Cointegration analysis among European crude oil, natural gas and coal prices between 1980 and 2015.

The beginning of cointegration theory lies in the fact that a lot of financial and macroeconomic series are non-stationary. But when common methods are applied, a problem arises and is called “spurious regression”. Spurious regression is a situation in which variables that are related appear to be statistically significant when the variables are unrelated. Non-stationarity is a property of many time series and arises when a variable doesn’t have a clear tendency to return to a constant value or linear trend. This property consequently leads to invalidate classical inference methods. Cointegration theory allows the study of such non-stationary time series which are stationary when a linear combination is applied. Then it allows specifying stable long-run relationships while analysing the short-run dynamic of variables under consideration. Two cointegration methods will be used in this thesis. The first one is the Engle-Granger (1987) method which has the characteristic to be very simple to implement but has the main limit to allow the analysis of only two variables at a time. In order to counter this limit, the multivariate Johansen’s (1991) approach will be used as the second cointegration method. In this thesis, we will apply cointegration theory among European price series of crude oil, natural gas and coal in a relative large sample of 35 years from 1980 to 2015. Such empirical research on cointegration among energy fossil fuels have already been led by Serletis and Herbet (1999), Villar and Joutz (2006), Mohammadi (2009), Bencivenga et al. (2010) and Westgaard et al. (2011). Nevertheless, none of them took as large a sample as in this thesis. Moreover, we also take into account data from the ten last years which are characterised by a high volatility, especially with the worldwide financial and economic crisis in 2008 and 2009. Based on monthly price series of Brent crude oil, natural gas and coal from European countries, and using the software R, several hypotheses are tested in this thesis: - Hypothesis n°1: There is (are) cointegration relationship(s) using the Engle- Granger (1987) method between prices of crude oil/natural gas, natural gas/coal, and coal/crude oil. - Hypothesis n°2: There is (are) cointegration relationship(s) using Johansen’s (1991) approach. - Hypothesis n°3: Considering a structural break, there is (are) cointegration relationship(s) using Johansen’s (1991) approach. Economic and financial price series exhibit, most of the time, the characteristic to be non-stationary. The problem with those kinds of series which have this property is that classical analytical methods cannot be used on them, at the risk of having as a result “spurious regression”. In order to get around this difficulty, we applied the cointegration theory on our variables in order to detect some hypothetical relationships among prices of crude oil, natural gas and coal. Two main methods were used with the first one being the Engle-Granger (1987) method which allows us to analyse the cointegration relationships between pairs of variables and the second one being the multivariate Johansen’s (1991) approach which allows us to determine the number of cointegration relationships from VAR models. The results from the Engle-Granger (1987) method (and from the Granger causality tests) show us that there are three cointegration relationships among our variables seeing that the prices of coal have an impact on the prices of crude oil and natural gas and the prices of crude oil have an impact on the prices of natural gas. After estimating their respective error correction model for each relation, it has been interpreted that all of them exhibit a long-run relationship, meaning that an error correction mechanism is present in order to compensate some potential disequilibrium. This mechanism helps to keep the evolution of the three price series on the same path in the long-run. Moreover, it seems that the growth of coal prices has a positive impact on the growth of crude oil and natural gas prices when the growth of crude oil prices has a negative impact on the growth of natural gas prices. This first step accomplished, we can say that our hypothesis n°1 is verified for those three relations. The second method used for cointegration analysis is Johansen’s (1991) approach and it allows the analysis of multiple variables at the same time and not only by pairs, as it was only possible with the Engle-Granger (1987) method. Based on the estimation of a VAR model with our three variables, the results of this second method show us the existence of one cointegration vector among the three variables which allows us the estimation of the VECM. The results from the estimated VECM show us that, like in the Engle-Granger (1987) method, there is an error correction mechanism but only in the relations relative to the crude oil prices and the natural gas prices. The relation relative to the coal prices does not have a significant error term in its relation. Concerning the short-term indicators, the results coincide with the Engle-Granger (1987) method. In fact, the growth of crude oil prices is positively dependent on the past values of the growth of coal prices and its own past growth in price values. The growth of natural gas prices are negatively linked to the past values of the growth of crude oil and coal but also to its own past growth in price values. And finally, the growth of coal prices is positively dependent on the past values of the growth of crude oil prices and on its own growth in price values. Based on those results, we can then assert that our hypothesis n°2 is verified and there is in fact a cointegration relationship among our variables. The third and final analysis used the same Johansen’s (1991) approach but with the difference that, in the estimated model, a structural break at an unknown date has been introduced. The method is based on Luetkepohl et al (2004) and allows the analysis of cointegration relationships when a structural break in our data is taken into account. The reason for this analysis is to determine if strong variations in our data have an impact on the presence of cointegration relationships we found earlier. The strong variations refer to the high volatility period resulting from the economic and financial crisis in 2008 and 2009 when the prices of our three variables experienced a huge drop. The results from this third cointegration analysis show us the existence of an additional cointegration vector in the estimated model compared to the previous analysis which gives us two cointegration vectors. The estimation of the VECM gives us the same interpretation as Johansen’s approach with an error correction mechanism in the relation relative to the crude oil and natural gas prices but not for the coal prices. With this last result, we can then validate our hypothesis n°3 and say that, despite the presence of a structural break in the model, there exist two cointegration relationships among our variables which have a long-run relationship. The fact that the presence of a structural break has a positive impact on the presence of cointegration relationships shows us that there are strong relations between crude oil, natural gas and coal prices, even if a high volatility period occurs in the prices series. In fact, such highly volatile periods, like the one from the ten last years, could have an important impact on the models’ estimations but it seems that the cointegration relationships among our variables do not react the same way and there is no decoupling effect. The results of this thesis could be particularly useful for the energy industries especially for hedgers who are looking to diminish risk during a crisis period. In fact, during high volatility periods, it is relatively difficult to reduce the risk linked to energy sources. The fact that the three prices seem to be cointegrated could be helpful to better anticipate the behaviour of energy prices during economical or financial crisis periods.