that both prices show rather strong comovement. [Insert Figure 1 about here] Table 1 presents descriptive statistics for the corresponding return series. Note that electricity returns are more volatile than are natural gas returns, as indicated by the standard deviation, which could be explained by the fact that natural gas is storable whereas electricity not. Electricity returns also exhibit the largest difference between maximum and minimum. Both return series are leptokurtic, but particularly so the one for electricity. The measures for skewness and kurtosis suggest a rejection of the normality hypothesis. The Jarque-bera statistic confirms this result. [Insert Table 1 about here]

3. Methodology and results

This section consists of two parts, analyzing price and volatility linkages between natural gas and electricity markets, respectively. In each case both the employed methodology and the results are presented.

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There were 16 missing values out of 1149 (1.4%) for the natural-gas price series.

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a. Price linkages

Initially, the stationarity of each of the two prices series investigated is studied. We adopt the Augmented Dickey-Fuller (ADF) test that has the unit root process as the null hypothesis. The results in Table 2 show that based on the ADF test, the null hypothesis of a unit root in electricity and natural gas logarithm prices cannot be rejected at the 5% level. 6

[Insert Table 2 about here]

Having established that electricity and natural gas logarithm prices are I(1), we move on to determine if they are cointegrated. If the two price series share a common stochastic trend, then they are considered cointegrated. This study tests for cointegration using the Johansen and Juselius (1990) procedure. The presence of cointegration relation forms the basis of the Vector Error Correction (VECM) specification. A VECM model is obtained from a vector autoregressive model (VAR) by adding an "equilibrium correction" term to it. It is a linear model of the form

y t y t 1 i y t i t

i 1

p

(1)

Where is a constant term, y t is a k-dimensional vector which contains k price series which are I(1) and which are to be tested for a cointegrating relationship, denotes the first difference operator; ' is the long-run impact matrix; i s are matrices of parameters and t is a vector of Gaussian white noise processes.

When the ADF test is applied to the first difference of individual time series, the null of unit root process is strongly rejected in both cases.

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The number of cointegrating relations among the components of the vector y t is represented by the rank of . If has rank r < k, then there exist k×r matrices and

each with rank r such that ' and y t ~ I (0) . Therefore, is the cointegrating

vector, and the components of are the adjustment parameters. The Johansen method provides two likelihood ratio tests to determine the number of cointegrating vectors: the trace test and the maximum eigenvalue test.

The number of lags in the VECM is 10, which is determined so that the residuals of the model appear free from serial correlation. Moreover, because the means of the log-bases are different from zero, the cointegration tests are run assuming the presence of an intercept. The results, presented in Table 3, show that both the trace and the maximum eigenvalue tests, indicate that the electricity prices series and the natural gas price series are cointegrated. Hence, the results confirm that prices in the two markets share one common stochastic trend.

[Insert Table 3 about here]

The existence of cointegration between both series allows us to implement the VECM which describes the deviations of the variables from the long-run equilibrium association and the short-run transmission mechanism. In our case, the VECM consists of two equations:

y1,t 1 1 1 y1,t 1 2 y 2,t 1 1i y1,t 1 1i y 2,t 1 1,t

i 1 i 1

p

p

y 2,t 2 2 1 y1,t 1 2 y 2,t 1 2i y 2,t 1 2i y1,t 1 2,t

i 1 i 1

p

p

(2)

Where y1,t and y 2,t refers to the electricity and natural gas logarithm prices, respectively,

i for i=1,2 are the adjustment parameters, 1 and 2 are the coefficients of the

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cointegrating vector, is a constant in the cointegrating vector, the parameters i for i=1,2 determine how the return in one market responds to the own lagged returns, i for i=1,2 determine how the return in one market responds to the lagged returns of the other market and, finally, i ,t for i=1,2 are the Gaussian white noise processes.

Under the VECM, the null hypothesis of non-causality is rejected if the sum of the regression coefficients on the independent variable is significantly different from zero and/or the error correction term is statistically significant. According to Granger (1988) and Miller and Russek (1990), in the error correction model there are two possible sources of causation, either through i or through i . In contrast to the standard Granger causality test, the error correction approach allows for the detection of Granger causality between variables, even if the coefficients on lagged difference terms are not jointly significant. Thus, i measures the long-run equilibrium while i measures the short-run causal relation. Granger (1988) notes that cointegration between two or more variables is already sufficient to indicate the presence of causality in at least one direction. In Table 4 we examine the VECM results. It is evident that the lagged error-correction term is negative and statistically significant at the 5% level in the electricity market equation, which implies a long-term causality from the natural gas market towards the electricity market. This long-run relationship captured in the data is of interest to price discovery in electricity in subsequent periods.

However, the reverse does not hold. This result is consistent with that of Emery and Liu (2002), indicating that electricity prices respond to departures from the equilibrium relationship, but natural gas prices do not. This asymmetric response makes sense, according to Emery and Liu (2002), considering that natural gas is an important resource for generating electricity, while generating electricity is only one of many uses for natural gas. Moreover, in the context of our work, one should take into account the fact the Zeebrugge natural gas market is one of the most liquid ones in Europe so as to it may be

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seen as a reference market in the Continental area, whereas the electricity forward market in this context is essentially Spanish.

When analysing the short-run relationship between both markets the focus is on the lagged returns. The p-values for the chi-square test that the coefficients for these lagged returns are jointly insignificant are reported in Table 4. It is observed that the sum of lagged coefficients is not significant in any equation. Therefore, there is causation from the natural gas market to the electricity market, with the error correction term being the source of causation.

[Insert Table 4 about here]

b. Volatility linkages To analyse volatility spillovers between electricity and natural gas markets we employ an asymmetric version of the BEKK model [Baba et al. (1989), Engle and Kroner (1995) and Kroner and Ng (1998)].

The compacted form of this model is:

H t C ' C B ' H t 1 B A' t 1 t' 1 A G ' t 1 t' 1G

(3)

where C, B, A and G are matrices of parameters to be estimated, being C upper-triangular and positive definite, t max( t ,0) are the Glosten et al. (1993) dummy series collecting

the stylized negative asymmetry from the shocks and, finally, Ht is the conditional

variance-covariance matrix in t.

The conditional variance for each market can be expanded for the bivariate BEKK as follows:

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2 2 2 2 2 2 2 12,t c11 b11 12,t 1 b21 2,t 1 2b11b21 12,t 1 a11 12,t 1 a 21 2,t 1 2 2 2 2a11 a 21 1,t 1 2,t 1 g 1112,t 1 g 21 2,t 1 2 g11 g 211,t 1 2,t 1

(4)

2 2 2 2 2 2 2 2 2 2,t c12 c 22 b12 12,t 1 b22 2,t 1 2b11b21 12,t 1 a12 12,t 1 a 22 2,t 1 2 2 2 2a11 a 21 1,t 1 2,t 1 g1212,t 1 g 22 2,t 1 2 g 11 g 211,t 1 2,t 1

In equation (3), the elements in C, B, A, and G matrices cannot be interpreted individually. Instead, we have to interpret the non-linear functions of the parameters which form the intercept terms and the coefficients of the lagged variances, covariances and error terms. We follow Kearney and Patton (2000) and calculate the expected value and the standard error of those non-linear functions. The expected value of a non-linear function of random variables is calculated as the function of the expected value of the variables. In order to calculate the standard errors of the function, a first-order Taylor approximation is used. This linearizes the function by using the variance-covariance matrix of the parameters as well as the mean and standard error vectors.

[Insert Table 5 about here]

Table 5 shows the results of estimating the BEKK model. Our findings indicate that the electricity volatility is directly affected by its own volatility and by the natural gas volatility. Thus, higher levels of electricity and/or natural gas conditional volatility in the past are associated with higher conditional volatility in the current period, as indicated by

2 the positive and significant coefficients on 12 and 2 , respectively. Interestingly,

electricity volatility is affected by its own shocks (note the significant estimated coefficient on 12 ) as well as by the natural gas shocks (note the significant estimated

2 coefficient on 2 ). Finally, the coefficient on 12 is significant indicating that electricity

volatility responds asymmetrically to its own shocks, i.e., negative shocks increase volatility more than positive shocks.

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The behaviour of natural gas volatility differs substantially from that of electricity volatility. It is observed that the volatility of the natural gas market is affected by its own volatility at the 5% level of significance (note the significant estimated coefficient on

2 2 ). Our findings also indicate that natural gas volatility is affected by its own shocks 2 (note the significant estimated coefficient on 2 ) but not by those originated in the

electricity market. Finally, natural gas volatility responds symmetrically to its own

2 shocks ( 2 is not significant), i.e., negative and positive shocks have the same effect on

volatility.

Overall, the model demonstrates the power of the natural gas market relative to the electricity market, because volatility transmission is unidirectional from the natural gas market to the electricity market. Therefore, causation goes from the natural gas market to the electricity market not only in price but also in volatility.

4. Concluding remarks

This paper explores the interrelations of Zeebrugge natural gas and Spanish electricity prices and volatilities. Results can be summarized as follows. First, the Johansen cointegration test shows that both series share a common trend, suggesting that both markets respond to common information. Second, the VECM clearly suggests that there is causation from the natural gas market to the electricity market, with the error correction term being the source of causation. Finally, the GARCH model indicates that volatility spillovers between both markets are in the same direction. A number of important implications are derived.

In fact, these connections are observed not only in prices but also in volatilities and indicate that volatility changes in the Zeebrugge natural gas market should be taken into account to explain the changes in volatility in the Spanish electricity market, so as to improve the accuracy of electricity price forecasts. In fact, Spanish electricity forward

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market participants may even take advantage of this pattern and anticipate a volatility rise in their market, following a volatility rise in the Zeebrugge natural gas market.

According to the above results, the Spanish electricity 1-month-ahead market is connected with the Zeebrugge natural gas 1-month ahead forward market both by their prices and their volatilities. Moreover, only unidirectional long-term causality running from the natural gas market to the electricity market is detected. Therefore, our findings allow us to confirm, that the Zeebrugge natural gas 1-month ahead forward price may serve as a reference price for natural gas in Spain.

Providing information on the dynamics of electricity and natural gas prices allows for a better understanding of price information flow among the markets. From a political point of view, the finding that the Spanish electricity and natural gas prices traded at Zeebrugge hub are cointegrated could mean a step forward towards the increasing integration of European energy markets, but it is also crucial for issues related to risk management. In particular, this finding is important at least at three levels: (i) it is worthy for financial market participants to understand the volatility transmission mechanism across sectors in order to facilitate optimal portfolio allocation decisions; (ii) it may provide arbitrage opportunities for electricity and/or natural gas traders; and (iii) it can be very useful for cross-market hedging operations to be conducted in these energy derivatives markets.

Acknowledgements

We are grateful for the financial support of the Spanish Ministry of Education and Technology and FEDER, under the project CGL2009-09604 and the Cátedra Finanzas Internacionales-Banco Santander. Usual caveats apply.

References

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Asche, F., Osmundsen, P., R. Tveteras (2002). European market integration for gas? Volume flexibility and political risk. Energy Economics, 24, 249-265. Asche, F. Osmundsen, P., M. Sandsmark (2006). The UK Market for Natural Gas, Oil and Electricity: Are the Prices Decoupled? The Energy Journal, 27, 2, 27-40. Bosco, B., Parisio, L., Pelagatti, M., F. Baldi (2007). A Robust Multivariate Long Run Analysis of European Electricity Prices. Fondazione Eni Enrico Mattei. 103. Comisión Nacional Energía (CNE) (2008). Informe sobre la Evolución de la Competencia en los Mercados de gAs y Electricidad. Periodo: 2005-2007. www.cne.es Dickey, D. A., W. A. Fuller (1981). Likelihood Ratios Statistics for Autorregresive Time Series with a Unit Root. Econometrica 49, 4, 1057-72. Emery, G.W., Q. Liu (2002). An analysis of the relationship between electricity and natural-gas futures prices. The Journal of Futures Markets, 22, 95-122. Engle, R. F., K. F. Kroner (1995). Multivariate Simultaneous Generalized Arch. Econometric Theory 11, 1, 122-150. Ewing, B., Malik, F., Ozfidan, O. (2002). Volatility transmission in the oil and natural gas markets. Energy Economics, 24, 525-538. Furió, D., V. Meneu (2010). Expectations and Forward Risk Premium in the Spanish Electricity Market. Energy Policy, 38, 784-793. Glosten, L. R., Jagannathan, R., D. E. Runkel (1993). On the Relation between the Expected Value and Volatility of Nominal Excess Return on Stocks. Journal of Finance 48, 5, 1779-1801. Granger, C. W. J. (1988). Some Recent Developments in a Concept of Causality, Journal of Econometrics 39, 199-211. Johansen, S., K. Juselius (1990). Maximum Likelihood Estimation and Inference on Cointegration with Application to the Demand of Money. Oxford Bulletin of Economics and Statistic, 52, 169-210. Kao, C., Wan J. (2009). Information transmission and market interactions across the Atlantic ­an empirical study on the natural gas market. Energy Economics, 31, 152-161.

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Kearney, C., A. J. Patton (2000). Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System. Financial Review 35, 1, 29-48. MacKinnon, J. G. (1991). Critical Values for Cointegration Tests. In: Long-run Economic Relationships: Readings in Cointegration. Oxford: Oxford University Press, Chapter 13. Miller, S., F. Russek (1990). Co-integration and error correction models: The temporal causality between government taxes and spending. Southern Economic Journal, 221-229. Mjelde, J.W., D.A. Bessler (2009). Market integration among electricity markets and their major fuel source markets. Energy Economics, 31, 482-491. Mohammadi, H. (2009). Electricity prices and fuel costs: Long-run relations and shortrun dynamics. Energy Economics, 31, 503-509. Muñoz, M.P., D.A. Dickey (2009). Are electricity prices affected by the US dollar to Euro exchange rate? The Spanish case. Energy Economics, in press, doi:10.1016/j.eneco.2009.05.011 Neumann, A., Siliverstovs, B., C. von Hirschhausen (2006). Convergence of European spot market prices for natural gas? A real-time analysis of market integration using the Kalman Filter. Applied Economics Letters, 13, 727-732. Serletis, A., A. Shahmoreadi (2006). Measuring and Testing Natural Gas and Electricity Markets Volatility: Evidence from Alberta´s Deregulated Markets. Studies in Nonlinear Dynamics & Econometrics, 10, 3, 10. Siliverstovs, B., L´Hégaret, G., Neumann, A., C. von Hirschhausen (2005). International Market Integration for Natural Gas? A Cointegration Analysis of Prices in Europe, North America and Japan. Energy Economics, 27, 603-615. U.S. Energy Information Administration (EIA), 2009. International Energy Outlook 2009. Report DOE/EIA-0484.

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6. Tables

Table 1. Descriptive statistics

Electricity 1-month ahead returns Natural gas 1-month ahead returns

Mean Minimum Maximum S.D. Skewness Kurtosis Jarque-Bera p-value

0.00014 -0.80 0.91 0.08 1.70 56.10 135446.1 0.00000

-0.00037 -0.39 0.36 0.06 0.47 12.73 4576.58 0.00000

Note: This table shows the descriptive statistics for the electricity and natural gas one-month-ahead forward returns (01/04/2005 ­ 05/29/2009). The number of observations is 1149. The Jarque-Bera statistic is used to test whether or not the series resembles normal distribution. Probability values are provided.

Table 2. Unit root tests

Electricity prices Natural Gas prices

ADF

-2.5908

-1.8443

Note: This table shows the unit root tests for the electricity and natural gas logarithm prices. The ADF refers to the Augmented Dickey and Fuller (1981) unit root tests. The null hypothesis of this test is the existence of one unit root. The critical value at 5% (1%) significance level of Mackinnon (1991) for the ADF test (process with intercept but without trend) is -2.8634 (-3.4362).

Table 3. Johansen (1988) tests for cointegration. Lags 10 Null r=0 r=1

trace (r )

24.216 2.259

Critical Value 20.261 9.164

max (r )

21.956 2.259

Critical Value 15.892 9.164

Note: trace (r) tests the null hypothesis that there are at most r cointegration relationships against the alternative that the number of cointegration vectors is greater than r. max (r) tests the null hypothesis that there are r cointegration relationships against the alternative that the number of cointegration vectors is greater than r + 1. Critical values at the 0.05 level are from MacKinnon-Haug-Michelis (1999).

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Table 4. Dynamics between electricity and natural gas prices

i

Joint test for

Joint test for y 2,t i (10) 7.7624 (0.65)

y1,t i (10)

y1,t

y 2,t

-0.0547 (-4.16) 0.0206 (1.77) 6.6566 (075)

Note: y1,t and y2,t refer to electricity and natural gas logarithm price series, respectively. i are the error correction terms. P-values displayed in parentheses.

Table 5. Results of the linearized multivariate BEKK model Electricity conditional variance equation

2 2 12,t 4.30x10 -5 0.3782 12,t 1 - 0.4797 12,t 0.1521 2,t 1 0.0216 1,t -1

8.52x10 -6 (5.0461)

0.0198 (19.0371)

0.0318 (-15.0533)

0.0185 (8.1932)

0.0045 (4.7668)

2 2 2 - 0.06391,t -1 2,t 1 0.0472 2,t -1 0.04951,t 1 - 0.05021,t -1 2,t 1 0.0127 2,t 1 0.0087 0.0040 0.0076 0.0833 0.0422 (-7.3083) (11.6345) (6.5111) (-0.6030) (0.3013)

Natural gas conditional variance equation

2 2 2 2,t 0.0001 0.0038 12,t 1 0.0776 12,t 1 0.3918 2,t 1 0.0001 1, t -1

3.01x10 5 (5.3503)

0.0023 (1.6586)

0.0234 (3.3052)

0.0200 (19.5625)

0.0001 (0.8189)

2 2 2 0.00371,t 1 2,t 1 0.0249 2, t -1 0.00041,t 1 0.01071,t 1 2,t 1 0.0687 2,t 1

0.0021 (1.7289)

0.0020 (12.1219)

0.0006 (0.6696)

0.0106 (1.0091)

0.0673 (1.0208)

2 Note: 12,t and 2,t denote the conditional variance for the electricity and the natural gas return series,

respectively. Below the estimated coefficients are the standard errors, with the corresponding t-values given in parentheses.

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7. Figures

Figure 1. Spanish electricity 1-month-ahead prices and Zeebrugge natural gas 1-month forward prices (April 2005 ­ May 2009)

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90

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60

Euros/MWh

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20

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0

OMEL electricity prices

Zeebruge Hub naturalgas prices

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