Review of Middle Eas Economics and Finance Volume 4, Number 008 Aricle 3 Transiory and Permanen Volailiy s: The Case of he Middle Eas Sock Markes Bashar Abu Zarour, Universiy of Paras Cosas P. Siriopoulos, Universiy of Paras Recommended Ciaion: Zarour, Bashar Abu and Siriopoulos, Cosas P. (008) "Transiory and Permanen Volailiy s: The Case of he Middle Eas Sock Markes," Review of Middle Eas Economics and Finance: Vol. 4: No., Aricle 3. DOI: 10.0/1475-3693.1060 Available a: hp://www.bepress.com/rmeef/vol4/iss/ar3 008 Berkeley Elecronic Press. All righs reserved.
Transiory and Permanen Volailiy s: The Case of he Middle Eas Sock Markes Bashar Abu Zarour and Cosas P. Siriopoulos Absrac Recen research has suggesed ha reurns volailiy may conain boh shor-run and long-run componens due o he exisence of heerogeneous informaion flows or heerogeneous agens (Andersen and Bollerslev 1997a, 1997b; Müller e al., 1997). This paper invesigaes he exisence of such volailiy decomposiion in daily index reurns daa for nine emerging markes in he Middle Eas region using he permanen-ransiory componen variance model of Engle and Lee (1993). The exisence of a componen srucure o volailiy is suppored by he exisence of a ransiory componen o volailiy and a permanen volailiy ha decays over a much longer horizon in hree markes in he Middle Eas, namely Jordan, Oman, and Saudi Arabia. The componen model was able o capure all srucure wihin he daa for Saudi Arabia on he basis of residual ess. However, some srucure in he residuals remains in he Oman and Jordan markes. KEYWORDS: volailiy decomposiion, Middle Eas sock markes,
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes 1. Inroducion There is a growing number of papers dealing wih he decomposiion of sock markes volailiy o is componens (Ghose and Kroner, 1996; Müller e al., 1997; Andersen and Bollerslev, 1997a, 1997b). The recen lieraure also sudies he decomposiion of sock reurn wihin he sae space framework ha allows for volailiy ransiion beween regimes for he reurn iself and for each of is componens (Nelson and Plosser, 198; Campbell and Mankiw, 1987). Several explanaions have been suggesed ha heerogeneous marke volailiy componens may exis a high frequency daa. For insance, Andersen and Bollerslev (1997b) sugges ha marke volailiy may reflec he aggregaion of numerous independen volailiy componens, each of which is endowed wih a paricular dependence srucure due o he arrival of heerogeneous informaion. This heerogeneous informaion exension of he informaion-flow approach o marke volailiy impars boh shor-run and long-run volailiy effecs. If he decay of he shor-run volailiy componen dominaes over inra-day frequencies, and he long-run volailiy componen dominaes over inra-day and lower frequencies, he aggregaion of such componen processes hen gives rise o he (near-) inegraed and long memory lower-frequency dependencies ha have been shown o characerize many reurns volailiies. Using an alernaive approach, Müller e al. (1997) argue ha such volailiy srucure may arise due o heerogeneous raders raher han heerogeneous informaion flows. Tha is, differen marke-agen ypes possessing differen ime horizons, such ha shor-erm raders evaluae he marke a a higher frequency and has shorer memory han long-run raders, resuling in a componen srucure o volailiy. Moreover, hey divide no only he marke agens bu also volailiy ino componens. A similar idea is presened in he model for condiional variance inroduced by Engle and Lee (1993) where wo componens ( permanen and ransiory ) are modeled wihou relaing hese o specific raders groups. This paper applies he componen model of Engle and Lee (1993) o nine new emerging markes in he Middle Eas region, in an effor o deermine wheher permanen and ransiory componens can be explicily idenified in such markes and, where presen, wheher he persisence of shor-run volailiy overwhelm he long-run componen. Daily sock index marke reurns are used, which are he highes frequency daa available for such markes. The reminder of his paper is organized along he following lines. Secion presens he markes under consideraion along wih he descripion and some basic characerisics of he daa se. Secion 3 shows he srucure and properies of he componen model. The and he componen models esimaes are presened in secion 4, while secion 5 summarizes and concludes he paper. Published by Berkeley Elecronic Press, 008 1
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3. Sock markes characerisics and daa By inernaional sandards, Middle Easern emerging markes under examinaion here are considered relaively new. Mos of hem sared operaing over he las wo decades, while ohers have been in exisence for much longer, bu unil recenly heir level of aciviy was no significan. Table 1 presens some marke indicaors as i is a he end of 005. For marke capializaion as an indicaor of marke size, Saudi Arabia sands o be he larges marke in he region followed by Abu Dhabi sock marke, while Palesine sock exchange sands o be he smalles one. Table 1 Marke Marke Capializaion, (Billion us$) Abu Dhabi 13.41 59 1.53% 95.0 Jordan 37.64 01 63.5% 97.57 Bahrain 17.63 47 4.10%.87 Saudi Arabia 646.1 77 170.80% 3690.91 Kuwai 13.89 156 78.53% 390.7 Dubai 111.99 30 98.49% 14.8 Oman 1.06 15 7.53% 13.0 Egyp 79.51 744 34.87% 111.78 Palesine 3.16 8 14.10% 6.11 Source: Arab Moneary Fund Daabase,AMDB Some Marke Indicaors, 005 No. of Lised Companies Turnover Raio Av. Daily Trading Value (million $) The number of lised companies by i self can provide an indicaion of he choices of firms available o an invesor. In his sense, Egyp sands ou among markes wih he larges number of lised companies. However, if he number of lised companies is used in conjuncion wih marke capializaion, i will indicae he average marke value for lised companies. In his case, Saudi Arabia has by far he highes marke value per lised company a abou $ 8391 million followed by Dubai $ 3733 million, wih Egyp having he lowes marke value per lised company ($ 107 million). In he case of urnover raio, as an indicaor of marke liquidiy, he Saudi sock marke sands o be he mos acive and liquid marke in he region a he end of 005. Is urnover raio reached 171% wih average daily rading value $ 3691 million. The daa used in his paper consis of daily closing prices of he general indices for each of he nine Middle Easern emerging equiy markes, namely he general sock marke indices of Abu Dhabi, Jordan, Bahrain, Saudi Arabia, Kuwai, Dubai, Oman, Egyp, and Palesine, which are value weighed indices. hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes The ime periods vary from marke o marke, bu usually run from abou 1 s January 199 o 31 July 005. The iniial and final daes vary among markes due o he esablishmen dae of he marke and; in several cases, o he availabiliy of he daa. The daa were colleced direcly from each sock marke. Table provides some saisical properies of daily sock marke reurns for he nine exchanges. Palesine exhibis he highes sandard deviaion (1.8370) followed by Egyp (1.6658), Oman, Kuwai, Dubai, Saudi, Jordan, Bahrain, and Abu Dhabi (0.5388). This shows ha Palesine and Egyp markes exhibi high flucuaions from he mean reurns. All nine counries have disribuions wih posiive excess kurosis and are seen o have heavy ails, ha is are lepokuric relaive o he normal. This implies ha he disribuion of sock reurns in hese sock exchanges end o conain exreme values. According o he Jacque-Berra es, normaliy is rejeced for all he reurns series examined. I can be observed ha Bahrain, Dubai and Saudi sock exchanges show he mos exreme values for he daily reurns compared o he oher markes, which indicaes ha he volailiy of hese markes is much higher. Oman exhibis he lowes mean reurns of 0.051 followed by Bahrain, Jordan, Saudi, Egyp, Dubai, Palesine, Abu Dhabi, and Kuwai. The difference beween he maximum and minimum reurns is much higher for Palesine (5.59), which implies ha he Palesine sock marke undergoes large flucuaions compared o he oher exchanges of he region. This is no surprising considering he relaive smallness and openness of ha sock marke (see able 1) and, consequenly, is vulnerabiliy o global shocks. Table Descripive Saisics for Daily Marke Reurns of he General Indices R = 100*log(p /p -1 ) Jordan Egyp Palesine Kuwai Saudi Bahrain AbuDhabi Dubai Oman 4Jan.,91-1Dec.,05 1Jan.,98-4Jan.,05 8Jul.,97-8Apr.,05 17Jun.,01-6Sep.,04 6Jan.,94-15Mar.,05 1Jan.,91-3Jun.,04 1Jul.,01-31Dec.,03 6Mar.,00-31Dec.,03 Jan.,97-13Oc.,04 Mean 0.0355 0.045 0.080 0.1876 0.0370 0.057 0.0847 0.0435 0.051 Median -0.0090-0.089 0.0000 0.1618 0.0368 0.0104 0.0558 0.006-0.0043 Maximum 4.7465 18.369 7.330 4.063 17.904 0.6189.8665 1.6679 15.5 Minimum -4.3097-10.9751-5.3643-5.6757-17.553-19.8569 -.4741-8.4913-13.560 Sd. Dev. 0.7341 1.6658 1.8370 1.0386 0.934 0.769 0.5388 1.0084 1.084 Skewness 0.3075 0.7695 0.5314-0.5134 0.1168 0.4033 0.143 7.8917 0.7877 Kurosis 7.7149 15.906 73.4889 6.9037 93.8064 366.710 7.873 03.514 50.9400 Jacque-Berra,940 10,651 44,349 466 1,058,905 18,31,581 640 1,850,786 18,045 Probabiliy 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Observaions 3,11 1,666 1,180 687 3,08 3,34 645 1,098 1,899 The daa for daily indices were colleced direcly from each sock marke. Published by Berkeley Elecronic Press, 008 3
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3 Table 3 shows he resuls of he uni roo es, which examines saionariy for all ime series boh in levels and firs differences. Three ess have been employed in his invesigaion: he augmened Dickey-Fuller, he Phillips-Perron, and he Kwaikowski-Phillips-Schmid-Shin (KPSS) ess (Dickey and Fuller 1979; Phillips and Perron 1988; Kwaikowski e al. 199). Table 3 Uni Roo Tess for Each Individual Series, Boh in Levels and Firs Differences Levels Firs Difference Variables ADF Lags PP Lags KPSS BW ADF Lags PP Lags KPSS BW KSEI -.9 IT 1 -.4 IT 9 0.3 IT 1-17.7 I 1 -.14 I 7 0.16 I 9 JSMI -1.1 IT 1.43 N 1 0.56 IT 43-11.59 I 16-43.63 I 1 0.9 I 1 BSEI -1.83 I 11-1.61 I 4 0.4 IT 44-14.08 I 10-65.95 I 6 0.16 I 4 DFMI -1.61 IT 1-1.56 IT 7 0.81 IT 5-33.01 IT 1-33.03 IT 8 0.03 IT 8 EFMI 0. IT 0.1 IT 6 0.81 IT 3-7.38 IT 1-3.95 IT 13 0.17 IT 5 OSMI -0.45 IT 6 0.74 N 15 0.98 IT 34-17.1 N 4-41.83 N 14 0.39 I 15 ABSMI.95 N 3 3.17 N 9 0.8 IT 1-1.18 I -.5 I 7 0.15 I 9 PSEI -.55 I 4 -.46 I 4 0.44 IT 6-13.8 N 5-34.94 I 4 0.33 I 3 SAUDI -1.8 IT 6-1.68 IT 8 0.83 IT 43-17.85 IT 7-57.46 IT 6 0.07 IT 17 Noe: All variables are in naural logs. All uni roo ess agree ha all variables are I (1). The lag selecion is based on he lowes values for AIC crierion. Superscrip N sands for no inercep and no rend. I for inercep only and no rend, and IT for boh inercep and rend. Significan saisics are in bold, and he series are saionary. BW sands for bandwidh. The resuls of hese hree ess show ha all variables appear o be nonsaionary in levels and saionary in he firs differences or inegraed of he firs degree. 3. The componen model The condiional variance in he (1,1) model h = ω + α( ε 1 ω) + β ( h 1 ω) (1) shows mean reversion o ω which is consan for all ime. By conras, he componen model allows mean reversion o a varying level q, modeled as: h q = ω + α ε ω) + β ( h ) () q ( 1 1 ω = ω + ρ( q 1 ω) + φ( ε 1 h 1 ) (3) here h is he volailiy, while q akes he place of ω and is he ime varying long run volailiy. Equaion () describes he ransiory componen h -q, which converges o zero wih powers of (α+β). Equaion (3) describes he long run componen q, which converges o ω wih powers of ρ. Typically ρ is beween hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060 4
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes 0.99 and 1 so ha q approaches ω very slowly. We can hen combine he ransiory and permanen equaions and wrie he volailiy as h = ( 1 α β)(1 ρ) ω + ( α + φ) ε 1 ( αρ + ( α + β) φ) ε 1 + ( β φ) h 1 ( βρ ( α + β) φ) h which shows ha he componen model is a (nonlinear) resriced (,) model Following Engle and Lee (1993), le r denoe he reurn on an asse, he expeced reurn being m, and define he condiional variance of ha reurn as h Var( r Ω 1) = E[( r m ) Ω 1] where Ω -1 denoes he se of all informaion available a ime -1. The simple (1,1) process (Bollerslev, 1986) is hen defined by: r = m + ε ( 4) h = + + ω αε 1 βh 1 (5) where (ω, α, β) are fixed parameers, ε is serially uncorrelaed wih zero mean and condiional variance h, and he sandardized error z = ε / h, is idenically and independenly disribued (iid) wih zero mean and uni variance. To illusrae he exension of he componen model over he model, consider he muli-sep forecas of he condiional variance in he (1,1) model in eq. (5). Defining he muli-sep variance forecas condiional on Ω -1 as h + k Var( r + k Ω 1), and given he assumpion ha he reurns process r is covariance saionary (i.e., α + β < 1), he (1,1) muli-sep condiional k variance forecas is given by h + k = ω[1 ( α + β ) ]/( 1 α β ), which, as k, converges o he uncondiional variance [ ( ) ω / 1 α β ] = Var ( r ) σ, allowing he (1,1) model o be re-expressed as: h σ + α ε σ + β h σ ( ) ( ) = 1 1 (6) where he erms in parenheses have expeced values of zero, reflecing he consancy of volailiy in he long run. In conras, he componen model exends he expression in eq. (6) o allow he possibiliy ha long-run volailiy is no consan. Tha is, by allowing a ime-varying permanen componen, q, and is lagged value, o replace he consan long-run volailiy, σ, above, where he lagged forecasing error ( ε 1 h 1 ) serves as he driving force for he imedependen movemen of ha permanen componen: h = q + α ( ε 1 q 1 ) + β ( h 1 q 1 ) (7) q = ω + ρq 1 + φ( ε 1 h 1 ) (8) Published by Berkeley Elecronic Press, 008 5
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3 and he auoregressive roo, 0 < (α+β) < ρ 1, accommodaes he ofen empirically relevan case of (near-) inegraion in volailiy for ρ values of (close o) uniy. Thus, condiional variance is decomposed ino a permanen or long-run componen, and a ransiory or shor-run componen defined simply as (h -q ). The condiional variance is covariance saionary in his model if he permanen componen and he ransiory componen are boh covariance saionary, as saisfied by ρ < 1 and (α+β) < 1, respecively. Those values also quanifying he persisence of shocks o hese componen processes. For 1 > ρ > (α+β), he ransiory componen decays more quickly han he permanen componen such ha he laer dominaes forecass of he condiional variance as he forecasing horizon is exended, and evenually converges o a consan as long as he permanen componen is saionary: h + k = q + k = ω /( 1 ρ ) as k, for 0 < ρ < 1. Furher, by subsiuion using Eq (7) and (8), noe ha he componen model may be expressed alernaively as eiher a (,) model, or a (1,1) model wih ime-varying inercep, he laer being: h ω + ( ρ α β ) q ] + ( α + φ) ε + ( β φ h = [ 1 1 ) 1 such ha for ω > 0, α > 0, β > φ > 0, 1 > ρ > (α+β) > 0, he condiional variance h is ensured o be non-negaive as long as q is non-negaive. Since subsiuion also allows he permanen componen o be expressed as a (,) process, he resuls of Nelson and Cao (199) may be used o verify consrains for he nonnegaiviy of q, which in urn can be shown also o be saisfied under he resricions already given. Noe ha he componen model reduces o he (1,1) model if eiher α = β = 0, or ρ = φ = 0. Thus, he model is only capable of describing, a mos, one elemen of he more general condiional variance componen specificaion, and only represens he permanen componen under he specific condiions α = β = 0, ρ = 1. 4. Empirical resuls Coefficien esimaes for boh and componen models obained by maximum likelihood, ogeher wih Bollerslev and Wooldridge (199) nonnormaliy robus sandard errors, are repored in able 4 for each of he nine sock markes on a daily basis. Residual diagnosics for boh models are repored in able 5, and includes momen measures, Jacque-Berra ess for deparures from normaliy, Engle ARCH-LM (Engle, 198 ) ess, and BDS ess (Brock e al., 1996, 1987) of he null ha he series in quesion are iid agains an unspecified alernaive. Moreover, he persisence of shocks is measured by (α+β) for boh and ransiory componen, and by (ρ) for he permanen componen. According o (9) hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060 6
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes Engle and Bollerslev (1986), if α+β = 1, a curren shock persiss indefiniely in condiioning he fuure variance. Since he sum of α+β (and ρ in he permanen componen) represens he change in response funcion of shocks o volailiy persisence, a value greaer han uniy implies ha response funcion of volailiy increases wih ime and a value less han uniy implies ha shocks decay wih ime (Chou, 1988). The closer o uniy is he value of persisence measure, he slower is he decay rae. The preliminary (1,1) resuls confirm he presence of persisence in volailiy for six ou of nine markes under examinaion, of 0.985, 0.997, 0.548, 1.059, 0.973, and 0.995 for Kuwai, Palesine, Dubai, Oman, Saudi Arabia, and Egyp, respecively, wih corresponding half-lives of 46 days, 55 days, 1 day, 1 days, 5 days, and 15 days, respecively. While he resuls from model indicae ha Abu Dhabi, Jordan, and Bahrain do no exhibi persisence in volailiy. These resuls are confirmed by Wald ess of he null ha persisence is inegraed for models. Furhermore, he resuls indicae ha Oman exhibis an increasing response funcion of volailiy and shocks do no decay wih ime. Published by Berkeley Elecronic Press, 008 7
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3 Table 4 Volailiy Model Esimaes Coefficien Esimaes Marke Model ω ρ φ α β Kuwai AbuDhabi Palesine Dubai Jordan Oman Saudi Arabia Bahrain Egyp 0.0000* - - 0.1903* 0.7947* (0.0000) - - (0.0449) (0.0449) 0.000 0.9610* 0.955-0.174 1.0410* (0.0001) (0.0506) (0.59) (0.76) (0.3370) 0.0000* - - 0.1918* 0.6819* (0.0000) - - (0.074) (0.0364) 0.0000* 0.8938* 0.198* 0.0761-0.5345 (0.0000) (0.051) (0.0878) (0.0666) (0.4895) 0.0000* - - 0.4431* 0.5536* (0.0000) - - (0.0410) (0.078) 0.0086 0.998* 0.3714* 0.1577* 0.3535 (0.67) (0.0546) (0.150) (0.0418) (0.61) 0.0001* - - 0.5995-0.0518 (0.0000) - - (0.601) (0.066) 0.0001* 0.5760 0.014 0.1173-0.0757 (0.0000) (0.419) (0.04) (0.0761) (0.0754) 0.0000* - - 0.196* 0.7196* (0.0000) - - (0.048) (0.087) 0.0001* 0.9960* 0.039* 0.1993* 0.6803* (0.0000) (0.0039) (0.0174) (0.090) (0.047) 0.0000* - - 0.961* 0.7631* 0.0000 - - -0.0666-0.0350 0.0308* 0.9999* 0.19* -0.0455* -0.875* (0.0176) (0.0000) (0.0055) (0.0055) (0.010) 0.0000* - - 0.357* 0.6197* (0.0000) - - (0.0151) (0.0134) 0.000 0.9885* 0.1439 0.356* 0.6606* (0.0003) (0.0181) (0.1114) (0.0763) (0.0947) 0.0000* - - 0.003-0.0448* (0.0000) - - (0.155) (0.0143) 0.0001* 0.6177-0.0039 0.1601 0.046 (0.0000) (0.4636) (0.0130) (0.1317) (0.051) 0.0000* - - 0.1353* 0.8601* (0.0000) - - (0.0098) (0.0077) 0.0008 0.9943* 0.130* 0.0771 0.480 (0.0014) (0.010) (0.000) (0.0571) (0.6400) All sandard errors, in parenheses, adjused by he mehod of Bollerslev and Woolridge (199) * indicaes significan a he 5% level. hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060 8
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes Table 5 presens residual diagnosics for hese models and for he componen models discussed below, and indicae ha he degree of non-normaliy found o be saisically significan for boh models and all markes, validaing our use of robus sandard errors hroughou. For he models specifically, remaining diagnosics indicae he presence of residual ARCH srucure in Egyp only. However, hese resuls conradic BDS saisics, which broadly found o be significan for all (1,1) residuals for all markes oher han Abu Dhabi. The componen model implies he presence of a higher order srucure, consisen wih hese residual diagnosics for (1,1) models. The resuls of he componen models for Jordan, Oman, and Saudi Arabia show ha here exiss a permanen-ransiory componen decomposiion for hese hree markes wih all parameers saisically significan. While for he oher six markes, he ransiory parameers (α+β), or a leas one of hem, in he componen model are found o be saisically no significan. For Jordan, Oman, and Saudi Arabia, he persisence of shocks o he permanen componen is very high, in excess of 0.99 in Jordan and Oman. The persisence of shocks o he ransiory componen was found o be of values 0.88, -0.918, and 0.896 for Jordan, Oman, and Saudi Arabia, respecively. For hese hree markes he resuls imply ransiory componen half-lives of 5 days, 8 days, and 6 days, respecively, indicaing full decay of a shock o he ransiory componen wihin few days. Moreover, corresponding permanen componen half-lives are 173 days, 6931 days, and 60 days for Jordan, Oman, and Saudi Arabia, respecively. Thus, he effec of a shock o he permanen componen condiional volailiy over several monhs, even years in he case of Oman, which indicaes ha he ransiory componen decays more quickly han he permanen componen. Such ha, he laer dominaes forecass of he condiional variance as he forecasing horizons is exended, and evenually converges o a consan as long as he permanen componen is saionary, since he null hypohesis ha 1 > ρ > (α+β) canno be rejeced for each of he hree markes (Jordan, Oman, and Saudi Arabia). Addiionally, in comparison wih hese half-lives calculaed using permanen componen persisence measures for Jordan, Oman, and Saudi Arabia, he models repored above undersae volailiy shock half-lives by a facor of over en in Oman and Jordan, and by more han wo for Saudi Arabia. Published by Berkeley Elecronic Press, 008 9
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3 Table 5 Residual Diagnosics BDS(,d) BDS(3,d) BDS(4,d) Marke Model Mean S.D. Sk. Ku. JB A4 A8 A1 d = σ d = σ/ d = σ d = σ/ d = σ d = σ/ Kuwai AbuDhabi Palesine Dubai Jordan Oman -0.0595 0.0171 0.0500-0.133 0.038-0.0385 0.9995 1.0000 0.9990 0.9115 1.0004 0.999-0.3450 0.148-0.1358 8.4779 0.313 1.63 5.513 9.3944 8.138 33.614 5.5139 4.615 194.015* 1098.85* 1300.59* 444044* 656.766* 37446.39* 0.0667 0.0584 0.4417 0.016 1.1018 0.3714 0.6393 0.1161 0.768 0.0101 1.5451 0.3051 0.459 0.3457 0.5470 0.0098 1.0701 0.981 0.408 1.4545.1966*.3680* 1.967*.6878* 0.444 1.84 4.518* 5.109*.0056* 3.6856* 0.183 1.5335.546* 4.8097*.8863* 3.575* 0.0667 1.3343 6.0503* 7.3897* 3.41* 5.3874* 0.339.050*.111* 6.9388*.931* 3.680* -0.0851.1195* 6.4753* 9.4895* 3.5840* 5.8535* -0.0417 0.0170 0.0567-0.0306 0.084-0.0488 0.9989 0.9996 1.003 1.0115 0.999 1.0439-0.99 0.1108-0.1180 8.6341 0.3391 0.8980 5.099 9.307 7.8544 31.9794 5.009 0.4575 135.441* 1067.61* 1160.355* 410189* 584.584* 4356.85* 0.1819 0.1004 0.89 0.0105 1.1766 1.834 0.5791 0.1511 0.6078 0.0078 1.3114 1.0138 0.4553 0.3409 0.4157 0.0075 0.9570 0.769 1.147 0.7104 1.510 5.7346* 1.3190 5.094* 1.017 1.1696 3.569* 7.8101* 1.585 5.7767* 1.1915 1.3476.1894* 7.9056*.3656* 5.670* 0.9755 1.1861 5.4640* 9.873*.7598* 7.188* 1.69.0966.34* 9.6160*.5045* 5.6508* 0.860 1.9995 6.3785* 11.858* 3.1489* 7.946* -0.0017 1.0000-0.1358 10.0894 6461.595* 0.1149 0.3330 0.508 0.0959 0.575 0.5649 1.0939 1.94.89* Saudi Arabia 0.0007 1.000-0.159 10.080 6451.574* 0.1683 0.4648 0.6064-0.4407-0.4888-0.0336 0.5 0.810 1.581 Bahrain Egyp 0.0313 0.9730 11.5473 4.54 444449* 0.035 0.0134 0.0098 9.751* 10.115* 1.773* 1.531* 13.75* 15.1557* 0.0198 0.939 11.534 408.8693 878361* 0.0548 0.086 0.0198 11.3507* 11.306* 13.4195* 13.4007* 14.6856* 15.9834* 0.031 0.9995 0.347 9.0956 611.18* 1.3879 1.943 4.17*.4040*.751* 4.0770* 4.76* 5.040* 6.410* 0.0313 0.9993 0.891 9.0364 551.098* 0.4597 0.7445 4.087* 0.8136 0.8390.7315* 3.5519* 3.9775* 5.508* Sk. and Ku. denoe measures of he second and hird momens of skewness and kurosis, on he basis of which he Jacque-Berra es for normaliy is calculaed; JB, Ai denoes he i-h order Engle (198) ARCH es, disribued as χ i ; BDS denoes he Brock e al. (1987) es for deparures from iid defined over (m, d ) where m denoes embedding dimension and d disance (deermined wih reference o he sample residual sandard deviaion, σ), asympoically disribued as N (0,1). * indicaes asympoic es significance a he 5% level (wih he excepion of momen measures). hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060 10
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes On he basis of Wald ess, he hypohesis of inegraion in variance (ρ=1) can be rejeced for all markes oher han Abu Dhabi a he 5% significance level. The resuls for Egyp imply complee dissipaion of he ransiory componen and reversion o an inegraed model. Reducion of he componen model o he (1,1) form is confirmed by Wald ess of he null hypohesis parameer resricions ha α = β =0, ρ = 1. Furhermore, residual diagnosics for he componen model in able 5 sugges ha he componen model is able o capure all srucure wihin Saudi Arabia daily sock reurns, while BDS saisics indicae some remaining residual srucure for boh Oman and Jordan. Thus, an alernaive variance specificaions o hose employed here using higher frequency daa (inra-day daa) may prove fruiful in furher modeling ime series under examinaion here. These resuls can have various explanaions especially in he case of Oman and Saudi Arabia. One explanaion could be due o exisence of heerogeneous raders wih differen ime horizon sraegies in hese markes. This could be corroboraed by he sharp flucuaions of he Gulf sock markes recenly ha can be aribued parly o he exisence of speculaive aciviies. Anoher explanaion could be due o heerogeneous informaion flows and he processing mechanism of new informaion in hese markes. Such informaion processes may affec he volailiy srucure given ha previous sudies pu he informaion efficiency for hese markes under quesion a leas in he weak form of he efficien marke hypohesis EMH (Haque e al. 004; Abraham e al. 00; Abu Zarour 007). 5. Conclusion Müller e al. (1997) have suggesed ha heerogeneous marke agens characerized by differen rading horizons, impars boh shor-run and long-run volailiy, such ha he shor-run effecs dominae over highly-frequency inervals while he impac of a highly persisen process dominaes over long horizons. Andersen and Bollerslev (1997b) have alernaively suggesed ha such srucure resuls from he arrival of heerogeneous informaion o a financial marke. However, he sandard model implicily assumes homogeneiy of he price discovery process and is unable o capure hese effecs. This paper examined explici volailiy decomposiion using he variance componen model of Engle and Lee (1993) using daily daa for nine emerging markes in he Middle Eas region. We sared he analysis by providing some marke indicaors for each marke under examinaion. Descripive saisics for daily marke reurns of he general indices have been provided, while he saionariy for all ime series boh in levels and firs difference have been examined by he means of uni roo es (ADF, PP, KPSS). Published by Berkeley Elecronic Press, 008 11
Review of Middle Eas Economics and Finance, Vol. 4, No. [008], Ar. 3 Several models have been used o decompose he volailiy srucure for each marke: (1,1), he inegraed and he componen model. The exisence of a componen srucure o volailiy is suppored by he exisence of a ransiory componen o volailiy and a permanen volailiy ha decays over a much longer horizon in hree markes only: Jordan, Oman, and Saudi Arabia. Furhermore, he componen model was able o capure all srucure wihin he daa on he basis of he residual ess for Saudi Arabia. However, his canno be said for Oman and Jordan as some srucure in he residuals remain in hese wo markes. The exension of he analysis conduced here o high frequency reurn daa, when available, for such new emerging markes, would provide ineresing avenues for furher research. References: Abu Zarour, B. (007) The Halloween Effec Anomaly: Evidence from he MENA Equiy Markes, Sudies in Business and Economics, Volume 13, No. 1. Abraham, A., Sayyed, F. and Alsakran, A. (00) Tesing he random walk behavior and efficiency of he Gulf sock markes, The Financial Review 37, 469-80. Andersen T. G., & Bollerslev, T. (1997a), Inra-day periodiciy and volailiy persisence in financial markes, Journal of Empirical Finance, 4, 115 158. Andersen T. G., & Bollerslev, T. (1997b), Heerogeneous informaion arrivals and reurn volailiy dynamics: Uncovering he long-run in high frequency reurns, Journal of Finance, 5, 975 1005. Bollerslev, T. (1986), Generalized auoregressive heeroscedasiciy. Journal of Economerics, 31, 307 37. Bollerslev, T., and Wooldridge, J. M. (199), Quasi maximum likelihood esimaion and inference in dynamic models wih ime varying covariances, Economeric Reviews, 11, 143 17. Brock, W., Decher, W. and Scheinkman, J. (1987), A es for independence based on he correlaion dimension, Mimeo, Deparmen of Economics, universiy of Wisconsin a Madison, and Universiy of Houson. Brock, W., Decher, W. and Scheinkman, J. (1996), A es for independence based on he correlaion dimension, Economerics Review, 15, 197-35. Campbell, J. Y and Mankiw, N. G. (1987), Are oupu flucuaion ransiory? Quarerly Journal of Economics 10, 857-880. Chou, R. (1988), Volailiy persisence and sock valuaion: some empirical evidence using, Journal of Applied Economerics, 3, 79-94. hp://www.bepress.com/rmeef/vol4/iss/ar3 DOI: 10.0/1475-3693.1060 1
Zarour and Siriopoulos: Volailiy Decomposiion in he Middle Eas Sock Markes Dickey, D. and Fuller, W. (1979) Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of American Saisical Associaion 74, 47-31. Engle, F. and Bollerslev, T. (1986), Modeling he persisence of condiional variances, Economeric Review, 5, 1-50. Engle, R. F. (198), Auoregressive condiional heeroscedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 50, 987 1007. Engle, R. F., & Lee, G. G. J. (1993), A permanen and ransiory componen model of sock reurn volailiy, Deparmen of Economics, UCSD, Discussion Paper No: 9-44R. Ghose, D., & Kroner, K. F. (1996), s of volailiy in foreign exchange markes: An empirical analysis of high frequency daa, Deparmen of economics. Universiy of Arizona, mimeo. Haque, M., Hassan, M., Maroney, N. and Sackley, W. (004) An empirical examinaion of sabiliy, predicabiliy and volailiy of Middle Easern and African emerging sock markes, Review of Middle Eas Economics and Finance, 19-4. Kwiakowski, D., Phillips, P., Schmid, P. and Shine, Y. (199) Tesing he null hypohesis of saionariy agains he alernaive of a uni roo, Journal of Economerics 54, 159-78. Müller, U. A., Dacorogna, M. M., Davé, R. D., Olsen, R. B., Pice, O. V., and von Weizsäcker, J. E. (1997), Volailiies of differen ime resoluions analyzing he dynamics of marke componens, Journal of Empirical Finance, 4, 13 39. Nelson, D. B., and Cao, C. Q. (199), Inequaliy consrains in he univariae model, Journal of Business and Economic Saisics, 10, 9 35. Nelson, C. R., and Plosser, C. I. (198), Trends and Random walks in macroeconomic ime series: Some evidence and implicaions, Journal of Moneary Economics, 10, 139-16. Phillips, P. and Perron, P. (1988) Tesing for a uni roo in ime series regression, Biomerika 75, 335-46. Published by Berkeley Elecronic Press, 008 13