The Middle East Business and Economic Review, Vol.22, No.1 (March 2010)

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1 The Middle Eas Business and Economic Review, Vol.22, No.1 (March 2010) CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering Isabelle Crisiani-d Ornano 1, Ahmed Ksaier 1, Jean-Eienne Carloi 2 Absrac The oil marke is disinc from oher financial markes. We apprehend he effecs of persisence observed from January 1 s, 1999 o November 7 h, 2008 o model he rajecory of is daily volailiy and price. In his inenion, we use he Hurs exponen in order o deermine he exisence of a long memory phenomenon. This long memory proves ha he oil chronicle poss a emporal dependence of is variables in he pas. Therefore, we seize is dynamics and deermine is shor run fuure rajecory. The decrease of he oil price volailiy ha we had anicipaed for he end of 2008 is really carried ou. JEL: C 22 C52 F31 Q43 Keywords: crude oil price, volailiy, forecasing. 1. Inroducion Since he mid-1980s, inernaional crude oil price was primarily influenced by he supply and demand condiions on oil marke bu was no rigidly conrolled as during he firs and second oil crises. However, he marke mechanism made he inernaional oil price frequenly volaile wih srong changes. There are significan exreme marke risks ha have led oil marke paricipans and governmens o suffer heavy poenial losses. As a resul, here has been an increasing ineres in sudying he oil marke risks and is measuremen. The oil price poss specific saisical properies, disinc from oher financial markes. I is necessary o apprehend is daily reurn and is volailiy o undersand is dynamics. By deermining he exisence of he long memory phenomenon in he daily oil reurn series (WTI), his paper aims - via FIGARCH model - a rying o offer a predicive capaciy of he volailiy and oil price. In his inenion, we should exceed he concep of independen variables, so much awaied by saisicians. On he oher hand, i is imporan o demonsrae ha a relaion beween hese disan variables in he pas 1 CEMAFI Universiy of Nice Sophia-Anipolis 2 Universiy of Paris-Sud 11 and Ecole de la Recherche de l'emlv

2 CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering conveys he presence of a long memory. This would enable us o seize he dynamics of he oil chronicle and o overview is forecas. Moreover, he search for his hypoheical long memory aims a measuring if he informaional shock occurrence generaes or no effecs on he fuure daa. Knowledge of sochasic process underlying crude oil price is imporan for no only pricing derivaives and hedging, bu also for policymaking and shor-erm forecasing. The srucure of his paper is as follows. Secion 2 describes he ime series properies and he empirical disribuion of oil price reurns from January 1 s 1999 o November 7 h Secion 3 delivers he inerpreaion of our resuls and Secion 4 concludes. 2. Modeling 2.1 Daa Our daa sample conains daily (5-day / week) crude oil price (WTI) going from January 1 s, 1999 o November 7 h, These daa come from he U.S. Deparmen of Energy. Fig Crude Oil Price Source Daasream We observe a relaively linear endency, which leads us o ry o neuralize he rend on he esimaors properies and o es he deecion of long memory. 2

3 Isabelle Crisiani-d Ornano, Ahmed Ksaier, Jean-Eienne Carloi The sudied period presens a high number of delays. If he sudy of his daily series shows a progressive decrease and a number of posiive and significan auocorrelaions hen we have he inuiion o deec a emporal dependence among he pas variables. This represenaion of he crude oil price shows a bullish endency up unil he summer 2008 and afer his period, a bearish endency. 2.2 Saisical characerisics Descripive saisics Oil price daa are convered ino a daily nominal percenage change, e.g. r = 100 Ln( wi / wi 1) for = 1, 2, K, T, in which r is he reurn for crude oil a ime, wi is he curren price and wi 1 is he previous 2 day price. Daily volailiy (variance) is assessed by daily squared reurn r. The dynamics of reurn and volailiy for he crude oil price are ploed and can be seen in Fig.2. Fig Crude Oil Reurn 60 Crude Oil Volailiy

4 CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering Descripive saisics for he crude oil price series are summarized in able 1. The mean of reurn is quie small bu he variance is higher. Boh skewness and kurosis saisics show ha he reurn disribuion is no normally disribued. Likewise, he Jarque-Bera es also rejecs he null hypohesis of normaliy in he disribuion of he sample reurn series. In addiion, he daily oil chronicle does no follow a normal disribuion bu is affeced by abrup modificaions. Table.1 Descripive Saisics Series Number of observaions Mean Sandard deviaion Skewness Kurosis Jarque-Bera WTI Saionariy es We use wo uni roo ess: ADF (Augmened Dickey Fuller) and KPSS (Kwiakowski, Phillips, Schmid, and Shin) ess in order o deermine wheher saionariy, inegraion, or fracional inegraion may be considered for daily daa. These ess differ in he null hypohesis. The null hypohesis of he ADF es means a ime series conains a uni roo, I(1) process whereas he KPSS es poses he null hypohesis of saionariy wih I(0) process. The empirical resuls of uni roo ess for sample reurn are displayed in able 2. According o he ADF es, we accep he rejecion of he null hypohesis a he 1% significance level. On he conrary, he KPSS es shows ha he reurn series are insignifican for he rejecion of he saionariy null hypohesis, which implies he saionariy of reurn series. 4

5 Isabelle Crisiani-d Ornano, Ahmed Ksaier, Jean-Eienne Carloi WTI Table.2 Uni Roo Tess ADF Inercep only Inercep and rend -51,78* -51,79* (-3,43) (-3,96) KPSS Inercep only Inercep and rend 0,096 0,056 (0,739) (0,216) Lagrange Muliplier es for he ARCH effec ARCH model has he form of an auoregressive model. Engle (1982) proposed he Lagrange Muliplier (LM) es in order o es he exisence of ARCH behavior based on he regression. The es saisic is given by TR², where R² is he deerminaion coefficien and T is he sample size. Under he null hypohesis here is no ARCH effec, he saisic es is asympoically disribued as chi-square disribuion wih q degree of freedom. The LM (= wih Significance Level ) es resul indicaes he exisence of ARCH effec in he series. Long memory es The parameer H, Hurs Exponen, displays he long memory propery of he ime series. A long memory ime series is said fracionally inegraed. The Hurs exponen akes value from 0 o 1 (0 < H < 1). If 0.5< H<1, he series indicaes persisen behavior or long memory. Table.3 presens Hurs es for daily reurn and volailiy, which displays high persisence, hus indicaing he exisence of a long memory effec 2.3 Empirical framework Table.3 Hurs es WTI Reurn Volailiy H Taking ino accoun he exisence of long memory, i is necessary o apply FARIMA model o rea his dependence of long run in erm of mean. Moreover, we can wonder abou he relevance of he GARCH, IGARCH and FIGARCH models o model he volailiy of crude oil price. FARIMA model The FARIMA model, which generaes he long memory propery in he firs condiional momen, is defined as below: d Φ L 1 L y µ = Θ L ε ( )( ) ( ) ( ) 5

6 CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering where µ is he mean of he process, d he fracional parameer, L is he backshif operaor, Φ ( L ), Θ ( L ) are he auoregressive (AR) and moving average (MA) polynomials: Φ p i ( L ) = 1 φ i L, Θ ( L ) = + i = 1 q 1 θ. i = 1 i i L ε is an innovaion sequence wih he condiional mean E ( ε / Ω 1 ) = µ E ( ε 2 / Ω 1 ) = h, where Ω 1 Tha is / 1 N ( 0, h ) Ω and a poenially ime varying condiional variance is he informaion se up on ime -1. ε, e.g.: ε = z h. Where z is a sequence of independen sandard normal variables wih variance. The fracional differencing operaor ( 1 L ) d is defined by he binomial expression: d d ( 1 d ) d ( 1 d )( 2 d ) 3 ( 1 L ) = 1 dl L ² L +K 2! 3! GARCH model To capure he volailiy propery of he condiional variance process, Bollerslev (1986) inroduced he GARCH model, which has been widely used in he financial lieraure up o now, and includes he volailiy clusering propery observed in he empirical financial ime series. The volailiy is a parameer used o evaluae he risk of diverse financial asses, so he reliable esimaion of volailiy is a significan ask in he financial field. The GARCH (1, 1) model is he mos popular in empirical research and is defined as follows: ε = z h h 2 = ω + αε 1 + β h 1 All parameers mus be posiive. α + β < 1, and he sum of ( α + β ) quanifies he persisence of shocks o volailiy. FIGARCH model The FIGARCH (Fracionally Inegraed Generalized Auoregressive Condiional Heeroscedasiciy) model allows us o model observed clusering on financial daa where a period of srong (weak) volailiy ends 6

7 Isabelle Crisiani-d Ornano, Ahmed Ksaier, Jean-Eienne Carloi o be followed by he same sequence. Therefore, FIGARCH model enables us o consider he characerisics of he long memory. The FIGARCH (p, d, q) model of Baillie and al. (1996), which capures he hyperbolic decay in he volailiy process is given by: d 2 Ψ L 1 L ε = ω + 1 β L v ( )( ) [ ( )] [ β( L) ] h = ω + 1 β( L) Ψ( L)( 1 L) d [ ] ε 2 1 where d (0 d 1) is he fracional differencing parameer. The FIGARCH model provides greaer flexibiliy for modeling he condiional variance because i accommodaes he covariance saionary GARCH model when d = 0, and he IGARCH model when d = 1, as special cases. For he FIGARCH model, he persisence of shocks o he condiional variance or he degree of long memory is measured hank o he fracional differencing parameer d. Thus, he aracion of he FIGARCH model is, for 0<d<1, sufficienly flexible o allow for an inermediae case of persisence. 3. Resuls In his paper, we model he ime varying condiional means and condiional variances of he daily oil price reurns by using he FARIMA-GARCH and he FARIMA-FIGARCH models Esimaion The esimaed parameers by FARIMA, GARCH, IGARCH, FIGARCH models are summarized in able 4. All parameers are saisically significan a 5%. 7

8 CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering Table.4 Esimaion resuls µ φ θ d FARIMA GARCH IGARCH FIGARCH (0.0004) (0.0005) (0.0004) (0.000) ω α β ψ d Log-v (0.0058) (0.0115) (0.004) LB(20) LB²(20) ARCH(4) (0.024) (0.549) (0.0439) (0.014) (0.608) (0.037) (0.013) (0.595) (0.035) According o log-v, which ranslaes he maximum of probabiliy, here logv = is he highes value, herefore FIGARCH model is he bes candidae in erm of predicive capaciy for he crude oil price. In addiion, he d parameer in FIGARCH is ranked beween 0 and 0.5, hus indicaing he volailiy persisence. Unlike he GARCH and IGARCH models, he FIGARCH model is able o capure persisence in he volailiy of crude oil price Forecasing In order o evaluae he forecasing abiliy for he crude oil price volailiy, we se up he FIGARCH model o projec fuure rajecory for he condiional variance wih 30 days forecasing horizon. The resuls of he forecasing horizon are ploed in Fig 3 (Condiional Variance). Thus, we can conclude ha he FIGARCH model generaes a bes forecasing accuracy relaive o he volailiy of oil price (WTI) 8

9 Isabelle Crisiani-d Ornano, Ahmed Ksaier, Jean-Eienne Carloi 6 Condiional Variance So, according o his graph, i arises from he seleced modeling FARIMA - FIGARCH ha i is possible o ake ino accoun he phenomenon of long memory, inheren in he sudied series. We observe ha he rajecory, which we had anicipaed before -here represened in doed line- was really achieved during his period. Our sudy made i possible o anicipae a decrease of he oil price volailiy from November 2008 onwards and i appears ha his endency has been confirmed. A he same ime, we observe ha boh he oil price fell under he bar of 40 dollars in December 2008 (is low level observed hese four las years) afer a veriginous blaze in July 2008 (147 dollars per barrel) and a persisence of he dearness of is price before he anicipaed fall. Conclusion Oil price dynamics is relevan for hedging, forecasing, and making policy. Our main objecive in his paper has been o aemp o find a model wih he bes abiliy o forecas volailiy of crude oil price. In his conex, we have evaluaed persisence in volailiy of he oil price (WTI) by using hree condiional models. By analyzing he condiional variance of he oil series, fracionally differeniaed from 1/1/1999 o 11/7/2008, we are able o measure he effecs on volailiy. By deermining he exisence of long memory, we could release a shor-erm forecas, which has been confirmed by he facs. 9

10 CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering I comes ou from our paper ha FIGARCH model seems o be he bes candidae o model volailiy because he link of dependence beween he variance and reurn is well esablished. Therefore, a predicive capaciy is possible and i appears ha he anicipaed rajecory of oil price was a poseriori achieved in December Thus, our findings should be able o help policymakers o enhance heir inervenions. References Askari, H. and Krichene, N., 2008, Oil price dynamics ( ), Energy Economics, 30, pp Baillie, R.T., Bollerslev, T. andmikkelsen, H.O., 1996, Fracionally inegraed generalized auoregressive condiional heeroskedasiciy, Journal of Economerics, 74, pp Bollerslev, T., 1986, Generalized auoregressive condiional heeroskedasiciy, Journal of Economerics, 31, pp Engle, R.F., 1982, Auoregressive condiional heeroskedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 50, pp Hammoudeh, S., Li, H. and Jeon, B. 2003, Causaliy and volailiy spillovers among peroleum prices of WTI, gasoline and heaing oil in differen locaions, The Norh American Journal of Economics and Finance, 14(1), pp Huang, Y. and Guo, F., 2007, The role of oil price shocks on China s real exchange rae China Economic Review, 18(4), pp Huang, B.N., Hwang, M.J. and Peng, H.P., 2005, The asymmery of he impac of oil price shocks on economic aciviies: an applicaion of he mulivariae hreshold model Energy Economics, 27, pp Indjehagopian, J. P., Lanz, F., Simon and V., 2000, Dynamics of heaing oil marke prices in Europe Energy Economics, 22(2), pp Jiao, J. L., Fan, Y., Zhang, J. T.and Wei, Y. M., 2005, The analysis of he effec of OPEC oil price o he World oil price, Journal of Sysems Science and Informaion, 1, pp Jimenez-Rodriguez, R. and Sanchez, M., 2005, Oil price shocks and real GDP growh: empirical evidence for some OECD counries Applied Economics, 37 (2), pp