Short & Long Term Relationship Analysis for forecasting crude oil prices

8/13/2019 Short & Long Term Relationship Analysis for forecasting crude oil prices

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Advances I n M anagement Vol. 6 (8) Aug. ( 2013 )

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Case Study:

An Empirical Analysis on Long Term and Short Term Relationship

between the Spot and Future Prices of India Crude Oil MarketPurushothaman S.* and Velmurugan P.S.

Department of Commerce, School of Management, Pondicherry University, Puducherry 605 014, INDIA

*[email protected]

AbstractThe present study is to test for the existence long termand short term relationships between Spot and future ofcrude oil prices from India (MCX). The crude oil spotand future price is collected. 2018 observations arecollected from Multi Commodity Exchange (MCX) from

29th

April 2005 to 31 st

December 2011. In the study weused Johansen co-integration and Vector errorcorrection model (VECM) respectively. The first step inthe analysis is stationarity of spot and future prices ofcrude oil through unit root test ADF and PP test. Twovariables are stationary at 1 st difference. Based on the

Johansen co-integration and Vector error correctionmodel (VECM), the price discovery is achieved from theboth the market and has long term and short termrelationship between them at 1%, 5% level of

significance.

Keywords: Indian Crude Oil Market, Spot and Future Prices,Short term, Long term, Relationship.

IntroductionCrude oil futures and spot prices reflect the same aggregatevalue of the underlying asset and considering thatinstantaneous arbitrage is possible; futures should neither leadnor lag the spot price. 1 However, the empirical evidence isdiverse, although the majority of studies indicate that futuresinfluence spot prices but not vice versa. The futures pricesrespond to new information more quickly than spot prices,due to lower transaction costs and flexibility of short selling. 2 The hedgers and speculators will react to the new information

by preferring futures rather than spot transactions.

Spot prices will react with a lag because spot transactionscannot be executed so quickly. 3 A large number of empiricalstudies has shown that most economic variables exhibit anasymmetric adjustment process. Some recent literaturesuggested that the dynamic relationship between spot andfutures prices may be characterized by a nonlinearequilibrium correction model due to factors such as non-zerotransaction costs, infrequent trading etc. 4

The dynamic interrelationship between spot and futuressuggested a nonlinear relationship between spot and futures.

Moreover, the co-integration and its corresponding errorcorrection model assume that the tendency to move toward along-run equilibrium is always present. However, it is

possible that an adjustment towards equilibrium need notoccur in every period. 6

The price transmissions between spot and futures in TaiwanTECM clearly indicated a bidirectional feedback causalityrelationship between the spot and futures markets.Asymmetric price transmissions between these two marketsare also found in the long run. 6 The price discovery functionof futures markets hinges on whether new information isactually reflected first in changes in futures prices or in spot

prices. Identifying the direction of information flows betweenspot and futures prices, then, appears to be an empirical issue.

There exist many studies exploring the linkage of spot andfutures prices for predictability, market efficiency andcointegration. 7 Some works find that spot and futures priceare not co-integrated, or they are co-integrated, but do notmove together one-for-one in the long run. Recent studiesfocus on investigating the non-linear causality between spotand futures oil markets. 1 However, our aim of the presentstudy is to test for the existence relationships between Spotand future of crude oil prices from Multi commodityExchange (MCX), which is used as an indicator of Indian oilmarket.

Review of Literature1. Apostolos Serletis 10 examined evidence concerning the

number of common stochastic trends in a system of three petroleum futures prices (crude oil, heating oil and

unleaded gasoline) using Johansens maximumlikelihood approach. The results indicate the presence ofonly one common trend.

2. Li-Hsueh Chen et al 11 studied new supportive evidencefor asymmetric adjustment in U.S. retail gasoline prices.The asymmetric transmission is found to occur not justthrough the spot markets of crude oil and refinerygasoline but also through their future markets. Furtherevidence also shows that the observed asymmetry in

price transmission primarily occurs downstream notupstream of the transmission process.

3. Ercan Ozen et al 12 examined short term or long termcausality between the futures transactions carried out in

* Auth or f or Corr espondence


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Izmir Derivatives Exchange (VOB) over Istanbul StockExchange Index (MKB30) and IMKB Index wasinvestigated.

To this end the 1024 days' cash price data and futures prices data belonging to the period between 4 February2005 and 27 February 2009 were used. Unit Root test,Co integration test and causality analysis depending onError correction model (VECM) were employed. Thefindings of the study proved that causality from VOBtowards IMKB was detected in long term. In short term,on the other hand, IMKB was detected in long term. Inshort term, on the other hand, IMKB was found to be thecausal of VOB.

4. Thai-Ha Le1 and Youngho Chang 13 investigated therelationship between the prices of two strategiccommodities: gold and oil. They studied through theinflation channel and their interaction with the index ofthe US dollar. They used different oil price proxies fortheir investigation and found that the impact of oil priceon the gold price is not asymmetric but non-linear.Further, results show that there is a long-run relationshipexisting between the prices of oil and gold. The findingsimply that the oil price can be used to predict the gold

price.

MethodologyThe empirical analysis in the present study is based on unitroot test through ADF and PP test, co-integration and VECMrespectively. The first step in the analysis is to subject thespot and future prices of crude oil to unit root tests or tests theseries for stationarity. The present study uses co-integrationand VECM test for long term and short term relationshipamong the spot and future prices of crude oil. The crude oilspot and future data 2018 observations are collected fromMulti Commodity Exchange (MCX) from 29 th April 2005 to31 st December 2011.

The Augmented Dickey-Fuller (ADF) TestSometimes, time series data are not in a stationary form. To

transform it into a stationary form, an easy way is todifference the time series data. One way is to use theAugmented Dickey-Fuller (ADF) statistic. The ADF testconstructs a parametric correction for higher-order correlation

by assuming that the series follows an AR (p) process andadding lagged difference terms of the dependent variable tothe right-hand side of the test regression as follow:

yt = yt-1 + x 1 + 1 yt-1 + 2 yt-2 + p yt-p+v t . (1)

where x 1 are optional exogenous repressors which mayconsist of constant or a constant and trend. The Null

hypothesis of the ADF t-test is

H0 : = 0 . (2)

which means that the data needs to be differenced to make itstationary. The alternative hypothesis is:

H0 : < 0 . (3)

which means that the data is trend stationary and needs to beanalyzed by means of using a time trend in the regressionmodel instead of differencing the data.

The test statistic is conventional t- ratio for :

t = /se() . (4)

The Phillips-Perron (PP) TestPhillips and Perron propose an alternative method of

controlling for serial correlation when testing for a unit rootcalled Phillips-Perron (PP) test. The PP method estimates thenon-augmented Dickey-Fuller test equation:

yt = yt-1 + x 1 + t . (5) It modifies the t- ratio of coefficient so that serialcorrelation does not affect asymptotic distribution of the teststatistic. The PP test is based on the statistic.

Johansen Co-integration TestThe purpose of the co-integration test is to determine whethera group of non-stationary series are co-integrated or not and it

explores the long-run equilibrium relationship among thevariables. Under this study, Joh ansens co-integration testshave been used to assess the long-run predictability amongspot and futures prices, using the Johansen co-integration test,assuming an n-dimensional vector X t with integration of onorder I, estimates a vector autoregressive models. Johansenand Juselius further improved the model by incorporating anerror correction depicted as follows:

kX t = c + i X t-1+t . (6)

i=1

k-1 Xt = + i Xt-i+i X t-k +t . (7) i=1

where X t is an n x1 vector of the I(1) variables representingCrude spot (St) and crude futures (Ft-n) prices respectively, is a deterministic component which may include a lineartrend term, an intercept term, or both, denotes the firstdifference operator, i is an n x r matrix of parametersindicating a and b, c is a vector of constants, k is lag length

based on the Akaike information criterion (AIC) Schwarzinformation criterion (SC) and 1t is a t random error termwhich indicates how many linear combinations of X t are

stationary.9


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Vector Error Correction ModelTo explain the VECM test, we will consider the often askedquestion in macroeconomics 8: Is it Crude oil Spot(CS) that

causes the Crude oil Future (CF) (CS CF ) or is it theCrude oil Future(CF) that causes Crude oil Spot (CS) wherethe arrow points to the direction of causality? The Grangercausality test assumes that the information relevant to the

prediction of the respective variables, CS and CF is containedsolely in the time series data on these variables. The testinvolves estimating the following pair of regressions:

.(8)

.(9)

where it is assumed that the disturbances CS and CF areuncorrelated. In passing note that, since we have twovariables, we are dealing with bilateral causality.

Empirical AnalysisAs per table 1, the mean of spot and future price crude is3520.753 and 3462.385 respectively. Standard Deviation ofspot and future price crude is 851.5361 and 859.9854respectively. The value for skewness is 0.740727 and0.701276 respectively. There is positive skewness possibleamong study period and the distribution has a long right tail.Kurtosis is 3.160560 and 3.256359 respectively.

The kurtosis exceeds 3, the distribution is leptokurtic relativeto the normal. Jarque-Bera test indicates that we do not rejectnull hypothesis of being normal distribution at 5%significance level. We rejected 1% significant level.However, the data is normal and time series is suitable to be

used for using any models.

The sample period of crude oil prices data from 2 nd January2005 to 31 st January 2012 are plotted with aid of Eviews. Wehave to determine the trend of the series of being constant,linear or non-linear and etc. The oil prices series is shown infigure 1. In figure 1 it can be seen that the oil prices havemainly fluctuated in the range of about Rs. 1897 andRs. 6245.

According to the ADF and PP test for spot and future price ofcrude oil in table 2, the ADF test statistic for spot and futureis -1.61385 and -1.4029 and strongly disagrees that the seriesis stationary. Thus, we do not reject the null hypothesis of

being non-stationary at level. The ADF test statistic for spotand future prices of crude oil are 046.7928 and -43.5226respectively. It strongly agrees that the series is stationary at1st difference. The PP test statistic for spot and future price ofcrude oil is -1.50561 and 1.49775 respectively. We do notreject the null hypothesis of being non-stationary. We rejectthe null hypothesis in 1% significant level.

Table 1Descriptive statistics of Crude Spot and

future PricesCrude future

priceCrude spot

priceMean 3520.753 3462.385

Median 3467.000 3401.000Maximum 6245.000 6299.000Minimum 1897.000 1695.000Std. Dev. 851.5361 859.9854Skewness 0.740727 0.701276Kurtosis 3.160560 3.256359

Jarque-Bera 186.7057* 170.9306*Probability 0.000000 0.000000

*1% level of significant

Fig. 1: Daily observation of Crude spot and future prices


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Table 2Unit Root Tests for Spot and Future prices of Crude Oil

Particulars At Levels 1 st difference

T-Value P-Value T-Value P-ValueADF Test Crude Spot -1.61385 0.4753 -46.7928* 0.0001

Crude Future -1.4029 0.5823 -43.5226* 0.0000PP Test

Crude Spot -1.50561 0.5308 -46.8413* 0.0001Crude Future -1.49775 0.5348 -43.5440* 0.0000

*1% level of significant

Table 3Co-integration Result Trace test results

Crude oil Hypothesis Eigen Value trace Statistics 5% Critical ValueSpot r=0 0.027294 57.98112** 15.49471

Future r1 0.001130 2.275322 3.841466

Table 4Maximum Eigenvalue results

Crude oil Hypothesis Eigen Value max Statistics 5% Critical ValueSpot r=0 0.027294 55.70579** 14.26460

Future r1 0.001130 2.275322 3.841466**5% level of significant

Table 5Crude Oil vector error correction model (VECM)

Commodity Constant S t F Z t-1(Error.

correction )[T-Stat]

ii=s,f(Error.

correction)[T-Stat]

S t-1

(Error.correction )

[T-Stat]

S t-2

(Error.correction)

[T-Stat]

F t-1 (Error.


F t-2 (Error.


Crude oil St 0.869488(1.33389)[ 0.65184]

-0.309371(0.02532)

[12.2179]**

-0.094535(0.02065)

[4.57870]**

0.663140(0.02492)

[ 26.6133]**

0.188261(0.02780)

[ 6.77302]**

0.082886(0.01408)

[ 5.88517]*

Ft 1.463796(1.42779)[ 1.02522]

0.007719(0.02710)[ 0.28481]**

-0.030385(0.02210)[1.37487]**

0.057196(0.02667)[ 2.14444]**

0.008625(0.02975)[0.28989]**

-0.058597(0.01508)[3.88693]**

*1%, **5% level of significant

Johansens Co -integrationAs the series were stationary at their first difference, their co-integration was tested using Johansen and Johansen andJuselius co-integration test. The aim of this test is todetermine whether a long-term relationship exists betweenthe variables, or not. Test results are presented on table 3 and4. As a result of the two tests Null hypothesis is rejected at

5% level of significant.

It was determined that there is a single co integration vector between the series. As a result of the two tests there is a long-term relationship between Spot and futures of Crude oil. Thetest reveals that one co-integration relationship exists betweenspot and futures markets of crude oil . Johansens max and trace statistics reveal that the spot and futures prices of crudeoil stand in a long-run relationship between them, hence bothseries have a conjugate movement in the long term.


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Vector error correction model (VECM)Vector error correction model (VECM) is chosen on basis ofAkaikes information criteria (AIC) The VECM estimationresults are presented in table 5. Crude oil spot price VECMResult noticed that Z st-1 =0.082886. This indicates the spot price series St has a greater speed of adjustment to the previous periods deviation from long-run equilibrium thanthe future price series. It is consistent with the fact that spot

price has to adjust itself to the prevailing future priceequilibrium than the spot price series.

Crude oil future price VECM result noticed thatZFt-1 = -0.058597 indicates the future price series Ft has anegatively adjustment to the previous periods deviation fromlong-run Vector error correction model (VECM) chosen on basis of Akaikes information criteria (AIC). The VECMestimation results are presented in table. VECM result noticedthat Z st-1 =0.082886. This indicates the spot price series St has a greater speed of adjustment to the previous periodsdeviation from long-run equilibrium than the future priceseries. It is consistent with the fact that spot price has toadjust itself to the prevailing future price. Crude oil future

price VECM result noticed that Z Ft-1 = -0.058597 indicatingthe future price series Ft has a negatively adjustment to the previous periods deviation from long-run equilibrium thanthe spot price series. A negative response implies the futures

prices will decrease the variation and approach theequilibrium at the next period .

This finding is consistent with the fact that on the deliverydate of each the future price has negatively to adjust itself tothe prevailing spot price. The results reveal that there is Bi-directional between the spot and future prices of Crude. Spotand Futures market significantly reacts to short-term variationand long-term equilibrium at the same time. Null hypothesisis rejected hence both the market of Crude oil is significant at1% and 5% level (based on the Error correction). Thus, theresults indicate that the price discovery is achieved from the

both the market and has short term relationship betweenthem.

ConclusionOur aim of the present study is to test for the existencerelationships between Spot and Future of crude oil pricesfrom Multi Commodity Exchange (MCX) which is used as anindicator of Indian oil market, the researcher are examiningdynamic relationships between spot and futures prices ofcrude oil. In this study the major objective is to find out longterm and short term relationship between the spot and futures

prices of Crude oil market from India. 2018 observations arecollected from Multi Commodity Exchange (MCX) from 29 th April 2005 to 31 st December 2011. In the study, we usedJohansen co-integration and Vector error correction model

(VECM) tests respectively. The first step in the analysisstationarity of spot and future prices of crude oil is through

unit root test ADF and PP test.

The ADF test statistic for spot and future prices of crude oilare 046.7928 and -43.5226 respectively. It strongly agreesthat the series is stationary at 1 st difference. The PP teststatistics for spot and future price of crude oil are -1.50561and 1.49775 respectively. We do not reject the nullhypothesis of being non-stationary at level. We reject the nullhypothesis at 1% significant level stationary at 1 st difference.As per Johansen and Juselius co-integration test, the aim ofthis test is to determine whether a long-term relationshipexists between the variables or not. As a result of the twotests Null hypothesis is rejected at 5% level of significant.Johansens max and trace statistics reveal that the spotand futures prices of crude oil stand in a long-run relationship

between them, hence; both series have a conjugate movement

in the long term.Based on the Vector error correction model (VECM), it isindicated the spot price s eries St has a greater speed ofadjustment to the previous periods deviation from long-runequilibrium than the future price series. It is consistent withthe fact that spot price has to adjust itself to the prevailingfuture price. Crude oil future price VECM Result is anegatively adjustment to the previous periods deviation fromlong-run equilibrium than the spot price series. Both themarket of crude oil is significant at 1% and 5% level. Thus,the results indicate that the price discovery is achieved fromthe both the market and has long term and short termrelationship between them.

References1. Bekiros Stelios D. and Diks Cees G.H., The RelationshipBetween Crude oil spot and future Prices: Cointegration, Linear and

Nonlinear Causality, 3 ( 2008 )

2. Silvapulle P. and Moosa I.A., The relationship between spot andfutures prices: evidence from the cruide oil market, The Journal of

Futures Markets , 19 , 175-193 ( 1999 )

3. Chiung Chiao Chang, Asymmetric Causal Relationship between spot and futures in Taiwan, International Research Journal of Finance and Economics, 2 (2008 )

4. Balke N. S. and Fomby T. B., Threshold Co-integration , International Economic Reviews , 38 , 627-645 ( 1997 )

5. Enders Walter and Siklos P. L., Co-integration and ThresholdAdjustment, Journal of Business and Economic Statistics , 19 , 166-177 ( 2001 )

6. Garbade K. and Silber W., Price movements and price discoveryin futures and cash markets, Review of Economics and Statistics, 65 (2), 289 297 ( 1983 )

7. Bekiros S.D. and Diks C.G.H., The relationship between crudeoil spot and futures prices: cointegration, linear and nonlinearcausality , Energy Economics , 30 , 2673-2685 ( 2008 )

8. Gujarati; Basic Econometrics, Fourth Edition, the McGraw-HillCompany, 699 ( 2004 )


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9. Jabir Ali and Gupta Kriti Bardhan, Efficiency in agriculturalcommodity futures markets in India, Emerald in sight , 166 ( 2009 ) 10. Apostolos Serletis, A cointegration analysis of petroleum

futures prices, Energy Economics, 16 (2) 93-97 ( 1994 ) 11. Li-Hsueh Chen, Miles Finney T. and Kon S. Lai, A thresholdcointegration analysis of asymmetric price transmission from crudeoil to gasoline prices, Economics Letters , 89 , 233 239 ( 2005 )

12. Ercan zen, Tunga Bozdoan and Muhittin Zgl, TheRelationship of Causality between the Price of Futures TransactionsUnderlying Stock Exchange and Price of Cash Market: The Case ofTurkey, Middle Eastern Finance and Economics ( 2009 )

13. Thai-Ha Le1 and Youngho Chang, Oil and Gold: Correlationor Causation? Nanyang Technological University, SingaporeWorking Paper Series No. 2011/22 ( 2011 ).

(Received 22 nd April 2013, accepted 2 nd June 2013)

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Short & Long Term Relationship Analysis for forecasting crude oil prices