Derek Bunn
email: dbunn@london.edu

Julien Chevallier
email: julien.chevallier04@univ-paris8.fr

Yannick Le Pen
email: yannick.lepen@dauphine.fr

Benoît Sévi
email: benoit.sevi@gmail.com

Fundamental and Financial Influences on the Co-movement of Oil and Gas prices

Keywords: JEL Classification: C22, C32, G15, E17 Oil Futures, Gas Futures, Common Factors, Approximate Factor Models, Excess Comovement

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Introduction

Whilst the evolution and volatility of commodity prices have always presented hedging and risk management concerns to producers and consumers, the so-called "financialization" of commodities through the active involvement of investors and speculators adds a new ingredient to the complexity of their price formations. This theme of increased investment and speculative activity in commodities became especially topical in relation to oil price behavior in the first decade of this century, with a view emerging that the financial effects may be substantial in linking commodity price indices to speculative volumes and to equity indices, but only alongside the changes in global economic fundamentals [START_REF] Hamilton | Causes and consequences of the oil shock of 2007-08[END_REF][START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF][START_REF] Tang | Index investment and financialization of commodities[END_REF]. For the individual commodities, however, whilst questions still remain on the relative effects of fundamental drivers and financial market activity, there is, in addition, a more subtle aspect relating to the changes in the relationships amongst the commodities themselves. If two or more commodities are part of the same asset class, traded perhaps as part of a commodity index, then it is plausible to expect that extra financial activity will further increase their correlation beyond that already attributable to their product fundamentals. This expectation now appears to follow as a conjecture from various strands of theoretical and empirical research. Thus, as a result of information frictions and adaptive learning from prices, more financial trading may increase the link between commodities and equity market indices, inducing a pro-cyclical tendency (e.g. [START_REF] Singleton | Investor flows and the 2008 boom/bust in oil prices[END_REF], which would plausibly also manifest a greater co-movement amongst the commodities involved. Furthermore, capital frictions have been shown to influence risk premia in commodity futures (e.g. [START_REF] Acharya | Limits to arbitrage and hedging: evidence from commodity markets[END_REF] and the consequent limits to arbitrage may again influence the correlations amongst commodities in the same asset class. More directly, it has been shown in general that as the objective function of investors becomes compromised by a need to outperform benchmark indices, index-focussed trading increases the correlations between asset prices comprising the indices (e.g. [START_REF] Basak | Asset prices and institutional investors[END_REF].

In order to test whether co-movement amongst heavily traded commodities is being significantly influenced by financial factors, it is therefore clearly necessary to do so in the context of a comprehensive representation of the underlying fundamental factors which may link their price behavior. With commodities being primary goods, global economic factors must therefore be fully specified in the modeling. We approach this methodological challenge by means of a filtration of commodity returns through a large approximate factor model, to explore common fundamental factors, followed by analysis of the effects of hedging and speculative trading proxies on the residual co-movements. As an application area, energy commodities are particularly amenable to this research question and we analyse an important pair of energy products, crude oil and natural gas, which are of substantial economic impact and predominate within the commodity indices (e.g. GSCI).

As a topical area, the fundamental aspects of the link between oil and gas prices have engaged substantial commentary and analysis. In general, the conventional view was one of strong linkage, as in [START_REF] Serletis | The message in North American energy prices[END_REF], mainly because of the history of product substitution between gas and fuel oil (e.g. for power generation, industrial boilers). Furthermore, especially within Continental Europe and South-East Asia, as well as elsewhere, the development of gas pipelines by the upstream oil producers had generally been associated with long-term gas contracts, index-linked to crude oil prices. Against this, there are some different market features. Oil markets are part of broader international markets, while natural gas markets are essentially regional. Surplus production of natural gas may arise since it is a co-product of oil. Gas supply is more inelastic than oil in the short-term, partly because of production and delivery logistics [START_REF] Villar | The relationship between crude oil and natural gas prices[END_REF]); likewise gas demand is less elastic because of its substantial component of residential heating (Ewing et al. (2002)) compared to the high transportation component for oil. Finally, more recent data suggests that linkages may have weakened with the advent of shale gas and, looking beyond the US, with the continuing deregulation of energy markets worldwide [START_REF] Ramberg | The weak tie between natural gas and oil prices[END_REF]).

In such a changing and multifaceted context of fundamental influences, empirical analysis has unsurprisingly revealed mixed results concerning the existence of a long-term relationship between gas and oil. From a cointegration framework, [START_REF] Serletis | The message in North American energy prices[END_REF] identified shared trends among the U.S. Henry Hub natural gas price and the fuel oil price during 1996-1997, as did [START_REF] Villar | The relationship between crude oil and natural gas prices[END_REF] for the Henry Hub natural gas price and the West Texas Intermediate (WTI) crude oil price during 1989-2005. They identified a stable relationship between oil and gas prices, despite periods where they may have appeared to 'decouple'. By using error correction models, [START_REF] Bachmeier | Testing for market integration, crude oil, coal and natural gas[END_REF] also found evidence of market integration among primary energy fuels in the U.S. during [1990][1991][1992][1993][1994][1995][1996][1997][1998][1999][2000][2001][2002][2003][2004]. Their analysis confirmed that oil and natural gas prices were cointegrated in the long run and exhibited strong evidence of market integration. Furthermore, [START_REF] Brown | What drives natural gas prices?[END_REF] showed that movements in crude oil prices had a prominent role in shaping natural gas prices in the U.S., once other drivers such as weather, seasonality, storage, and production disruptions have been taken into account. Yet, also based on vector error-correction models and common cycle tests, [START_REF] Serletis | Testing for common features in North American energy markets[END_REF] claimed that Henry Hub and WTI did not have common price cycles, and that progressive decoupling of US energy prices was a result of deregulation. Furthermore, [START_REF] Hartley | The relationship of natural gas to oil prices[END_REF] found evidence that the link between natural gas and crude oil prices in the U.S. was indirect, acting through competition at the margin between natural gas and residual fuel oil (being the price of the main competitive oil product). More precisely, the residual fuel oil price caused movements in the natural gas price, while the converse was not true.1 Despite this large body of work on market integration between gas and oil, the cointegration approach appears too restrictive for our purposes. In seeking to go beyond tests for linkage and dynamic error correction, we a looking to identify what may be the common underlying factors of co-movement in these two commodities, amongst an extensive set of global macro variables, as well as with regard to financial hedging and speculative proxies. To find the common factors, we use the large approximate factor model methodology following Stock and Watson (1999, 2002a,b, 2006); [START_REF] Bai | Large dimensional factor analysis[END_REF]. Large approximate factor models have been used in a number of financial applications, with, in particular, [START_REF] Ludvigson | The empirical risk return relation: A factor analysis approach[END_REF], 2009[START_REF] Kapetanios | A testing procedure for determining the number of factors in approximate factor models with large datasets[END_REF] investigating the risk-return trade-off and the bond premium. Thus, in our study, we extract from a large dataset of macroeconomic and financial variables the factors that are able to explain oil and gas returns in the U.S. futures markets. We show that a few factors can explain a significant proportion of both returns, which is an indication of similar fundamentals for oil and gas dynamics. This appears to be the first study aiming at explaining oil and gas returns with factors extracted from a large dataset. Furthermore, compared to the wellknown dataset by Stock and Watson (2002a,b), ours also includes variables from emerging economies known to contribute to the price formation of market for energy commodities. Indeed, we find that the factor with the highest explanatory power for oil is mostly connected with real macroeconomic variables from emerging countries. Furthermore, we show that the correlation between the unexplained parts of the returns (residuals after filtration by the factors) can be explained by trading activity proxies, which would be consistent with the financialization conjecture for related energy commodities. In particular, we find that the speculative activities increase the correlations, whereas the hedging activities reduce it.

The remainder of the paper is structured as follows. Section 2 presents the dataset and Section 3 reviews the approximate factor modeling methodology. Section 4 reports the empirical analysis of oil and gas returns using this methodology and Section 5 contains the analysis of residual autocorrelation. Section 6 focuses on the trading activity proxies and Section 7 concludes.

Data

We look at the main global oil and natural gas prices from the U.S. The natural gas futures are the Henry Hub price in $/MMBTU, whilst the crude oil futures are the WTI prices in $/BBL.

The dataset is composed of 196 monthly observations from 01/11/1993 to 01/03/2010. Raw prices and returns are respectively displayed in Figures 1 and2.

Descriptive statistics for returns are reported in Table 1. These statistics show evidence of excess kurtosis for each return series. Returns also record a negative skewness for crude oil but not natural gas. The Jarque-Bera test rejects the hypothesis of a Gaussian distribution for each return. Heteroskedasticity is present in the data, which may explain the non-normality.

Oil and gas prices have unit roots and are cointegrated. The raw correlation between U.S. crude oil and natural gas returns is positive and significant (as judged by the p-value).

Whilst the cointegration tests established the linkages, to understand the common macro drivers more explicitly, factors are extracted from 187 macroeconomic and financial variables representative of developed and emerging countries. Our dataset differs in its composition from the widely known large factor datasets of [START_REF] Stock | Implications of dynamic factor models for VAR analysis[END_REF] and [START_REF] Ludvigson | Macro factors in bond risk premia[END_REF] which consist mainly of U.S. national data.2 Since we aim at explaining crude oil and natural gas returns, we include data from the main developed economies (128 variables) and also from emerging countries (59 variables). Therefore our dataset is representative of the world economy, and high-level demand from emerging countries will be included in the information conveyed by the estimated factors. These variables can also be classified into 103 real variables (73 for developed countries, 30 for emerging countries) and 84 nominal variables (55 for developed countries and 29 for emerging countries). Following the analysis in [START_REF] Boivin | Are more data always better for factor analysis[END_REF], we do not include as many variables as could be possible. Indeed, those authors demonstrate that including too many variables rarely leads to a better estimation of factors. In a recent contribution, [START_REF] Caggiano | Are more data always better for factor analysis? Results for the euro area, the six largest euro area countries and the UK[END_REF] provide strong empirical support to the findings of [START_REF] Boivin | Are more data always better for factor analysis[END_REF] in the Euro area. Thus, inclusion in our dataset followed two principles: (i) to gather, as far as possible, a balanced panel between developed and developing countries, and (ii) to limit the dimensionality of the dataset so as to avoid measurement error problems in the factor analysis. All data are extracted from Thomson Financial DataStream. The list of the 187 time series is given in the Appendix, where a coding system indicates how the data are transformed to ensure stationarity. All of the raw data are standardized prior to estimation.

The large approximate factor methodology

With a sample of i = {1, . . . , N} cross-section units and t = {1, . . . , T } time series observations, we formulate:

x it = λ i F t + e it
where F t is the vector of the r common factors. e it is referred to as the idiosyncratic error, and λ i as the factor loadings of the (static3 ) common factors. F t , {λ i } i=1,...,N , {e it } i=1,...,N t=1,...,T are unknown and have to be estimated from {x it }. With X t = (x 1t , . . . , x Nt ) , e t = (e 1t , . . . , e Nt ) and Λ = (λ 1 , . . . , λ N ) , we have the vector form notation :

X t = ΛF t + e t
If we assume that F t and e t are uncorrelated with zero mean, and operate the normalization

E(F t F t ) = I d , we have: Σ = ΛΛ + Ω
where Σ and Ω denote, respectively, the population covariance matrices of X t and e t .

In classical factor analysis, F t and e t are assumed to be serially and cross-sectionally uncorrelated. Moreover the number of observations N is fixed. The 'large dimensional approximate factor model' initiated by Stock and Watson (2002a,b) differs from previous factor models in two ways (at least): (i) the sample size tends to infinity in both directions, and (ii) the idiosyncratic errors are allowed to be 'weakly correlated'4 across i and t.

We assume k factors, and use the principal components method to estimate the T × k matrix of factors F k and the corresponding N × T loadings matrix Λ k . These estimates solve the following optimization problem :

minS(k) = (NT ) -1 N i=1 T t=1 (x it -λ k i F k t ) 2 subject to the normalization Λ k Λ k /N = I k .
If we define X as the T ×N matrix with t th row X t , this classical principal component problem is solved by setting Λk equal to the eigenvectors of the largest k eigenvalues of X X. The principal components estimator of F k is given by:

F k = X Λk /N
Computation of F k requires the eigenvectors of the N × N matrix X X. When N > T, a computationally simpler approach uses the T × T matrix XX . Consistency of the principal component estimator as N and T → ∞ is demonstrated by Stock and Watson (2002a) and [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF]. [START_REF] Bai | Inferential theory for factor models of large dimensions[END_REF] gives the asymptotic distribution of the principal component estimator.

We use the information criteria by [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF] and the sequential test by [START_REF] Kapetanios | A testing procedure for determining the number of factors in approximate factor models with large datasets[END_REF] to determine the number of factors. The information criteria by [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF] can be seen as an extension to factor models of usual information criteria. If we note Ŝ

(k) = (NT ) -1 N i=1 T t=1 (x it -λk i F k t )
2 the sum of squared residuals (divided by NT ) when k factors are considered, the information criteria have the following general expressions:

P CP i (k) = Ŝ(k) + kσ 2 g i (N, T ) IC i (k) = ln( Ŝ(k)) + kg i (N, T )
where σ2 is equal to Ŝ(k max ) for a pre-specified value k max , and g i (N, T ) is a penalty function.

We allow a maximum of k max = 20 factors, and apply the four penalty functions g i (N, T ), i = 1, .., 4 proposed by [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF]. The estimated number of factors minimizes the aforementioned information criteria.

We also apply the sequential test by [START_REF] Kapetanios | A testing procedure for determining the number of factors in approximate factor models with large datasets[END_REF] to determine the number of factors.

This test is based on the property that if the true number of factors is k 0 , then, under some regularity conditions, the k 0 eigenvalues (in decreasing order) of the population covariance matrix Σ will increase at rate N while the others will remain bounded. If we denote by λk , k = 1, ..., N the N eigenvalues of the sample covariance matrix Σ, the difference λkλk max +1 will tend to infinity for k = 1, ..., k 0 but remain bounded for k = k 0 + 1, ..., k max where k max is some finite number such that k 0 < k max . The null hypothesis that the true number of factors

k 0 is equal to k (H 0,k : k 0 = k) against the alternative hypothesis (H 1,k : k 0 > k) is therefore
tested with the test statistics λkλk max +1 . If there is no factor structure, λkλk max +1

properly normalized by a sequence of constant τ N,T should converge to a law limit. In the presence of factors, it should tend to infinity. The law limit and the rate of convergence τ N,T → ∞ have to be estimated by resampling technique. The test procedure is sequential.

In a first step, we test (H 0,k :

k 0 = k = 0) against (H 1,k : k 0 > 0).
If we reject the null hypothesis, then we consider the null (H 0,k : k 0 = k + 1 = 1). We stop once we cannot reject the null hypothesis. [START_REF] Kapetanios | A testing procedure for determining the number of factors in approximate factor models with large datasets[END_REF] refers to this algorithm as MED (maximal eigenvalue distribution).

The estimated numbers of factors are displayed in Table 2, where it is evident that there is clearly no agreement on the optimal number of factors. This result is similar to previous empirical studies, which also show substantial variations in determining the number of factors.

According to the information criteria by [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF], the optimal number of factors runs from the 2 to 9. The sequential test by Kapetanios (2009) selects 2 factors.

Additional information on the autocorrelation and the explanatory power of the estimated factors F t is displayed in Table 3. We notice that the first 3 factors only explain 20% of the variance of the 187 time series, while we reach 36% with 9 factors. Hence, we choose to consider the set of the first 9 factors as potential set of regressors. The factor autocorrelations (up to 3 lags) provided in Table 3 show that most factors are persistent.

Factor analysis of oil and gas returns

We consider the first 9 factors to comprise the set of potential regressors. Since a preliminary analysis factor-by-factor shows that factors 3 and 9 have low explanatory powers (compared to the others), we choose to exclude them from our set of regressors. We then consider all combinations of the 7 remaining factors, and select the subset which minimizes the multivariate BIC criterion (as in Stock and Watson (2002) and [START_REF] Ludvigson | Macro factors in bond risk premia[END_REF]). All results are reported in Table 4.

Following this process, we choose the set Ft = ( F 1 t , F 2 t , F 7 t ) and estimate the following SUR regression:

r 1,t = α 1 + β 1 Ft + u 1,t = α 1 + β 1,1 F 1 t + β 1,2 F 2 t + β 1,7 F 7 t + u 1,t r 2,t = α 2 + β 2 Ft + u 2,t = α 2 + β 2,1 F 1 t + β 2,2 F 2 t + β 2,7 F 7 t + u 2,t
We consider extra explanatory variables by adding for each energy market monthly stock/inventories changes computed as Δs it = log(S i,t /S i,t-1 ), where S i,t stands for the stock level at date t (see [START_REF] Brown | What drives natural gas prices?[END_REF]). 5 In addition, we include the dummy variable Du, which captures the disruption in oil and gas supply caused by the Hurricanes Ivan in September 2004

and Katrina in August 2005.

The minimization of the BIC criterion leads us to select the same set of factors as previously, and to estimate:

r 1,t = α 1 + β 1 Ft + γ 1 Δs 1,t + θ 1 Du + v 1,t = α 1 + β 1,1 F 1 t + β 1,2 F 2 t + β 1,7 F 7 t + γ 1 Δs 1,t + θ 1 Du + v 1,t r 2,t = α 2 + β 2 Ft + γ 2 Δs 2,t + θ 2 Du + v 2,t = α 2 + β 2,1 F 1 t + β 2,2 F 2 t + β 2,7 F 7 t + γ 2 Δs 2,t + θ 2 Du + v 2,t
5 These data are extracted from the US Department of Energy website.

The results of these estimations are reported in Table 4. Firstly, we find a higher explanatory power for crude oil than for natural gas. The R 2 associated with regression (1.a) is equal to 0.34 for oil, and to 0.07 for gas in regression (1.b). This distinction applies across all regressions (1.a) to (3.b). This result may be explained by the fact that gas markets are more regional and hence international factors are less likely to have a good explanatory power for these series (compared to oil).

Regarding the estimated coefficients, the first factor F 1 appears to be statistically significant only for oil returns. This finding is stable across the regressions (1.a), (2.a) and (3.a).

Concerning the factors F 2 and F 7 , we notice the remarkable stability of the signs obtained across all regressions, as well as their statistical significance (except F 7 in regression (3.a)).

The coefficient estimates for the extra explanatory variables are not significant, except for changes in stock/inventories. With the significant negative sign for stocks, as in other studies (e.g. [START_REF] Brown | What drives natural gas prices?[END_REF]), this is intuitively consistent with conventional fundamental expectations for the effect of stocks on price movements.

In order to interpret the factors, we follow [START_REF] Ludvigson | Macro factors in bond risk premia[END_REF], by regressing each original variable on each single factor and then, for graphical convenience, as in Figure 3, sorting the variables along the horizontal axis (in our case, beginning with real variables and then with nominal variables), to show the variables for which high marginal R 2 are obtained. Thus, we classify our 187 series into four categories according to the characteristics real/nominal variables and developed/emerging countries. A finer classification would be difficult to illustrate and is relevant, in our opinion, only when a single country is under consideration.6

Factor F 1 can easily be interpreted as a real factor, since it records its highest explanatory power for real variables. More particularly, F 1 is mostly associated with real variables from emerging countries.7 It is significant for oil market returns, but does not indicate any effect on gas returns. The association of F 1 with crude oil returns can be interpreted as an evidence of the growing weight of emerging countries in oil imports during the time period considered.

This finding is consistent with the rather weak support of previous studies to the popular view that oil prices have been driven more by financial activities, rather than real supply and demand variables, and in this respect supports the findings by [START_REF] Hamilton | Causes and consequences of the oil shock of 2007-08[END_REF] and [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF] that real demand from emerging economies has been partly responsible for the rise in oil prices over the recent period. More importantly, because we include in our database a number of Asian variables, it seems that their explanatory power is rather large and supports the view of the demand-shock-based dynamics.

Unlike F 1 , the other factors indicate common macro effects on both gas an oil returns. F 7 has its highest factor loadings for a small set of real economic activity variable from developed countries (most notably western housing starts and car registrations) and is significant across all variables, including both oil and gas. Factor F 2 is a significant, more broadly loaded factor for both oil and gas (with relatively higher loadings on Asia-Pacific economies than

F 7 ).
Evidently there is a substantial basis from factors 2 and 7 for asserting that gas has a linkage with oil due to common economic and other global drivers, but, from the first factor, oil also has its own distinct global economic driver linked to the growth of the emerging economies.

Correcting residual correlation for heteroscedasticity

In this section, we proceed, as in [START_REF] Kallberg | Time-series and cross-sectional excess comovement in stock indexes[END_REF], to correct the residual correlations for the heteroscedasticity. The main idea is to compute the sample correlation, and then to correct it for the effect of change in volatility by using [START_REF] Forbes | No contagion, only interdependence: measuring stock market co-movements[END_REF]'s methodology to obtain an unbiased estimate of correlation. When applied on a rolling basis, this estimation technique is able to track the true conditional correlation. Note that the resulting estimate is nonparametric. As mentioned by [START_REF] Kallberg | Time-series and cross-sectional excess comovement in stock indexes[END_REF], the financial literature contains various empirical applications where rolling filters are found to perform quite well in comparison with parametric specifications. This correction for heteroscedasticity has been used in the context of financial contagion where time-varying volatility is unambiguously present in the data.

Having estimated the commodities returns' conditional mean equation, we use the residuals ûi,t to compute the residuals correlation coefficient:

ρij t = cov(û i,t , ûj,t ) [var(û i,t )var(û j,t )] 1/2
Boyer et al. (1999), [START_REF] Loretan | Evaluation "correlation breakdowns" during periods of market volatility[END_REF] and [START_REF] Forbes | No contagion, only interdependence: measuring stock market co-movements[END_REF] show that the correlation coefficient is conditional on returns volatility. Hence, in the presence of heteroscedasticity, the usual sample correlation may be biased upward or downward. These authors propose a correction for this bias, and define an unconditional correlation measure under the assumption of no omitted variables or endogeneity. The unconditional correlation is defined as:

ρ * ij,t = ρij,t [1 + δi,t (1 -(ρ 2 ij,t )] 1/2
where the ratio δi,t = var(û i,t ) var(û i,t ) LT -1 corrects the conditional correlation ρij,t by the relative difference between short-term volatility var(û i,t ) and the long-term volatility var(û i,t ) LT of the i ith return. As we do not make any ex ante assumption on the direction of propagation of shocks from one commodity to another, we alternatively assume that the source of these shocks is commodity i (in ρ * ij,t ) or commodity j (in ρ * ji,t ). Therefore, ρ * ij,t and ρ * ji,t may be different.

As we have only two returns, we compute the two unbiased measures of correlation, by using the change in volatility in oil and gas residuals that is to say, if the source of shock is 1:

ρ * 12,t = ρ12,t [1 + δ1,t (1 -(ρ 2 12,t ))] 1/2
and, if the source of shock is 2:

ρ * * 12,t = ρ12,t [1 + δ2,t (1 -(ρ 2 12,t ))] 1/2
Besides, we compute the mean of excess squared correlation coefficients:

ρ * t = 1 2 (ρ * 12,t + ρ * * 12,t )
In this analysis, we treat the covariance matrix of returns residuals as observable, and construct time series of rolling excess squared correlations for each commodity i. We consider a time-varying model:

r 1,t = α 1,t + β 1,t Ft + u 1,t r 2,t = α 2,t + β 2,t Ft + u 2,

Financial Impacts on the US oil-gas residual correlation

We now seek to test the financialization conjecture as an explanation for the remaining residual correlation in the filtered oil and gas returns for the U.S. More particularly, we investigate the potential impact of trading activity variables in the oil and gas futures markets on the relationship between oil and gas futures returns. Trading and speculative activities has indeed been established as one influence in the rise of energy prices during the 2000-2008 period (Büyüksahin and Harris (2011), [START_REF] Singleton | Investor flows and the 2008 boom/bust in oil prices[END_REF], and we also expect this to be manifest in excess co-movement of our commodities.

One instrument for trading activity is inspired by [START_REF] Han | Investor sentiment and option prices[END_REF] relation. Thus, it appears that a higher hedging activity, which is by nature more specifically related to one market or another, is associated with a lower residual correlation. Conversely, when the speculative activity is strong, the impact on residual correlation is detected on both oil and gas markets, as agents in this case tend to invest in energy futures markets through commodity indices [START_REF] Tang | Index investment and financialization of commodities[END_REF]), and the consequent explanation of residual returns co-movement is consistent with the financialization conjecture. Finally, as judged by the R 2 of 19%, this analysis of financial trading has explained a substantial part of the remaining residual correlation present in our filtered series for the U.S.

Conclusion

A consequence of the streams of research that have suggested that increased financial engagement in commodity futures will link commodity returns more closely to equity indices [START_REF] Tang | Index investment and financialization of commodities[END_REF]Büyüksahin and Harris, 2011;[START_REF] Singleton | Investor flows and the 2008 boom/bust in oil prices[END_REF] and that index-focused investment by itself may increase the correlations amongst the assets within the index [START_REF] Basak | Asset prices and institutional investors[END_REF], is the expectation that financial flows into commodities may also manifest increased correlations between actively traded commodities. We tested this on U.S. oil and gas futures and find support for the conjecture. Moreover we find significant evidence that speculation, with its focus on index trading, increases the correlation between oil and gas, whilst hedging, which is based more on individual forward contracts, actually decreases this correlation. Both of these are plausible effects and consistent with the "financialization" observations. Expanding the set of commodities to include coal futures is an obvious extension.

The methodological challenge in obtaining these results is substantial. Since commodities are global products, they generally have a complex set of fundamental drivers, and this is certainly the case for oil and gas. Oil itself requires careful structural modeling [START_REF] Hamilton | Causes and consequences of the oil shock of 2007-08[END_REF][START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF] and the theme of oil-gas linkage has been a lengthy and on-going debate amongst energy economists [START_REF] Ramberg | The weak tie between natural gas and oil prices[END_REF]. We therefore undertook a comprehensive fundamental filtration of oil and gas returns before seeking to associate financial activity with the residual correlations. From a large dataset of macroeconomic and financial variables we found that two factors can explain a significant proportion of both returns, which is an indication of similar economic fundamentals for oil and gas dynamics. This appears to be the first study explaining oil and gas returns with factors extracted from a large dataset in the Stock and Watson (2002a,b) tradition, but ours also includes more international variables from emerging economies. Indeed, we find that the factor with the highest explanatory power for oil is mostly connected with real macroeconomic variables from emerging countries, and this was the one key factor that was not shared in common with gas. Given that gas markets tend to be more local with lower gas penetration in developing countries, this is a consistent result.

Whilst the large dataset factor filtration was effective, it is an area for further methodological refinement, as it is crucial for the subsequent residual estimations. Thus, we considered, as in most of the factor-models literature, the factors as if they were observed, whilst they are actually estimated. Despite this, the assumption should only have a limited impact on our results. However it could be relevant to investigate the small sample case using some simulation techniques as in [START_REF] Ludvigson | The empirical risk return relation: A factor analysis approach[END_REF], 2009and 2010) and [START_REF] Gospodinov | Commodity prices, convenience yields, and inflation[END_REF].

The evolving nature of these fundamentals is more challenging, as dynamic representations may become necessary. Overall, however, the analysis undertaken here appears to give robust and consistent results to the subtle question of estimating the financial effects on commodity inter-correlations in the context of complex global fundamentals. Note: ρ * 2 t is the unconditional average squared residual correlation. Han oil and Han gas are the speculative trading activity proxies computed from CFTC futures data for oil and gas, respectively. DeRonnetal oil and DeRonnetal gas are the proxy for hedging pressure in futures markets for oil and gas, respectively. N is the number of observations. * denotes significance at the 5% level. Note: 'conditional squared gross returns correlation' is the squared correlation of raw returns not corrected for heteroskedasticity. 'unconditional average square gross returns correlation' is the ρ * 2 t computed from raw returns. 'unconditional average square residual correlation' is ρ * 2 t computed from OLS residuals. The confidence band represents the minimal value above which squared correlation is significant at the 5% level. It is computed from the t-squared ratio test

Tables

= (ρ * ijt ) 2 [1 -ρ * ijt ] -1 (N -2) ∼ F (1, N -2). *

Figures

t2 ijt = (ρ * ijt ) 2 [1 -ρ * ijt ] -1 (N -2) ∼ F (1, N -2).

Appendix: list of the 187 variables considered in the computation of the common factors

Note: In the Trans column, we report the transformation used to ensure the stationarity of each variable. ln denotes the logarithm, Δ ln and Δ 2 ln denote the first and second difference of the logarithm, lv denotes the level of the series, and Δlv denotes the first difference of the series.

Developed countries

Series

  , who computed the net position of large speculators in S&P 500 futures based on data from the U.S. Commodity Futures Trading Commission (CFTC). Indeed, the CFTC requires large traders holding positions above a specified level to report their positions on a daily basis. Then, the CFTC aggregates the reported data, and releases the breakdown of each Tuesday's open interest in its Commitments of Traders Report (CoT). This report contains the number of long positions and the number of short positions for both 'commercial' traders and 'non-commercial' traders. Commercial traders are required to register with the CFTC by showing a related cash business for which futures are used as a hedge. The non-commercials are large speculators. Hence, it is possible to calculate a trading activity proxy as the number of long non-commercial contracts minus the number of short non-commercial contracts, scaled by the total open interest in S&P 500 futures. We apply this methodology to the case of the U.S. crude oil and natural gas futures data, which provides us with two regressors denoted Han oil and Han gas. We use another measure of trading activity based on the work by de Roon et al. (2000), which proxies the hedging pressure in futures markets. The variable corresponds to the difference between the number of short hedge positions and the number of long hedge positions, divided by the total number of hedge positions. The idea behind this proxy is to focus on the positions of traders who are hedgers, only thereby estimating the pressure of hedging in the futures market. The application of this methodology in our setting returns the regressors DeRonnetal oil and DeRonnetal gas. By regressing the unconditional average squared residual correlation (i.e. the ρ * 2 t ) on the four exogenous regressors Han oil, Han gas, DeRonnetal oil and DeRonnetal gas, we obtain the estimation results reported in Table 6. Whilst columns (5.a) and (5.b), show the separate regressions for the two proxies with little significance, in column (5.c), the four regressors are considered jointly in the same regression and the results are more satisfactory in the sense that all coefficients are significant. It seems that Han (2008)'s proxy for the speculative activity in the U.S. oil and gas futures market is positively related to the unconditional average squared residual correlation. Conversely, de Roon et al. (2000)'s proxy for hedging pressure appears negatively related to the residual cor-

Figure 3 :

 3 Figure 3: Marginal R 2 of macroeconomic and financial variables regressed on the estimated factors no. 1, 2 and 7.

Figure 4 :

 4 Figure 4: Mean excess squared correlation for raw returns and OLS residuals

Table 1 :

 1 Descriptive statistics for U.S. monthly returns.

		Oil (US) Gas (US)
	Mean	0.0077	0.0040
	Maximum	0.3045	0.9694
	Minimum	-0.4340	-0.8496
	Std. Dev.	0.0991	0.2176
	Skewness	-0.5770	0.0555
	Kurtosis	4.6766	5.5875
	Jarque-Bera	33.83*	33.83*
	Nb. of Obs.	196	196
	correlation	0.2095
	p-value	0.0032

Note:(i) monthly returns are computed as log difference of raw prices. Commodity prices are cash prices except crude oil where the current month contract price is taken as a proxy for the cash price. (ii) '*' denotes a rejection of the null hypothesis of a Gaussian distribution at the 5% level. (iii) The p-value is computed by transforming the residual correlation to create a t-statistic having (N -2) degrees of freedom, with N the number of observations.

Table 2 :

 2 Static factors selection results

	Method No of static factors
	MED	2
	IC 1	3
	IC 2	2
	IC 3	20
	IC 4	20
	P CP 1	9
	P CP 2	7
	P CP 3	20
	P CP 4	20

Note: MED denotes the number of factors given by the Maximum Eigenvalue Distribution algorithm. ICi and P CPi denote, respectively, the number of factors given by the information criteria IC and P CP estimated with the penalty function gi(N, T ).

Table 3 :

 3 Summary statistics for F t,i for i = 1, ..., 9

	factor i	ρ 1	ρ 2	ρ 3	R 2 i
	1	0.1614 0.1256 0.3176 0.0975
	2	0.1357 0.0805 0.3110 0.1619
	3	-0.0748 0.0145 -0.0294 0.2030
	4	-0.0765 -0.0910 0.1508 0.2355
	5	-0.2180 -0.0763 0.1213 0.2654
	6	0.1801 0.0388 0.0267 0.2927
	7	0.0721 0.2765 0.2744 0.3185
	8	0.4086 0.5013 0.3332 0.3418
	9	-0.0066 -0.0305 -0.0379 0.3636

Note: For i = 1,..,9, Fit is estimated by the method of principal components using a panel of data with 187 indicators of economic activity during 1993:12-2010:3. The data are transformed (taking logs and first difference where appropriate) and standardized prior to estimation. ρi denotes the i th autocorrelation. The relative importance of the common component,R 2 i , is calculated as the fraction of total variance in the data explained by factors 1 to i.

Table 4 :

 4 Fitting U.S. crude oil and natural gas returns. Data from 01/12/1993 to 01/03/2010. th factor estimated using principal component methods. t-statistics are reported in parenthesis under the estimates. A constant whose estimate is reported in the second row is always included in the regressions. (v) The

	US market	Crude oil Natural gas Crude oil Natural gas Crude oil Natural gas	(1.a) (1.b) (2.a) (2.b) (3.a) (3.b)	Intercept 0.0077 0.0040 0.0085 0.0038 0.0089 0.0053	(1.34) (0.27) ( 1.49) (0.25) ( 1.53) (0.34 )	F 1 -0.1217*** -0.0355 -0.1195*** -0.0458 -0.1199*** -0.0471	(-6.95) (-0.77) (-6.58) (-0.94) (-6.59) (-0.96)	F 2 -0.1489*** -0.1583*** -0.1503*** -0.1553*** -0.1507*** -0.1565***	(-7.63) (-2.71) (-6.73) (-2.63) (-6.73) (-2.65)	F 7 0.1454*** 0.2574*** 0.1322*** 0.2487*** 0.1335*** 0.2517***	(3.99) (2.85) (3.67) ( 2.66) (3.68) ( 2.69)	Δs oil -0.9966* -0.9742*	(-1.90) (-1.83)	Δs gas -0.3017 -0.3113	(-1.16) (-1.19)	Du -0.0072 -0.0227	( -0.31) (-0.3744)	R 2 0.3481 0.0728 0.3597 0.0777 0.3600 0.0783	R 2 0.3381 0.0583 0.3462 0.0584 0.3431 0.0541	Arch-LM (2) 3.26 27.59** 0.73 26.99** 0.69 26.99**	Residual correl. 0.0961 0.1081 0.1077	p-value 0.1802 0.1315 0.1328	p-value is computed by transforming the residual correlation to create a t-statistic -2) degrees of freedom. (vi) For each test ***, **, and * having (N	Arch-LM (2) stands for Engle's ARCH Lagrange Multiplier test denote rejection of the null hypothesis at, respectively, the 1%, 5% and 10% levels. (vii)	with a lag order equal to 2.

Note: (i) Columns (1.a) and (1.b) report the OLS estimates of the regression of monthly US crude oil and natural gas returns on the contemporaneous variables named in the left column. (ii) Columns (2.a), (2.b), (3.a) and (3.b) report the FGLS estimates for the oil and gas returns. (iii) The dependent variable is the nominal log return for each commodity listed in row 1. F i denotes the i

Table 5 :

 5 Descriptive statistics on squared correlations

		ρ * 2ret t	ρ * 2OLS t
	μ	0.1793* 0.1048
	σ	0.1413 0.1065
	F ρ * 2	51%	22%
	C ρ	0.8306
	Notes: This table reports summary statistics for the excess squared
	unconditional correlation of OLS residuals ρ * 2OLS t squared unconditional correlation of raw returns ρ * 2ret , and the benchmark t . F ρ * 2 is the
	mean percentage of squared unconditional correlation significant at the
	5% level using the t-square ratio test t2 ijt

  denotes significance at the 5% level. Cρ is the correlation between each pair ρ * 2OLS

	t	and ρ * 2ret

t

. μ stands for the mean, and σ for the standard deviation.

Table 6 :

 6 Regression of average excess correlation on trading activity proxies for US oil and gas returns -time period 1998:02 to 2010:03.

				ρ * 2 t
			(5.a)	(5.b)	(5.c)
	Intercept	0.0783* 0.0844* 0.0832*
			(4.39)	( 5.16)	( 5.06)
	DeRonnetal oil	0.0511		-0.2015*
			(1.22 )		(-2.21)
	DeRonnetal gas -0.0562*		-0.1143*
			(-2.05)		(-3.01)
	Han oil		0.5014	2.2669*
				(1.76)	(3.49)
	Han gas		0.1260	0.8370*
				(0.72)	(3.54)
	N			137
	R 2	0.0307	0.0287	0.1914
	R	2	0.0162	0.0142	0.1669

  Ventes Liées et Concurrence sur les Marchés Energétiques Marion PODESTA 07.01.67 Universal Service Obligations: The Role of Subsidization Schemes and the Consequences of Accounting Separation François MIRABEL, Jean-Christophe POUDOU et Michel ROLAND 07.01.68 Concentration des Marchés et Comportements Collusifs : des Conflits entre HHI et Les tarifs d'achat stimulent-ils la production d'électricité renouvelable en France ? Critique du mode de fixation/indexation des tarifs H07 et de son impact sur l'installation de petites centrales hydrauliques Dorian LITVINE 11.03.89 Les tarifs d'achat stimulent-ils la production d'électricité renouvelable en France ? Identification de l'effet de seuil décourageant la rénovation des petites centrales hydrauliques Joining the CCS Club! Insights from a Northwest European CO 2 pipeline project Olivier MASSOL et Stéphane TCHUNG-MING 13.05.98 Les distorsions induites par les énergies intermittentes sur le marché spot de l'électricité François BENHMAD et Jacques PERCEBOIS 13.09.99 La demande potentielle d'électricité verte chez les clients professionnels en Languedoc Roussillon : Analyse de la désirabilité pour une offre de qualité Dorian LITVINE 13.09.100 Fundamental and financial influences on the co-movement of oil and gas prices Derek BUNN, Julien CHEVALLIER, Yannick LE PEN et Benoît SEVI

	01.01.20 03.11.43 06.10.66 11.02.88 01.02.21 04.01.44 01.06.22 01.06.23 01.09.24 01.10.25 02.01.26 02.06.27 02.06.28 02.06.29 02.07.30 02.07.31 02.07.32 02.07.33 02.09.34 02.09.35 02.09.36 03.10.37 03.10.38 03.11.39 03.11.40 03.11.41 03.11.42 06.05.65 05.09.60 06.01.61 06.02.62 06.02.63 06.03.64 10.07.87 09.09.86 09.07.85 09.05.84 09.04.83 09.02.82 05.07.59 05.04.58 09.02.81 05.04.57 09.01.80 04.12.53 05.01.54 05.01.55 05.04.56 08.12.79 08.09.78 08.09.77 08.04.76 04.05.45 04.06.46 04.07.47 04.07.48 04.08.49 04.10.50 04.10.51 04.11.52 07.03.69 11.03.90 11.04.91 07.06.70 11.04.92 07.06.71 11.12.93 08.01.72 12.03.94 12.10.95 08.02.73 08.03.74 12.11.96 08.03.75 12.11.97	Stock index The industrialization of knowledge in life sciences Convergence between public research 95 Stock index: US USSHRPRCF Δ ln US DOW JONES INDUSTRIALS SHARE PRICE INDEX (EP) NADJ 96 Stock index: France FRSHRPRCF Δ ln FR SHARE PRICE INDEX -SBF 250 NADJ 97 Stock index: Germany BDSHRPRCF Δ ln BD DAX SHARE PRICE INDEX, EP NADJ 98 Stock index: UK UKOSP001F Δ ln UK FTSE 100 SHARE PRICE INDEXNADJ (2005=100) 99 Stock index: Japan JPSHRPRCF Δ ln JP TOKYO STOCK EXCHANGE -TOPIX (EP) NADJ (1968=100) Interest rate 100 Interest rate: US USFEDFUN Δlv US FEDERAL FUNDS RATE (AVG.) 101 Interest rate: US USCRBBAA Δlv US CORPORATE BOND YIELD -MOODY'S BAA, SEASONED ISSUES 102 Interest rate: US USGBOND Δlv US TREASURY YIELD ADJUSTED TO CONSTANT MATURITY -20 YEAR 103 Interest rate: France FRPRATE Δlv FR AVERAGE COST OF FUNDS FOR BANKS / EURO REPO RATE 104 Interest rate: France FRGBOND Δlv FR GOVERNMENT GUARANTEED BOND YIELD (EP) NADJ 105 Interest rate: Germany BDPRATE Δlv BD DISCOUNT RATE / SHORT TERM EURO REPO RATE 106 Interest rate: Germany BDGBOND Δlv BD LONG TERM GOVERNMENT BOND YIELD -9-10 YEARS 107 Interest rate: UK UKPRATE Δlv UK BANK OF ENGLAND BASE RATE (EP) 108 Interest rate: UK UKGBOND Δlv UK GROSS REDEMPTION YIELD ON 20 YEAR GILTS (PERIOD AVERAGE) NADJ 109 Interest rate: Australia AUPRATE Δlv AU RBA CASH RATE TARGET 110 Interest rate: Australia AUBOND Δlv AU COMMONWEALTH GOVERNMENT BOND YIELD 10 YEAR (EP) 111 Interest rate: Japan JPPRATE Δlv JP OVERNIGHT CALL MONEY RATE, UNCOLLATERALISED (EP) 112 Interest rate: Japan JPGBOND Δlv JP INTEREST-BEARING GOVERNMENT BONDS -10-YEAR (EP) Exchange rate 113 Exchange rate: DM to US $ BBDEMSP Δ ln GERMAN MARK TO US $ (BBI) -EXCHANGE RATE 114 Exchange rate: SK to US $ SDXRUSD Δ ln SD SWEDISH KRONOR TO US $ (BBI, EP) 115 Exchange rate: £ to $ UKDOLLR Δ ln UK £ TO US $ (WMR) -EXCHANGE RATE 116 Exchange rate: Yen to $ JPXRUSD Δ ln JP JAPANESE YEN TO US $ 117 Exchange rate: Aus.$ to US $ AUXRUSD Δ ln AU AUSTRALIAN $ TO US $ (MTH.AVG.) Producer price index 118 PPI: US USPROPRCE Δ ln US PPI -FINISHED GOODS SADJ 119 PPI: Canada CNPROPRCF Δ ln CN INDUSTRIAL PRICE INDEX: ALL COMMODITIES NADJ 120 PPI: Germany BDPROPRCF Δ ln Cross Hedging and Liquidity: A Note BD PPI: INDL. PRODUCTS, TOTAL, SOLD ON THE DOMESTIC MARKET NADJ (2005=100) 121 PPI: UK UKPROPRCF Δ ln UK PPI -OUTPUT OF MANUFACTURED PRODUCTS (HOME SALES) NADJ 122 PPI: Japan JPPROPRCF Δ ln JP CORPORATE GOODS PRICE INDEX: DOMESTIC -ALL COMMODITIES NADJ Consumer price index 123 CPI: US USCONPRCE Δ ln US CPI -ALL URBAN: ALL ITEMS SADJ 124 CPI: Canada CNCONPRCF Δ ln CN CPI NADJ 125 CPI: France FRCONPRCE Δ ln FR CPI SADJ 126 CPI: Germany BDCONPRCE Δ ln BD CPI SADJ 127 CPI: UK UKD7BT F Δ ln UK CPI INDEX 00 : ALL ITEMS-ESTIMATED PRE-97 2005=100 NADJ 128 CPI: Japan JPCONPRCF Δ ln JP CPI: NATIONAL MEASURE NADJ Emerging countries Series Number Short name Mnemonic Trans Description Industrial production 129 IP: Brasil BRIPTOT G Δ ln BR INDUSTRIAL PRODUCTION VOLA index 2002=base 130 IP: China (cement) CHVALCEMH Δ ln CH OUTPUT OF INDUSTRIAL PRODUCTS -CEMENT VOLN 131 IP: India INIPTOT H Δ ln policies and industrial strategies Benoît SÉVI IN INDUSTRIAL PRODN. (EXCLUDING CONSTRUCTION & GAS UTILITY) VOLN index 132 IP: India INIPMAN H Δ ln IN INDUSTRIAL PRODUCTION: MANUFACTURING VOLN index 133 IP: Korea KOIPTOT.G Δ ln KO INDUSTRIAL PRODUCTION VOLA (2005=100) 134 IP: Mexico MXIPTOT H Δ ln MX INDUSTRIAL PRODUCTION INDEX VOLN 135 IP: Mexico MXIPMAN H Δ ln MX INDUSTRIAL PRODUCTION INDEX: MANUFACTURING VOLN 136 IP: Philippines PHIPMAN F Δ ln PH MANUFACTURING PRODUCTION NADJ 2000 prices 137 IP: South Africa SAIPMAN.G Δ ln SA INDUSTRIAL PRODUCTION (MANUFACTURING SECTOR) VOLA Orders and capacity utilization 138 Operating ratio: Brazil BRCAPUTLR Δlv BR CAPACITY UTILIZATION -MANUFACTURING NADJ 139 Mach. ord.: Korea KONEWORDA Δ ln KO MACHINERY ORDERS RECEIVEDCURN 140 Manufct. prod capa.: Korea KOCAPUTLF Δlv KO MANUFACTURING PRODUCTION CAPACITY NADJ (2005=100) Consumption 141 Retail sales: Korea KORETTOTF Δ ln KO RETAIL SALES NADJ (2005=100) Wages and labor 142 Labor cost: Brazil BRLCOST.F Δ ln BR UNIT LABOR COST NADJ Unemployment 143 U rate: Korea KOUNTOTQ pc Δlv KO UNEMPLOYMENT RATE SADJ International trade 144 Exports: Brazil BREXPBOPA Δ ln BR EXPORTS (BOP BASIS) CURN 145 Exports: China CHEXPGDSA Δ ln CH EXPORTS CURN 146 Exports: India INI70 A Δ ln IN EXPORTS CURN 147 Exports: Indonesia IDEXPGDSA Δ ln ID EXPORTS FOB CURN 148 Exports: Korea KOEXPGDSA Δ ln KO EXPORTS FOB (CUSTOMS CLEARANCE BASIS) CURN 149 Exports: Philippines PHEXPGDSA Δ ln PH EXPORTS CURN 150 Exports: Singapore SPEXPGDSA Δ ln SP EXPORTS CURN 151 Exports: Taïwan TWEXPGDSA Δ ln TW EXPORTS CURN 152 Imports: Brazil BRIMPBOPA Δ ln BR IMPORTS (BOP BASIS) CURN 153 Imports: China CHIMPGDSA Δ ln CH IMPORTS CURN 154 Imports: Indonesia IDIMPGDSA Δ ln ID IMPORTS CIF CURN 155 Imports: Korea KOIMPGDSA Δ ln KO IMPORTS CIF (CUSTOMS CLEARANCE BASIS) CURN 156 Imports: Singapore SPIMPGDSA Δ ln SP IMPORTS CURN 157 Imports: Taïwan TWIMPGDSA Δ ln TW IMPORTS CURN 158 Terms of trade: Brazil BRTOTPRCF Δ ln BR TERMS OF TRADE NADJ (2006=100) Series Number Short name Mnemonic Tran Description Money and credit 159 Money supply: Brazil BRM1 A Δ ln BR MONEY SUPPLY -M1 (EP) CURN 160 Money supply: Brazil BRM3 A Δ ln BR MONEY SUPPLY -M3 (EP) CURN 161 Money supply: China CHM0 A Δ ln CH MONEY SUPPLY -CURRENCY IN CIRCULATION CURN 162 Money supply: China CHM1 A Δ ln CH MONEY SUPPLY -M1 CURN 163 Money supply: India INM1 A Δ ln IN MONEY SUPPLY: M1 (EP) CURN 164 Money supply: India INM3 A Δ ln IN MONEY SUPPLY: M3 (EP) CURN 165 Money supply: Indonesia IDM1 A Δ ln ID MONEY SUPPLY: M1 CURN 166 Money supply: Indonesia IDM2 A Δ 2 ln ID MONEY SUPPLY-M2 CURN 167 Money supply: Korea KOM2 B Δ 2 ln KO MONEY SUPPLY -M2 (EP) CURA 168 Money supply: Mexico MXM1 A Δ ln MX MONEY SUPPLY: M1 (EP) CURN base=end of period 169 Money supply: Mexico MXM3 A Δ 2 ln MX MONEY SUPPLY: M3 (EP) CURN 170 Money supply: Philippines PHM1 A Δ ln PH MONEY SUPPLY -M1 (METHO BREAK AT 12/03) CURN 171 Money supply: Philippines PHM3 A Δ 2 ln PH MONEY SUPPLY -M3 (METHO BREAK AT 12/03) CURN 172 Money supply: Russia RSM2 A Δ 2 ln RS MONEY SUPPLY-M2 CURN Stock index 173 Stock index: Brazil BRSHRPRCF Δ 2 ln BR BOVESPA SHARE PRICE INDEX (EP) NADJ 174 Stock index: Hong-Kong HKSHRPRCF Δ ln HK HANG SENG SHARE PRICE INDEX (EP) NADJ (31 july 1964 =100) Exchange rate 175 Exchange rate: Br.R. to US $ BRXRUSD Δ 2 ln BR BRAZILIAN REAIS TO US DOLLAR (AVG) 176 Exchange rate: Ch.Y. to US $ CHXRUSD Δ 2 ln CH CHINESE YUAN TO US DOLLAR (AVERAGE AMOUNT) 177 Exchange rate: In.R. to US $ INXRUSD Δ 2 ln IN INDIAN RUPEES PER US DOLLAR (RBI) 178 Exchange rate: Id.R. to US $ IDXRUSD Δ 2 ln ID INDONESIAN RUPIAHS TO US DOLLAR 179 Exchange rate: Mx.P. to US $ MXXRUSD Δ 2 ln MX MEXICAN PESOS TO US $-CENTRAL BANK SETTLEMENT RATE (AVG) 180 Exchange rate: RS.R. to US $ RSXRUSD Δ 2 ln RS RUSSIAN ROUBLES TO US $ NADJ Consumer price index 181 CPI: Brazil BRCPIGENF Δ 2 ln BR CPI -GENERAL NADJ 182 CPI: China CHCONPRCF Δ ln CH CPI NADJ 183 CPI: India INCONPRCF Δ ln IN CPI: INDUSTRIAL LABOURERS(DS CALCULATED) NADJ (2001=100) 184 CPI: Korea KOCONPRCF Δ ln KO CPI NADJ (2005=100) 185 CPI: Mexico MXCONPRCF Δ 2 ln MX CPI NADJ (JUN 2002=100) 186 CPI: Philippines PHCONPRCF Δ ln PH CPI NADJ 187 CPI: Russia RSCONPRCF Δ 2 ln RS CPI NADJ Jean Pierre MIGNOT et Christian PONCET The Competitive Firm under both Input and Output Price Uncertainties with Futures Les enjeux du transport pour le gaz et l'électricité : la fixation des charges d'accès Markets and Basis risk Jacques PERCEBOIS et Laurent DAVID Benoît SÉVI Les comportements de fraude fiscale : le face-à-face contribuables -Administration fiscale Cécile BAZART La complexité du processus institutionnel de décision fiscale : causes et conséquences Cécile BAZART Droits de l'homme et justice sociale. 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Third Party Access pricing to the network, secondary capacity market and economic Dérégulation et R&D dans le secteur énergétique européen Jacques PERCEBOIS Marie-Laure GUILLERMINET Alain MATHIEU économique nous aide t-elle à comprendre les évolutions ? en mutation : le cas d'un équipement électronucléaire Les biocombustibles en France : des produits fatals aux cultures dédiées Prix internationaux du pétrole, du gaz naturel, de l'uranium et du charbon : la théorie La décision d'investissement et son financement dans un environnement institutionnel François MIRABEL Renaud MENARD David KOLACINSKI Les péages urbains pour une meilleure organisation des déplacements difficile Démocratie, croissance et répartition des libertés entre riches et pauvres Vincent GIRAULT Minimum Operating Level Investissement dans le réseau électrique : une conciliation Pascal FAVARD, François MIRABEL et Jean-Christophe POUDOU Yannick LE PEN et Benoît SÉVI une analyse par la théorie économique approach L'approvisionnement gazier sur un marche oligopolistique : On the non-convergence of energy intensities: evidence from a pair-wise econometric Vincent GIRAULT Renaud MENARD Structure de la concurrence sur la chaîne du gaz naturel : le marché européen Accroissement de la capacité de transport électrique : investissement stratégique ? Alain MATHIEU Yannick LE PEN et Benoît SÉVI agricoles forward markets Les biocarburants face aux objectifs et aux contraintes des politiques énergétiques et Volatility transmission and volatility impulse response functions in European electricity Benoît SÉVI Marion PODESTA et Jean-Christophe POUDOU On the Exact Minimum Variance Hedge of an Uncertain Quantity with Flexibility Optimal nonlinear pricing, bundling commodities and contingent services Benoît SÉVI Olivier ROUSSE Why are technological spillovers spatially bounded ? A market orientated approach Competition in health care markets and vertical restraints Edmond BARANES et David BARDEY La Mise en Place d'un Marché de Permis d'Emission dans des Situations de Concurrence Imparfaite Olivier ROUSSE Funding Universal Service Obligations with an Essential Facility: Charges vs. Taxes and subsidies, Charles MADET, Michel ROLAND, François MIRABEL et Jean-Christophe POUDOU Stockage de gaz et modulation : une analyse stratégique, Edmond BARANES, François MIRABEL et Jean-Christophe POUDOU Horizontal Mergers In Internet Edmond BARANES et Thomas CORTADE La promotion des énergies renouvelables : Prix garantis ou marché de certificats verts ? 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Several cointegration studies have also investigated the relationship between oil and gas prices in the UK, where a fully liberalized, actively traded, gas market has existed since the early 1990s.[START_REF] Panagiotidis | Oil and gas markets in the UK: Evidence from a cointegrating approach[END_REF] found a linear relationship between UK gas prices and Brent oil price during1996-2003.

The original dataset in[START_REF] Stock | Implications of dynamic factor models for VAR analysis[END_REF] covers the period 1959:01 to 2003:12. It is slightly extended in[START_REF] Ludvigson | Macro factors in bond risk premia[END_REF] to cover the period 1964:01 to 2007:12.

We adopt the static approach following D'Agostino and Giannone (2012) who show that there is no clear advantage of using dynamic factor models.

Although Forni and al. (1999) andStock and Watson (2002) use different sets of assumptions to characterize 'weak correlations', the main idea is that cross-correlations and serial correlations have an upper bound.

[START_REF] Ludvigson | Macro factors in bond risk premia[END_REF] rely indeed on a finer classification, but they only use U.S. variables. We do not think that this methodology is applicable when several economies are considered if we want to preserve some interpretability.

Recall that factors are not identified, unless we impose some constraints to estimate them. Therefore, the sign of the coefficient of F1 in the crude oil return equation has no meaning per se.

Even if these periods correspond to lagged values with our rolling analysis, they fall into the corresponding data points in 1999, 2004 and 2005 when these changes were captured.