A DCC Analysis of Two Stock Market Returns Volatility with an Oil Price Factor: An Evidence Study of Singapore and Thailand s Stock Markets

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1 Journal of Convergence Informaion Technology Volume 4, Number 1, March 9 A DCC Analysis of Two Sock Marke Reurns Volailiy wih an Oil Price Facor: An Evidence Sudy of Singapore and Thailand s Sock Markes *Correspondingsauhor Deparmen of Hospial and Healh Care Adminisraion, Chia Nan Universiy of Pharmacy & Science, 6, Erh-Jen RD., Sec.1, Jen-Te, Tainan, Taiwan. hwj79@mail.chna.edu.w, mjmchyan@mail.chna.edu.w doi: /jci.vol4.issue1.horng Absrac This paper uses he Singapore and he Thailand s sock prices of maerial from January 4, o July, 7, discussing he model consrucion and heir associaions of beween Singapore and Thailand s sock markes, and also uses Suden's disribuion o analyze he proposed model. The empirical resuls show ha he muual affecs of he Singapore and he Thailand s sock markes may consruc in bivariae IGARCH (1, 1) model wih a DCC. The empirical resul also shows ha beween Singapore and Thailand s sock marke reurns exiss he posiive relaions- namely wo sock marke reurn s volailiy are synchronized influence, he average esimaion value of he DCC coefficien of wo sock marke reurns equals o Also, Singapore and Thailand's sock markes do no have he asymmerical effec in he research daa period. These evidences may sugges sock marke invesors or inernaional fund managers- before invesing in Singapore mus consider he Thailand sock price reurn s volailiy risk and is connecion. Therefore, in he sock marke, invesors and managers may no neglec he influence of he foreign counry s sock marke reurn volailiy behavior; oherwise, his decision will no achieve he anicipaed effec. Keywords Sock marke reurns, Singapore srai imes sock index, Bangkok se sock index, oil price, DCC, bivariae IGARCH model, Suden s disribuion, asymmerical effec. 1. Inroducion In recen years, under he inernaionalizaion and a liberalized idal curren, and urging he inernaional invesmen and he circulaion of capial increase, expers also caused beween he counry and he counry he sock marke a relaed ascension. Singapore's economical physique belongs parly o an island economy, where posiive includes o he foreign rade unfolds where ies beween Thailand and Singapore are close. We know ha Singapore is one of Asian four dragons, also Singapore economy of growh in 6 is 7.9%, and he forecas value of he grow rae is % in he fuure. And Singapore is also he Asia main financial cener, is foreign exchange marke is he fourh big rading marke in he world. We also know ha Thailand is also he major economical financial sysem in he Associaion of Souh-eas Asia Naions. Also, Thailand is geographically close o Singapore, herefore he relaion beween Thailand and Singapore sock markes is worh furher discussing. Beween he research sock marke he reurn volailiy mehod has many models, such as auoregressive moving average (ARMA) model, bu from scholar Engle (198) proposes he auoregressive condiionally heeroskedasiciy (ARCH) model and Bollerslev (1986) proposes he generalized auoregressive condiionally heeroskedasiciy (GARCH) model. Ye where his kind of model comparaively may cach he financial propery he variaion number is no he fixed characerisic. Bu aferwards, scholars like Nelson (199) discovered ha negaive direcion in he markes will have a differen influence on he fuure sock price volailiy. Bu he GARCH model supposes he seled ime condiional variance for he preceding issue of condiional variance, wih error erm a square funcion; herefore, error erms boh he posiive and negaive did no exis o he condiional variance influence. Therefore, several condiion variaions can change along wih error erm size value, bu canno change along wih he posiive and negaive marks. To improve his flaw, Nelson (1991) proposes he so-called exponenial GARCH model and Glosen, Jaganahan and Runkle (1993) propose he so-called hreshold GARCH model. For he research of asymmeric problems, one may also 63

2 A DCC Analysis of Two Sock Marke Reurns Volailiy wih an Oil Price Facor: An Evidence Sudy of Singapore and Thailand s Sock Markes refer o Poon and Fung (), Chrisie (198), French, Schwer and Sambaugh (1987), Campell and Henschel (199), Koumos and Booh (1995), and Koumos (1996). Aferwards, sudies of he reurn volailiy mehod grew vigorously, proposing such hings as he mulivariae GARCH model. For examples, see Yang (5), Yang and Doong (4), Granger, Hung and Yang (), and Bollerslev (199) for he applicaion of bivariae GARCH model. In his paper, he Suden s disribuion is adoped and he maximum likelihood algorihm mehod of BHHH (Bernd e. al., 1974) is used o esimae he model s unknown parameers. The programs of RATS and EVIEWS are used in his paper. Beside, one also discusses he influence of he oil price reurn on he Singapore and Thailand sock markes. This paper is organized as follows. Secion descibes he daa characerisics of Singapore and Thailand s sock prices and he volailiy of heir reurns, and he daa characerisic of oil prices; Secion 3 gives he asymmeric es of bivariae GARCH model wih a DCC; Secion 4 gives he propoded model of bivariae GARCH wih a DCC and is esimaed parameers, and an analysis of relaed Singapore and Thailand s sock reurns; Secion 5 gives he empirical resuls of he proposed model; Secion 6 gives he conclusion.. Daa characerisics.1 Basic saisics and rend chars ( RTHAIL ) for every day closing price naural logarihm difference, rides 1 again, his namely RTHAIL = 1 (log( THAIL / THAIL )), in which THAIL represens he -h dae of he Thailand s sock closing price. ; The oil price marke reurn ( ) for every day closing price naural logarihm difference, rides 1 again, his namely = 1 (log( OP / OP )), in which OP represens he -h dae of he WTI s oil price closing price. In Figure 1, he Singapore and Thailand s sock price reurn volailiy shows he clusering phenomenon, so ha we may know he Singapore sock marke and Thailand s sock marke have cerain relevance. And reurn rae of oil price can also affec he sock marke. By he uni roo es as below, he reurn rae of he Singapore s sock index, he reurn rae of he Thailand sock index, and he reurn rae of he oil price are all saionary sequences. The basic saisics of hese sequences are saed in Table 1. According o Table 1, as shown by he Jarque-Bera saisics under he null hypoheses of normal disribuion, hose hree markes do no obey he assumpion of normal disribuion. Therefore, he heavy ails disribuion is used o evaluae he proposed model. The research sample period was from January 4, o July, 7, and he maerial origin akes from Taiwan economy journal (TEJ), a daabase in Taiwan. Among hem, he Singapore sock price is he Singapore srai imes sock price index, he Thailand s sock price for Bangkok se sock price index. The oil price is he WTI oil price. The oil price daa origin akes from Energy Informaion Adminisraion (EIA), a daabase in U.S. In he daa processing aspec, he markes do no do business on respecive Singapore and Thailand s holidays; herefore when a sock marke is closed, his aricle delees he idenical ime sock price maerial and conforms o he oher sock marke's common rading day; herefore wo variable samples afer processing each will be 1738 from now on. The Singapore sock marke reurn ( ) for every day closing price naural logarihm difference, rides 1 again, his namely = 1 (log( SING / SING 1)), in which SING represens he -h dae he Singapore sock closing price; The Thailand s Sock marke reurn 64

3 Journal of Convergence Informaion Technology Volume 4, Number 1, March resuls is lised in Table. I shows ha he reurn rae of he Singapore s sock index, he reurn rae of he Thailand sock index, and he reurn rae of he oil price do no have he uni roo characerisic- namely, he hree markes are saionary ime series daa, under α =1% significance level RTHAIL Figure 1. Tend chars of Singapore and Thailand s sock price index reurn rae, and he reurn rae of oil price. Table 1. Basic saisics of he research daa Saisics SING THAIL RTHAIL Mean Sandard deviaion J-B (p-value) (.) 165 *** (.) 7.7 (.) 833 *** (.) Sample Saisics OP Mean Sandard deviaion J-B (p-value) (.) (.) Sample Noe: (1) J-B denoes he normal disribuion es of *** Jarque-Bera. () denoes significance a levelα =1%.. Uni roo es and Co-inegraion es This paper furher uses he uni roo ess of ADF (Dickey and Fuller, 1979 and 1981) and KSS (Kapeanios e al., 3) o deermine he sabiliy of he ime series daa. The ADF and KSS examinaion Table. Uni roo es of ADF and KSS mehods ADF RTHAIL Saisic Criical value (α =1%), (α =5%) KSS RTHAIL Saisic Criical value -.8 (α =1%), -. (α =5%) ADF Saisic Criical value (α =1%), (α =5%) KSS Saisic Criical value -.8 (α =1%), -. (α =5%) Noe: *** denoes significance a he 1% level. By he coinegraion es of Johansen (1991), we know ha he saisics of is no significan under λ max he level α = 5% in Table 3. This demonsraes ha hose hree markes of he he reurn rae of he Singapore s sock index, he reurn rae of he Thailand sock index, and he reurn rae of he oil price do no have co-inegraion of heir relaions. Therefore, we are no considered he model of error correcion. Table 3. Johansen co-inegraion es (VAR lag=4) Null H λ max Criical value None A mos A mos Noe: The lag of VAR is seleced by he AIC rule (Akaike, 1973). The criical value is given under he 5% level..3 ARCH effec es Based on he formula (1) and () as below, we uses he mehods of LM es (Engle, 198) and F es (Tsay, 4) o es he condiionally heeroskedasiciy phenomenon. In Table 4, he resuls of he ARCH effec es show ha hese wo markes have he condiionally heeroskedasiciy phenomenon exiss. 65

4 A DCC Analysis of Two Sock Marke Reurns Volailiy wih an Oil Price Facor: An Evidence Sudy of Singapore and Thailand s Sock Markes This resul suggess ha we can use he GARCH model o mach and analyze i. The deail is omied here. Table 4. ARCH effec es Engle LM es Tsay F es Saisics (p-value) (.) (.) RTHAI L Engle LM es Tsay F es Saisics (p-value) (.) (.) Noe: *** denoes significance a levelα =1%. 3. Asymmeric es of he bivariae ARCH model wih a DCC The bivariae IGARCH(1, 1) model wih a DCC can be consruced in he nex secion. The asymmeric es mehods (Engle and Ng, 1993) are used he following wo mehods as: negaive size bias es and join es. Table 5 asymmerically examines he resul for he Singapore sock marke as: (1) The posiive size bias es does no reveal (α =1%). () The join es does no reveal ( α =1%). Table 5 asymmerically examines he resul for he Thailand sock marke as: (1) The posiive size bias es does no reveal ( α =1%). () The join es does no reveal (α =1%). The resuls of asymmeric es sugges ha he proposed model does no need o use he asymmeric GARCH model. Table 5. Asymmeric es of he bivariae IGARCH Asymmeric Posiive size Join es es bias es F saisic (p-value) (.331) (.4473) Asymmeric Posiive size Join es es bias es RTHAIL F saisic (p-value) (.8145) (.795) Noes: p-value <α denoes significance. (α =5%) 4. Proposed model A dynamic condiional correlaion (DCC) and he bivariae GARCH(1, 1) model is proposed in his secion, is model may be expressed as = + φ 1 φ1rthail + φ 1 + a (1) 1, RTHAIL = + ϕ RTHAIL 1 ϕ 1 + ϕ 1 + a (), ' a = ( a1,, a, ) ~ Tv (,( ν ) H / ν ) (3) h, = α 1 + αa1, 1 + βh, + η1 (4) h α α a β h η, = + 1, 1 + 1, + q (5) = + + 1ρ 1 a1, a, / h, h, ρ exp( q ) /(exp( q ) + 1) (6) = h 1, = ρ h, h (7), Where Tv (, ( v ) H / v) denoes he bivariae Suden s disribuion, is mean is equal o and is covariance marix is equal o ( v ) H / v, and v is he degree of freedom. The DCC and he bivariae GARCH model can also refer o he papers of Engle () and Tse and Tsui (1). 5. Empirical resuls Table 6 shows he esimae resuls for he Singapore s sock index reurn rae and Thailand sock index reurn rae by he DCC and he bivariae IGARCH(1, 1) model. we know ha he esimaed value of is coefficien wheher remarkable, examines each coefficien significance by he P-value. In selecs in sample period, he Singapore sock price reurn receives he previous one periods impac ( φ 1 =.37) of he Thailand sock price reurn, and i has no caused he Singapore sock price reurn o fall a lae effec impac; The Thailand s sock price reurn receives he he previous one periods impac ( ϕ =.495), and i has no appeared o cause he Singapore s sock price reurn o fall he lae effec. The Singapore sock price reurn also receives he previous one periods impac of he oil price reurn ( φ =.7), and he Thailand sock price reurn also receives he previous one periods impac =.94) of he oil price reurn. On he oher ϕ ( hand, he average esimaion value ( ρˆ =.3876) of he DCC coefficien of he Singapore sock price reurn and he Thailand s sock price reurn volailiy is significan, and shows he Singapore sock price reurn he volailiy is a posiive influence on Thailand s sock 66

5 Journal of Convergence Informaion Technology Volume 4, Number 1, March 9 price reurn volailiy. The synchronized muual influence, when variaion of risk of he Thailand s sock price reurn increases, enables he money marke invesor o see risk of he Singapore sock price reurn also increase; likewise, when variaion of risk of he Thailand s sock price reurn reduces, he invesor sees he risk of he Singapore sock price reurn reduce as well. In addiion, esimaed value of he degree of freedom for he Suden's disribuion is 5.691, under he significance levelα =1%. This is remarkable, and shows his research maerial has he hick ail disribuion. Moreover, Singapore sock reurn condiional variance and he Thailand s sock reurn condiional variance all can affec he Singapore and Thailand s sock price reurn volailiy. Also models seen in Table 6 ha, in he condiional variance equaion, we have α + β + η1 = 1 and α 1 + β 1 + η = 1 wih boh equals o 1, conforms o parameer of he IGARCH model condiion supposiion. This also demonsraes he bivariae IGARCH(1, 1) model wih a DCC may cach beween he Singapore sock price reurn and he Thailand s sock price reurn volailiy process. Table 6. Parameer esimaion of he DCC and he bivariae EGARCH(1, ) model Parameer φ φ 1 φ Coefficien (p-value) (.5966) (.165) (.79) Parameer ϕ ϕ ϕ 1 Coefficien (p-value) (.767) (.848) (.68) Parameer α 1 α β Coefficien (p-value) (.484) (.) (.) Parameer η 1 α α 1 Coefficien (p-value) (.81) (.14) (.) Parameer β 1 η Coefficien (p-value) (.) (.416) (.) Parameer 1 Coefficien ν (p-value) (.) (.) (.) Parameer ρ min ρ max ρ Coefficien (p-value) (.) Noe: p-value<α denoes significance. (α =1%,α =5%,α =1%); α is he significance level. min ρ denoes he minimum value of ρ and max ρ denoes he maximum value of ρ. To es he inappropriaeness of he DCC and he bivariae IGARCH(1, 1) model, he es mehod of Ljung and Box (1978) is used o examine auocorrelaion of he sandard residual error. This model does no show an auocorrelaion of he sandard residual error, he deails are omied. Therefore, he DCC and he bivariae IGARCH(1, 1) model are more appropriae. 6. Conclusions The empirical diagnosis resul shows ha regarding Singapore and Thailand s sock price reurn volailiy, he reciprociy may consruc in he bivariae Suden's disribuion and he bivariae IGARCH(1, 1) model wih a DCC; his model also passes hrough a sandard residual error relevance and ARCH effec examinaion showing he use of bivariae IGARCH(1, 1) model wih a DCC, which evaluaes wo sock markes reurn he volailiy processes is appropriae. The empirical diagnosis resul also shows ha he average esimaion value ( ρˆ =.3876) of he DCC coefficien of wo sock markes reurn is he posiive relaion- he Singapore sock reurn volailiy is affecing he Thailand s sock reurn, also he Thailand s sock reurn volailiy is affecing he Singapore sock reurn, bringing forh a synchronizaion. The empirical resul also shows ha Singapore and Thailand s sock price marke reurn volailiy receives he impac of he oil price reurn volailiy. The empirical resuls presen ha he volailiy process do no have asymmerical in he Singapore and Thailand s sock markes. The empirical resuls also show ha he Singapore sock reurn rae s volailiy rae ruly has an affec on he Thailand s sock marke reurn rae s volailiy. However, he proposed model is differen from he model of he bivariae GARCH wih a consan condiional correlaion (CCC). Based on he paper of (Engle, ), he DCC and he bivariae GARCH model have 67

6 A DCC Analysis of Two Sock Marke Reurns Volailiy wih an Oil Price Facor: An Evidence Sudy of Singapore and Thailand s Sock Markes a beer explanaory abiliy compared o he radiional bivariae GARCH model wih a CCC. 7. References [1] H. Akaike, Informaion heory and an exension of he maximum likelihood principle, In nd. Inernaional Symposium on Informaion Theory, edied by B. N. Perov and F. C. Budapes: Akademiai Kiado, 1973, pp [] E.K. Bernd, B.H. Hall, R.E. Hall, and J.A. Hausman,. Esimaion and inference in nonlinear srucural models, Annals of Economic and Social Measuremen, 4, 1974, pp [3]T. Bollerslev, Generalized Auoregressive Condiional Heroscedasiciy, Journal of Economerics,, 1986, pp [4] A.A. Chrisie, The Sochasic Behavior of Common Sock Variances: Value, Leverage and Ineres Rae Effecs, Journal of Financial Economics 1, 198, pp [5] J.Y. Campell, and L. Henschel, No news is good news: An asymmeric model of changing volailiy in sock reurns Journal of Financial Economic,, 199, pp.81-8 [6] T. Bollerslev, Modeling he coherence in shor-run nominal exchange raes: a mulivariae generalized ARCH model, Review of Economics and Saisics,7, 199, pp [7] D.A. Dickey, and W.A. Fuller, Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion, 74, 1979, pp [8]D.A. Dickey, and W.A. Fuller, Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica, 49, 1981, pp [9] R.F. Engle, Auoregressive condiional heeroskedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 5, 198, pp [1] R.F. Engle, and V.K. Ng, Measuring and Tesing he Impac of News on Volailiy, Journal of Finance, 48(5), 1993, pp [] R.F. Engle, Dynamic condiional correlaion- a simple class of mulivariae GARCH models, Journal of Business and Economic Saisics,,, pp [1] S. Johansen, Esimaion and hypohesis esing of coinegraion vecor in Gaussian vecor auoregressive models, Economerica, 59, 1991, pp [13] G. Kapeanios, Y. Shin, and A. Snell, Tesing for a uni roo in he nonlinear STAR framework, Journal of Economerics, (), 3, pp [1] C. Kearney, The causes of volailiy in a small, inernaionally inegraed sock marke: Ireland, July June 1994, Journal of Financial Research, 1, 1998, pp [] G.M. Ljung, and G.E.P. Box, On a measure of lack of fi in ime series models, Biomerika, 65, 1978, pp [1] C.C. Nieh, and C.F. Lee, Dynamic relaionship beween sock prices and exchange raes for G-7 counries, The Quarerly of Economics and Finance, 41, 1, pp [13] D.B. Nelson, Saionariy and persisence in he GARCH(1,1) model, Economeric Theory 6, 199, pp [14] D.B. Nelson, Condiional heeroscedasiciy in asse reurns: A new Approach, Economerica, 59, 1991, pp [15] Tsay, R.S., Analysis of Financial Time Series. New York: John Wiley & Sons, Inc., 4. [16] Y.K. Tse, and Alber K.C. Tsui, A mulivariae GARCH model wih ime-varying correlaions, Journal of Business & Economic Saisics, (3),, pp [17] S.Y. Yang, and S.C. Doong, Price and volailiy spillovers beween sock prices and exchange raes: empirical evidence from he G-7 counries, Inernaional Journal of Business and Economics 3(), 4, pp [18]K.R. French, G.W. Schwer, and R.E. Sambaugh, Expeced Sock Reurns and Volailiy, Journal of Financial Economics, 19, 1987, pp.3-9. [19]C.W. Granger, J.B. Hung, and C.W. Yang, A bivariae causaliy beween sock prices and exchange raes: evidence from recen Asian Flu, The Quarerly Review of Economics and Finance 4,, pp []L.R. Glosen, R. Jagannahan, and D.E. Runkle, On he Relaion Beween he Expeced Value and he Volailiy on he Nominal Excess Reurns on Socks, Journal of Finance 48, 1993, pp [1]G. Koumos, and G.G. Booh, Asymmeric volailiy ransmission in inernaional sock markes, Journal of Inernaional Money and Finance 14, 1995, pp

7 Journal of Convergence Informaion Technology Volume 4, Number 1, March 9 []G. Koumos, Modeling he Dynamic Inerdependence of Major European Sock Markes, Journal of Business Finance and Accouning 3, 1996, pp [3]G.M. Ljung, and G.E.P. Box, On a measure of lack of fi in ime series models, Biomerika 65, 1978, pp [4]D.B. Nelson, Saionariy and persisence in he GARCH(1,1) model, Economeric Theory 6, 199, pp [5]W.P.H. Poon, and H.G. Fung, Red chip or H shares : Which China-backed securiies process informaion he fases?, Journal of Mulinaional Financial Managemen 1,, pp [6]S.Y. Yang, (5). A DCC analysis of inernaional sock marke correlaions: he role of Japan on he Asian Four Tigers. Applied Financial Economics Leers 1(), 5, pp