The linear and non-linear relationships between cocoa’s futures prices of the ICE and LIFFE : the influence of Ivorian cocoa

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The linear and non-linear relationships

between cocoa’s futures prices of the ICE

and LIFFE: the influence of Ivorian cocoa.

Mees Middelweerd Student ID: 6281524 / 10001301

Supervisor: Prof. dr. C.G.H. Diks

Bachelor’s Thesis Econometrics

Faculty of Economics and Business, University of Amsterdam

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Table of Contents

1. Introduction ... 2

2. The non-parametric Diks-Panchenko test ... 4

3. Data and methodology ... 6

4. Empirical results ... 8

4.1 Linear and non-linear causality relationships in raw data ... 9

4.2 Linear and non-linear causality relationships in VECM residuals ... 10

4.3 Linear and non-linear causality relationships in GARCH-BEKK filtered VECM residuals ... 10

5. Conclusion ... 13

References... 15

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1. Introduction

The evolution of the commodity futures markets is one hard to neglect. One of the first forward contracts of a commodity good dates back to 1851 in Chicago (Peck, 1985), making it possible to sell or buy grain on a future date for a price agreed upon today. The interest in these sort of contracts has continued to grow ever since. In 1920 the Commodity Exchange, trading solely in metals, was introduced. However, it was only a few years later that the New York Cocoa Exchange made the first ever cocoa bean future available. After that, the commodity futures markets experienced great growth. According to Nardella (2007) the most important of these is the cocoa market. She states that from 1986 to 2005 the share of open interest by non-commercial traders in the New York cocoa futures market has increased with an astonishing 400%.

New York and London are the only two places in the world where cocoa futures are being traded. In New York it is the former Coffee, Sugar and Cocoa Exchange, now merged with the Intercontinental Exchange (ICE), that controls the trading. The other being the London International Financial Futures Exchange (LIFFE). A future contract includes ten metric tons of cocoa beans with several months of delivery: March, May, June, July, September and December. Therefore, a future can be seen as a commitment to buy or sell a specific amount of cocoa beans at a particular time. Cocoa future contracts were not created to secure the procurement of one’s company or providing an offset for farmers to reduce the risk of overproduction, instead it has been invented trying to manage the price risk, measured in price variability (Morgan, Rayner, Ennew, 1994).

Although used primarily as a measure for price risk, a futures price can also be used as a tool in determining relationships with other markets, as the price of a futures contract is a common feature to work with in financial markets. Fung, Tse, Yau and Zhao (2013) analyze the lead-lag relationships between foreign markets by comparing sixteen commodity futures contracts traded in China with those from the US, the UK, Japan and Malaysia. In their paper they focus on the role of China as a market leader setting the prices for commodity goods. Hence, they examine the data of sixteen goods traded in the Chinese market: aluminum, copper, zinc, gold, natural, early long-grain non-glutinous rice, white sugar, hard white wheat, strong gluten wheat, cotton, No. 1 soybeans, No. 2 soybeans, soybean meal, crude soybean oil, corn, and RBD palm olein. Fung, Tse, Yau and Zhao conclude that they found results indicating a lead-lag relationship between some pairs of goods when looking at three sets of returns: close-to-close, open-to-close and close-to-open.

Evidence proving the ability of one market setting the price for another commodity good market can have enormous economic impact and will certainly affect the behavior of traders. However, although comprehensible when only looking at goods traded in the Chinese market, Fung, Tse Yau and Zhao (2013) left out a very interesting case to examine. This thesis will be focused on the cocoa market; more specifically, the existence of linear and nonlinear lead-lag relationships between the futures prices traded at the two markets: LIFFE and ICE. Besides futures prices, the spot price is also commonly used to valuate a trading product. Nevertheless, according to Griffioen (2003) this is not a relevant price when dealing with the cocoa market. He goes back to the principles of the cocoa market to explain his statement. He states that it is only relevant for a farmer, with his crop on the land, to know what he will get for his harvest in the future. Griffioen believes that there is no actual spot price: in the soft commodity market it is the futures prices that determine the conventional spot prices.

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An important factor to take into account when looking at the futures prices of both the London International Financial Futures Exchange and the Intercontinental Exchange, is the influence of Ivory Coast on the cocoa market. Ivory Coast is the world leader in production and export of cocoa beans. According to the statistics of the International Cocoa Organization (2012) 1,400 million metric tons of cocoa beans were produced in Ivory Coast in the year 2011-2012; meaning that they make up roughly 35% of the world’s production. Fung, Tse, Yau and Zhao (2013) found evidence for the futures market being influenced by the volume of trading. Therefore, the influence of a country such as Ivory Coast should not be neglected when studying possible lead-lag relationships between the two trading markets.

Testing for the existence of linear and nonlinear lead-lag relationships between the futures prices of the LIFFE and ICE will be based on the empirical framework discussed in the paper by Bekiros and Diks (2008). First of all, linear and nonlinear linkages are being examined by the non-parametric Diks-Panchenko causality test. Controlling for cointegration, a linear Granger Causality test will also be applied on the raw data. Secondly, the series of residuals, obtained by using a VAR or VECM model1 in order to filter the return series, are examined by the non-parametric Diks-Panchenko causality test. Not only will the bivariate VAR or VECM model be applied to each pair of the time series, the residuals of a model where all three variables are taken into account will also be examined to check whether or not the other variable has an effect. Lastly, by using a GARCH-BEKK model the hypothesis of nonlinear non-causality is going to be tested, taking into account the conditional

heteroskedasticity in the data. Similar to the non-parametric Diks-Panchenko test in the second step, the GARCH-BEKK model will be both used in a bivariate and in a three-variate way.

The rest of this thesis consists of five sections. In Section 2 the theory behind the non-parametric Diks-Panchenko test will be explained. After that, the data being used for this research are introduced. Section 3 provides an introduction to the methodology necessary in order to look at possible lead-lag relationships. Section 4 presents and discusses the empirical results. Finally, this thesis will make some concluding remarks and suggestions for future research.

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2. The non-parametric Diks-Panchenko test

In order to fully understand this research, the non-parametric Diks-Panchenko test for causality will be explained more thoroughly. Diks and Panchenko came up with this alternative for the Hiemstra-Jones (1994) test, because this test severely over-rejects when the null hypothesis is true. By taking into account the possible variation in conditional distributions present under the null hypothesis, Diks and Panchenko (2006) came up with a variant of the Hiemstra-Jones test. This test is actually compatible with Granger causality testing. In the field of econometrics, Granger causality testing is a useful instrument for illustrating dependence relationships between time series. These relationships can be characterized as followed. Assuming {(Xt,Yt) t≥1} is a bivariate strictly stationary time series. If past and current values of X contain additional information on future values of Y that is not entailed in the past and current Yt-values, {Xt} can be seen as a strict Granger cause of {Yt}. If the past values of Xt and Yt are denoted as FX,t and Fy,t, indicating a period up to time t. Then, if for some k ≥ 1:

(𝑌𝑡+1, … , 𝑌𝑡+𝑘)|(𝐹𝑋,𝑡, 𝐹𝑌,𝑡)~(𝑌𝑡+1, … , 𝑌𝑡+𝑘)|𝐹𝑌,𝑡 (1) {Xt} is not a Granger cause of {Yt}. When testing for Granger non-causality, k = 1 is mostly used; implying that the one-step ahead conditional distribution of {Yt} is being compared with and without past and present observed values of {Xt}. Dealing with stationary time series, the most accustomed way of testing for Granger causality is to assume a parametric, linear, time series model for the conditional mean 𝐸 (𝑌𝑡+1|(𝐹𝑋,𝑡, 𝐹𝑌,𝑡)). That way, by comparing the residuals of a fitted autoregressive model of Yt with those when Yt is regressed on the past values of both {Xt} and {Yt} causality can be tested. Now, let 𝑿_𝑡𝜗𝑋 _{= (𝑋}

𝑡+1−𝜗𝑋, … , 𝑋𝑡) and 𝒀𝑡 𝜗𝑌 _{= (𝑌}

𝑡+1−𝜗𝑌, … , 𝑌𝑡), (𝜗𝑋, 𝜗𝑌≥ 1). Generally, the null hypothesis that past observations of 𝑿_𝑡𝜗𝑋_{do not contain extra information about 𝑌}_{𝑡+1, besides the} information already given by 𝒀_𝑡𝜗𝑌_{, is tested. This is mathematically stated as:}

𝐻0: 𝑌𝑡+1 |(𝑋𝑡 𝜗𝑋_{; 𝑌} 𝑡 𝜗𝑌_{) ~ 𝑌} 𝑡+1| 𝑌𝑡 𝜗𝑌_. ₍₂₎

Eq. (2) simplifies to a statement about the invariant distribution of the vector 𝑾𝑡= (𝑿𝑡 𝜗𝑋_{, 𝒀}

𝑡 𝜗𝑌_{, 𝑍}

𝑡) with dimension (𝜗𝑋+ 𝜗𝑌+ 1), with 𝑍𝑡 = 𝑌𝑡+1, when coping with a strictly stationary bivariate time series. Bekiros and Diks (2008) suggest in their paper to keep the notation simple and to concentrate on the null hypothesis, referring to the invariant distribution of (𝑿_𝑡𝜗𝑋_{, 𝒀}

𝑡 𝜗_𝑌

, 𝑍𝑡). The time index is being dropped and 𝜗𝑋= 𝜗𝑌= 1 is assumed. Thus, under 𝐻0, the conditional distribution of Z given (X, Y) = (x, y) is equal to Z given Y=y. Restating Eq. (2) in terms of ratios of joint distributions in order to explicitly show that X and Z are independent, given Y=y for each fixed value of y:

𝑓𝑋,𝑌,𝑍_𝑓 (𝑥,𝑦,𝑧) 𝑌(𝑦)

=

𝑓_𝑋,𝑌(𝑥,𝑦) 𝑓_𝑌(𝑦)

∙

𝑓_𝑌,𝑍(𝑦,𝑧) 𝑓_𝑌(𝑦)

.

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It can be shown (Diks & Panchenko, 2006) that the reformulated 𝐻0implies:

𝑞 ≡ 𝐸[𝑓𝑋,𝑌,𝑍(𝑋, 𝑌, 𝑍)𝑓𝑌(𝑌) − 𝑓𝑋,𝑌(𝑋, 𝑌)𝑓𝑌,𝑍(𝑌, 𝑍)] = 0. (4)

Bekiros and Diks (2008) let 𝑓̂(𝑊𝑤 𝑖) denote a local density estimator of a 𝑑𝑤 –variate random vector

W at 𝑊𝑖defined by 𝑓̂(𝑊𝑤 𝑖) = (2𝜀𝑛)−𝑑𝑊(𝑛 − 1)−1∑𝑗,𝑗≠𝑖𝐼𝑖𝑗𝑊 where 𝐼𝑖𝑗𝑊= 𝐼(‖𝑊𝑖− 𝑊𝑗‖ ≤ 𝜀𝑛) with 𝐼(∙) the indicator function and 𝜀𝑛 the bandwidth, depending on the sample size n. Taking this estimator into account, the test statistic is a scaled sample version of Eq. (4):

𝑇𝑛(𝜀𝑛) = 𝑛−1

𝑛(𝑛−2)∙ ∑ (𝑓̂𝑖 𝑋,𝑍,𝑌(𝑋𝑖, 𝑌𝑖, 𝑍𝑖)𝑓̂𝑌(𝑌𝑖) − 𝑓̂𝑋,𝑌(𝑋𝑖, 𝑍𝑖)𝑓̂𝑌,𝑍(𝑌𝑖, 𝑍𝑖)). (5) Diks and Panchenko (2006) proved that Eq. (5) satisfies, under strong mixing, for 𝜗𝑋= 𝜗𝑌= 1 and in the case that 𝜀𝑛= 𝐶𝑛−𝛽(𝐶 > 0,

1 4< 𝛽 < 1 3) : √𝑛(𝑇𝑛(𝜀_𝑆𝑛)−𝑞) 𝑛 𝐷 → 𝑁(0,1), (6)

with → 𝐷 denoting convergence in distribution. 𝑆𝑛is being used in their article as an estimator of the asymptotic variance of 𝑇𝑛(∙) . The null hypothesis will be rejected when the left-hand-side of Eq. (6) is too large, suggesting a one-tailed version of the test.

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3. Data and methodology

This section is organized in the following way. Firstly, the type of data used in this research is described. Then the split of the data into two periods is explained. Moreover, the modification of the data, necessary to correctly compare the time series with each other, is covered. The last part of this section comprises the theory behind the different tests used in this research.

Data

The data consist of time series of daily continuous futures prices for the London International Financial Futures Exchange and the Intercontinental Exchange. Working with continuous futures prices means that the contract with the nearest expiration date, the so-called front-month contract, is considered. Around the expiration date the price series roll over onto the next front-month. As mentioned earlier, a future contract includes ten metric tons of cocoa beans. However, both the LIFFE and ICE futures cocoa prices present the market value of a metric ton of cocoa at a specific day, measured in pounds and dollars respectively. In addition to the different currencies, the trading hours of the two markets differ as well. The ICE cocoa futures contracts are traded from 9:00 am to 7:00 pm (GMT), while the LIFFE cocoa futures contracts market is open from 9:30 am to 4.30 pm (GMT). Though, in this research only the settlement price will be examined; this is the average price a futures contract is traded at a specific date. Therefore, the influence of the small difference in trading hours of the two markets will be ignored.

Besides the futures contracts, the daily prices of cocoa from the Ivory Coast are being taken into account as well. These daily prices represent the number of dollars needed to either buy or sell a metric ton of cocoa from Ivory Coast, the world leader in the production of cocoa.

The data cover two periods of equal lengths; the split is determined by one of the most tragic events in the history of the United States of America: the 9/11 attacks. Anticipating the market chaos and catastrophic loss of value in the wake of the attacks, the stock market closed for four days. The last time this had ever happened was in March 1933 during the Great Depression (“How 9/11 attacks still affect the economy today”, 2013). Although almost every sector was hit by steep declines in prices, it took the stock market less than one month to regain its price levels prior to the attacks (“How September 11 affected the US stock market”). Therefore, two periods will be defined, namely P1 which spans October 30, 1991 to October 30, 2000 (2349 observations) and P2 October 30, 2001 to October 30, 2010 (2349 observations). By dividing the data into two periods, changes in dynamics between the three variables over time can be shown.

Methodology

In order to be able to correctly compare the different time series, one has to account for a few things. First of all, the prices of the LIFFE futures contracts are converted in US dollars, using the noon buying rates in New York, collected from the Federal Reserve Bank of New York (this approach is inspired by the article of Fung, Zhe, Yau and Zhao (2013)). Then, it is necessary to take the inflation into account. By taking the natural logarithm of the prices corrected for inflation the data can be tested for evidence on cointegration with the Dickey-Fuller test. This test will determine whether the VECM or VAR model will be applied . The VAR model is one way to construct a linear Granger

causality test. If 𝒀𝑡 is the vector of all the endogenous variables and 𝑛 the number of lags, then the VAR model for the first differences is stated:

∆𝒀𝑡 = ∑𝑛𝑖=1𝐴𝑠∆𝒀𝑡−𝑖+ 𝜀𝑡, (7)

with 𝒀𝑡= [𝑌1𝑡, … , 𝑌𝜖𝑡] being a 𝑛 x 1 vector, 𝐴𝑠the 𝑛 x 𝑛 parameter matrices and 𝜀𝑡the residual vector for which 𝐸(𝜀𝑡) = 0. In case of this research, the VAR model will be bivariate:

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∆𝑋𝑡 = 𝐴(𝑛)∆𝑋𝑡+ 𝐵(𝑛)∆𝑌 + 𝜀∆𝑋,𝑡, (8)

∆𝑌𝑡 = 𝐶(𝑛)∆𝑋𝑡+ 𝐷(𝑛)∆𝑌 + 𝜀∆𝑌,𝑡,

𝑡 = 1,2, … , 𝑁

with A(𝑛), B(𝑛), C(𝑛) and D(𝑛) denoting all polynomials in the lag operator and ∆𝑋𝑡 and ∆𝑌𝑡 the first differences of {Xt} and {Yt}. However, a VAR model cannot be used in case of cointegration. In order to account for the possible effects of cointegration a VECM model is needed. The VECM model is stated as:

∆𝒀𝑡 = 𝛾 + 𝛱𝒀𝑡−1+ ∑𝑝−1𝑗=1𝛤𝑗∆𝒀𝑡−𝑗+ 𝜀𝑡, (9)

with 𝛾 is φ(1) µ (µ represents the mean), 𝛱 is equal to -φ(1) and p the number of lags. The bivariate VECM model is given by:

∆𝑋𝑡 = −𝑝1([1 − 𝜃] [ 𝑌𝑡−1 𝑋𝑡−1]) + 𝐴(𝑛)∆𝑋𝑡+ 𝐵(𝑛)∆𝑌𝑡+ 𝜀∆𝑋,𝑡, (10) ∆𝑌𝑡 = −𝑝2([1 − 𝜃] [ 𝑌𝑡−1 𝑋𝑡−1]) + 𝐶(𝑛)∆𝑋𝑡+ 𝐷(𝑛)∆𝑌𝑡+ 𝜀∆𝑌,𝑡, 𝑡 = 1,2, … , 𝑁

[1 − 𝜃] denoting the vector of cointegration, 𝜃 the coefficient of cointegration and (−𝑝1 − 𝑝2)′ the vector of adjustment coefficients.

Then, to examine the linear and nonlinear linkages, the Granger causality test based on either the VECM or VAR specification and the non-parametric Diks-Panchenko test on the log-differenced time series of the futures prices will be used. After this, the series of residuals obtained by both pairwise and three-variate VECM/VAR filtering will be subject to the Diks-Panchenko test. The last part of this research will involve a GARCH-BEKK model to test the hypothesis of nonlinear non-causality, while taking into account the conditional heteroskedasticity in the data. Again this test will be done twice: for the pairwise and three-variate version. The GARCH-BEKK model is defined as followed:

𝐻𝑡 = 𝐶′𝐶 + ∑ 𝐴′𝑗𝑘𝜀𝑡−𝑗𝜀′𝑡−𝑗𝐴𝑗𝑘+ ∑𝑝𝑗=1𝐺′𝑗𝑘𝐻𝑡−𝑗𝐺𝑗𝑘, 𝜀𝑡 = 𝐻𝑡 1/2

𝑣𝑡, 𝑞

𝑗=1 (11)

where 𝑝 and 𝑞 are the parameters of the model. 𝐴𝑗𝑘 and 𝐺𝑗𝑘are (N x N) ordinary matrices, wile 𝐶 is an (N x N) upper triangular matrix, 𝜀𝑡|𝜑𝑡−1~(0, 𝐻𝒕) with 𝐻𝑡 the conditional covariance matrix and 𝜑𝑡−1 the information set at time 𝑡 − 1. The whitening matrix transformation 𝐻1/2𝜀𝑡 delivers the residuals. Similar to Bekiros and Diks (2008), it is assumed that 𝐻𝑡is positive definite.

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4. Empirical results

Before testing for linear and nonlinear Granger causality, one has to account for non-stationarity and the existence of cointegration in a time series. First of all, the Augmented Dickey-Fuller (ADF) test is used to test the logarithmic levels and logarithmic returns on non-stationarity. The ADF test is applied to the model:

∆𝑦𝑡 = 𝛼 + 𝛽𝑡 + 𝛾𝑦𝑡−1+ 𝛿1∆𝑦𝑡−1+. . +𝛿𝑝−1∆𝑦𝑡−𝑝+1+ 𝜀𝑡, (12) with 𝛼 a constant, 𝛽 the coefficient of the trend and 𝑝 is the number of lags included. This test is carried out with the null hypothesis 𝛾 = 0 against the alternative hypothesis 𝛾 < 0. In other words, this test examines if the futures price of for example the LIFFE at time t-1 has an influence on the price difference at time t. The Schwartz Information Criterion (SIC) is used to determine the number of lags for the logarithmic levels and logarithmic returns. The logarithmic returns are denoted by 𝑟. Table 2 shows the different outcomes of the ADF test for the six time series for both P1 and P2. According to the ADF-statistic, the null hypothesis cannot be rejected for all the series of the logarithmic levels for P1 and P2. However, the null hypothesis for the logarithmic returns can be rejected for both P1 and P2, meaning that these time series appear to be stationary.

Table 1 - Unit root tests

Variables ADF-statistic (P1) ADF-statistic (P2)

ICE (0) 0.6974 0.0911 rICE (0) 0.0001** 0.0000** LIFFE (0) 0.7642 0.1468 rLIFFE (0) 0.0000** 0.0000** Ivory Coast (0) 0.6477 0.1147 rIvory Coast (0) 0.0001** 0.0001**

All variables are in logarithms and the ADF-statistic is measured in p-values. (**) indicates the p-values corresponding to a 99% confidence level. Between the parentheses the number of lags is stated. These are selected using the SIC.

Secondly, after checking for stationarity, the Johansen test is applied to control for possible

cointegration. The Johansen test, using the trace statistic, works with Eq. (9) and tests the following: 𝐻0∶ 𝑟𝑎𝑛𝑘(𝛱) = 𝑣 𝑣𝑒𝑟𝑠𝑢𝑠 𝐻1∶ 𝑟𝑎𝑛𝑘(𝛱) ≥ 𝑣 + 1.

An intercept in CE is assumed when applying the Johansen test. However, a deterministic-trend restriction is not imposed, since the logarithmic levels appear to be non-stationary according to Table 1. In case of the three-variate implementation the Johansen test identified two cointegrating vectors in both P1 and P2. Implementing the pairwise model, one cointegrating vector was found for all the pairs in P1 and P2. Appendix A contains the statistical evidence for all the performed

Johansen tests. As mentioned in the previous paragraph, the presence of cointegration implies the use of a VECM model, stated in Eq. (9), instead of a VAR model.

After determining stationary time series and testing for the existence of cointegration, the different tests for Granger causality can be applied. The empirical methodology contains three steps. Every step described, is carried out using both the three-variate model and the bivariate model. In the beginning, the linear Granger causality test and the non-parametric Diks-Panchenko test are executed on a VECM model of the logarithmic prices.

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4.1 Linear and non-linear causality relationships in raw data

The results of the tests on the VECM specification are unified under the header raw data. When looking at Table 2, for the raw data, two unidirectional linear Granger causality relations can be determined for the multivariate implementation in both periods: ICE → IVO and LIFFE → IVO. The linear Granger causality of the relationship LIFFE → IVO being a little less significant than ICE → IVO. The linear Granger causality test on the raw data shows also a bi-directional relationship between the ICE and LIFFE. However, in PII no statistical significance was found for the linear Granger causality ICE → LIFFE. The results for the pairwise implementation in Table 3 show the same relationships. An exception is the great statistical significance for the linear Granger causality from IVO to LIFFE in Table 3, whereas Table 2 states that there is no causality to be found for these variables. So in the three-variate model the influence of Ivory Coast on the LIFFE, clearly present in the pairwise model, has disappeared. Also, the linear causality in the relationship LIFFE→ IVO for the pairwise model has a higher degree of statistical significance in PI than when the three-variate model is implemented.

The results of the non-parametric Diks-Panchenko test for the multivariate model are the same as for the pairwise model. Tables 2 and 3 reveal a bi-directional relationship between the ICE and LIFFE for both PI and PII. Moreover, there is great statistical significance for a unidirectional relationship from the ICE to IVO for both periods. The results for PI display a bi-directional relationship between IVO and LIFFE, while for PII there is no non-linear causality found between these variables.

Table 2 - Causality results (three-variate)

Variables Panel A: linear Granger causality Panel B: non-linear Granger causality

X Y Raw data VECM residuals GARCH-BEKK

residuals

Raw data VECM residuals GARCH-BEKK

residuals X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X

PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII

ICE LIFFE ** * ** ** * ** * ** * * * ** * * ICE IVO ** ** ** ** ** ** ** ** IVO LIFFE * ** ** * ** ** ** ** **

ICE, LIFFE and IVO denote the log-levels of the prices (in dollars) for the Intercontinental Exchange, the London Interational Financial Futures Exchange and cocoa produced in Ivory Coast, respectively. (*) and (**) denote the statistical significance at 5% and 1% level respectively. The relation X → Y can be interpreted as follows: rx does not Granger cause ry. PI: 23/9/1994 – 10/9/2001 and PII:

25/9/2001 – 10/9/2008.

Panel A: Cointegration was present in all the raw data (log-levels) and the lag length of the VECM specification was set using the

Schwartz Information Criterion (SIC). The number of lags identified is three in PI and three in PII. The Johansen cointegration test, assuming an intercept in CE and no deterministic trend in data, identified two cointegrating vectors in both PI and PII using the trace statistic. A VAR specification, with SIC determining the number of lags (3 for all variables in both PI and PII), was used to determine the causality on the VECM residuals. The GARCH-BEKK residuals were obtained using a diagonal GARCH-BEKK (1,1) model with constant coefficient, diagonally restricted and backcast equal to 0.7 (default Eviews setting).

Panel B: The data used are log-returns. The number of lags was set to one when testing for nonlinearity. Because the data showed

signs of cointegration the nonlinear causality test was applied to the VECM residuals. The number of lags (using SIC) and the number of cointegrating vectors (using the Johansen test) for the VECM specification are the same as in Panel A. The GARCH-BEKK residuals were obtained in the same way as the ones in Panel A.

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4.2 Linear and non-linear causality relationships in VECM residuals

Next, the residuals of the VECM models are subject to the linear Granger causality test in order to test for possible linear structures after the VECM filtering. The non-parametric Diks-Panchenko test is also applied to ensure that the effects found in the previous step are strictly nonlinear.

The results of the linear Granger causality tests on both the three-variate model and the pairwise one demonstrate no linear relationships at all for the VECM residuals. All the relationships found in the raw data have disappeared after the VECM filtering.

When looking at the multivariate model, the results show a bi-directional non-linear relationship between the ICE and LIFFE for PI as well as PII. There is also strong statistical significant evidence for the unidirectional non-linear relationship ICE → IVO. For the first period, the results show a non-linear causality from IVO to LIFFE, whereas in PII this relationship is the other way around. The pairwise implementation reveals almost the same results after the VECM filtering only the non-linear causality between IVO and LIFFE in PI being bi-directional instead of unidirectional.

Table 3 - Causality results (pairwise)

Variables Panel A: linear Granger causality Panel B: non-linear Granger causality

X Y Raw data VECM residuals GARCH-BEKK

residuals

Raw data VECM

residuals

GARCH-BEKK residuals

X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X X → Y Y → X

PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII PI PII

ICE LIFFE ** * ** ** * ** * ** * * * ** * *

ICE IVO ** ** ** ** ** ** * **

IVO LIFFE ** ** ** ** *

**

** * ** ** * **

ICE, LIFFE and IVO denote the log-levels of the prices (in dollars) for the Intercontinental Exchange, the London Interational Financial Futures Exchange and cocoa produced in Ivory Coast, respectively. (*) and (**) denote the statistical significance at 5% and 1% level respectively. The relation X → Y can be interpreted as follows: rx does not Granger cause ry. PI: 23/9/1994 – 10/9/2001 and PII:

25/9/2001 – 10/9/2008.

Panel A: Cointegration was present in all the raw data (log-levels) and the lag length of the VECM specification was set using the

Schwartz Information Criterion (SIC). The number of lags, stated between brackets, identified are: ICE-LIFFE [4], ICE-IVO [3] and LIFFE-IVO [3] in PI and for PII: ICE-LIFFE [2], ICE-IVO [3] and IVO-LIFFE [3]. The Johansen cointegration test, assuming an intercept in CE and no deterministic trend in data, identified for all pairs one cointegrating vector in both PI and PII, again using the trace statistic. A VAR specification, with SIC determining the number of lags (3 for all pairs of variables in both PI and PII), was used to determine the causality on the VECM residuals. The GARCH-BEKK residuals were obtained using a diagonal GARCH-BEKK (1,1) model with constant coefficient, diagonally restricted and backcast set to 0.7 (default Eviews setting).

Panel B: The data used are log-returns. The number of lags was set to one when testing for nonlinearity. Because the data showed

signs of cointegration the nonlinear causality test was applied to the VECM residuals. The number of lags (using SIC) and the number of cointegrating vectors (using the Johansen test) for the VECM specification are the same as in Panel A. The GARCH-BEKK residuals were obtained in the same way as the ones in Panel A.

4.3 Linear and non-linear causality relationships in GARCH-BEKK filtered VECM residuals

Lastly, the residuals of a GARCH-BEKK model (see Eq. (11)) are examined to test the hypothesis of nonlinear non-causality, while controlling the residuals for possible conditional heteroskedasticity in the data.

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Similar to the VECM filtering, no linear linkages can be found after the GARCH-BEKK filtering for both the three-variate and bivariate model. However, the non-parametric Diks-Panchenko test for the multivariate model shows a strong unidirectional causality from ICE to IVO in PI as well as in PII. In the first period a bi-directional non-linear relationship is observable between ICE and LIFFE. In the second period this bi-directional causality turns into an unidirectional linkage from ICE to LIFFE. The non-linear causality IVO → LIFFE in PI switches direction in PII.

Implementing a pairwise model instead of the three-variate model, the bi-directional non-linear causality in PI shifts to PII, leaving PI with only a unidirectional causal relationship from ICE to LIFFE. With the pairwise implementation, the unidirectional linkage in PI from IVO to LIFFE turns into a bi-directional relationship. Besides the small difference in statistical

significance for the relationship ICE → IVO in PI, all the other relationships are the same as with the multivariate model.

The results for the GARCH-BEKK filtered VECM residuals are displayed in Figs 1 and 2 as diagrammatical representations to clearly show the causality that is left after both the VECM and GARCH-BEKK filtering. The degree of statistical significance reported in Table 2 and 3 with (*) and (**) are translated into a single and double arrow, respectively.

Period 1 Period 2

Fig. 1. Diagrammatical representation of causalities on three-variate GARCH-BEKK filtered VECM residuals.

Period 1 Period 2

Fig. 2. Diagrammatical representation of causalities on bivariate GARCH-BEKK filtered VECM residuals.

LIFFE IVO ICE LIFFE IVO ICE LIFFE IVO ICE LIFFE IVO ICE

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Summarizing, after the GARCH-BEKK filtering of the VECM residuals in PI the statistical significance for the linkage ICE → IVO in case of the pairwise implementation is reduced, indicating that the non-linear relationship is influenced by simple volatility effects. Nonetheless, the remaining significant non-linear linkages show that the first and second moment effects are not the only ones causing non-linear causality. Furthermore, the reduction of the ICE ↔ LIFFE relationship in PII for the three-variate model to a unidirectional linkage from ICE to LIFFE indicates that the non-linear causality, which survived the VECM filtering, was caused by conditional

heteroskedasticity. The pairwise GARCH-BEKK filtering shows that the statistical significance for the bidirectional relationship in PI between ICE and LIFFE can also be attributed by simple volatility effects.

The pairwise model in this thesis is a great way to display the individual effects of each variable onto the other, which creates a better understanding of all the different relationships within the cocoa industry. However, in order to draw correct conclusions from this research, the indirect influences of variables through other variables should be taken into account as well. This makes the multivariate specification a better and all-embracing model.

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This thesis focused on the existence of linear and non-linear lead-lag relationships between the futures prices traded at the London International Financial Futures Exchange and the

Intercontinental Exchange in New York. Also the daily prices of Ivorian cocoa were taken into account; expecting Ivory Coast to be a major influence, being world leader in production and export of cocoa beans. The data covered two periods, that is PI which spans October 30, 1991 to October 30, 2000 (2349 observations) and P2 October 30, 2001 to October 30, 2010 (2349 observations).

The results of the linear Granger causality tests imply the following. Both the pairwise and the three-variate model showed great statistical significance for the futures prices of the ICE affecting the daily prices of Ivorian cocoa in both PI and PII when testing on raw data. There is also empirical evidence for a bi-directional linear causality between the futures prices of the ICE and LIFFE in PI. In PII, however, the futures prices of the LIFFE were leading the prices of ICE. Additionally, in PI Ivorian cocoa showed linear Granger causality to the LIFFE in the pairwise model. Nevertheless, this relationship is not observable in the three-variate implementation; only the linear effects are accounted for in this test, suggesting that there is some non-linear causality in this model causing the relationship from Ivorian cocoa to the LIFFE to disappear.

Moreover, the results of the non-linear Granger causality tests indicate, whilst linear relationships were eliminated through VECM filtering and spillover volatility effects were controlled for by GARCH-BEKK filtering, a strong unidirectional causality from the ICE futures prices to the Ivorian daily prices in both periods. In the first period the results suggest also that the futures prices of the ICE and LIFFE influence each other in a non-linear way. This bi-directional relationship implies that the causality may vary at any point in time. Taking this into account, the results reveal that the pattern of the lead-lag relationship between the ICE and LIFFE changed over time during the first period. In the second period, however, statistical evidence infers that the prices of the ICE lead the prices of the LIFFE. Apparently, after the stock exchange shut down for four days, there has been a change in dynamics between the LIFFE and ICE. Lastly, it was shown that in PI the daily prices of Ivorian cocoa influence the futures prices of the LIFFE, whereas in PII this non-linear causality is reversed. So, it is clear that the dynamics have changed when comparing the results from PI and PII. Nonetheless, the Diks-Panchenko test works in a bivariate way, able to compare only two variables at a time. This implies that the results after GARCH-BEKK filtering do not account for the non-linear indirect influences of other variables. This can be the explanation of the noteworthy change of direction of causality between the daily prices of Ivorian cocoa and the LIFFE, from PI to PII. The research done in this thesis provides a better understanding of the linear and non-linear structures within the cocoa industry. Remarkably, both the results of the linear and non-linear tests show that the assumption made in the introduction about how the daily prices of Ivorian cocoa would influence the cocoa futures market isn’t quite correct. In fact, the test results show a causality from the futures prices of the ICE to the daily cocoa prices produced in Ivory Coast and not the other way around. In other words, the world leader of cocoa supply does not have an effect on the prices of futures contracts traded in New York. However, Ivory coast does have an influence on the futures traded at the LIFFE in the first period, the direction of this influence, though, is reversed in the second period as was shown in previous section. All in all, this thesis shows that there is no strong evidence for the prices of Ivorian cocoa influencing both trading markets, which leads to the

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an interesting subject for future research is the exploration of linear and non-linear linkages between both the futures prices of cocoa traded on the markets ICE and LIFFE and other, more trustworthy, commodity goods, such as gold or silver.

In addition, it is very interesting to examine the possible opportunities of arbitrage, inferring to the strong evidence for Granger causality from the ICE to the daily prices of Ivorian cocoa. Future research, therefore, could include tests for no-arbitrage. According to Stoll and Whaley (1990), the spot price and the futures price should be the same, corrected for any ‘cost of carry’ that might be entailed when dealing with futures contracts instead of the actual good. It can be interesting to see if this theory holds up, given the results of causality in this thesis.

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References

Bekiros, S., Diks, C. (2008, March 27). “The relationship between crude oil spot and futures prices: Cointegration, linear and nonlinear causality.” Energy Economics, 30: 2673-2685.

Cocoa Market Update. (2012, March). Retrieved October 2, 2013 from:

http://worldcocoafoundation.org/wp-content/uploads/Cocoa-Market-Update-as-of-3.20.2012.pdf Davis, M. (2011, September 9). How September 11 Affected The U.S. Stock Market. Retrieved October 18,2013 from: http://www.investopedia.com/financial-edge/0911/how-september-11-affected-the-u.s.-stock-market.aspx

Diks, C., Panchenko, V. (2006, April 27). “A new statistic and practical guidelines for nonparametric Granger causality testing.” Journal of Economic Dynamics and Control, 30: 1647-1669.

Fung, H., Tse, Y., Yau, J., Zhao, L. (2013, April). “A leader of the world commodity futures markets in the making? The case of China's commodity futures.” International Review of Financial Analysis, 27: 103-114.

Griffioen, G. (2003, March). “Technical Analysis in Financial Markets.” Tinbergen Institute research series, 305.

Hiemstra, C., Jones, J.D. (1994). “Testing for linear and nonlinear Granger causality in the stock price-volume relation.” Journal of Finance, 49: 1639-1664.

How the 9-11 attacks still affects the economy today. (2013, October). Retrieved October 18, 2013 from: http://useconomy.about.com/od/Financial-Crisis/f/911-Attacks-Economic-Impact.htm Morgan, C., Rayner, A., Ennew, C. (1994, November). “Price instability and commodity futures markets.” World Development, 22: 1729-1736.

Nardella, M. (2007, April 4). “Price efficiency and speculative trading in cocoa futures markets.” Reading University of Agricultural Economics Society, 81.

Peck, A. (1985). “The Economic Role of Traditional Commodity Futures Markets.” Washington DC: American Enterprise Institute for Public Policy Research, pp. 1-81.

Stoll, H., Whaley, R. (1990). “The Dynamics of Stock Index and Stock Index Futures Returns.” The Journal of Financial and Quantitative Analysis, 25: 441-468.

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Appendix A

Results of the Johansen test for the three-variate model, P1:

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.017829 55.82771 35.19275 0.0001

At most 1 * 0.011743 23.21235 20.26184 0.0191

At most 2 0.000990 1.795778 9.164546 0.8179

Trace test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Results of the Johansen test for the three-variate model, P2:

None * 0.024737 69.11541 35.19275 0.0000

At most 1 * 0.009995 23.70378 20.26184 0.0161

At most 2 0.003024 5.490829 9.164546 0.2339

Results of the Johansen test for the pairwise implementation ICE-LIFFE, P1:

None * 0.011930 23.54777 20.26184 0.0170

At most 1 0.000993 1.800055 9.164546 0.8171

Results of the Johansen test for the pairwise implementation ICE-LIFFE, P2:

None * 0.009502 23.31845 20.26184 0.0184

At most 1 0.003302 5.999848 9.164546 0.1907

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Results of the Johansen test for the pairwise implementation ICE-IVO, P1:

None * 0.013599 26.54789 20.26184 0.0059

At most 1 0.000950 1.723373 9.164546 0.8319

Results of the Johansen test for the pairwise implementation ICE-IVO, P2:

None * 0.022290 46.73523 20.26184 0.0000

At most 1 0.003231 5.866453 9.164546 0.2013

Results of the Johansen test for the pairwise implementation LIFFE-IVO, P1:

None * 0.016131 31.29621 20.26184 0.0010

At most 1 0.000999 1.812525 9.164546 0.8147

Results of the Johansen test for the pairwise implementation LIFFE-IVO, P2:

None * 0.010557 25.27410 20.26184 0.0093

At most 1 0.003322 6.032478 9.164546 0.1882