A DCC Analysis of Two Exchange Rate Market Returns Volatility with an Japan Dollars Factor: Study of Taiwan and Korea s Exchange Rate Markets

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1 A DCC Analysis of Two Exchange Rae Marke Reurns Volailiy wih an Japan Dollars Facor: Sudy of Taiwan and Korea s Exchange Rae Markes *,Correspondingauhor * Deparmen of Hospial and Healh Care Adminisraion, Chia Nan Universiy of Pharmacy & Science, 6, Erh-Jen RD., Sec., Jen-Te, Tainan, Taiwan. Deparmen of Informaion Managemen, Chia Nan Universiy of Pharmacy & Science, 6, Erh-Jen RD., Sec., Jen-Te, Tainan, Taiwan. hwj79@mail.chna.edu.w, joyce@mail.chna.edu.w doi:.456/jci.vol4.issue4. Absrac This paper discuss he associaions and model consrucion beween Taiwan and Korea s exchange rae markes during he period from January o July 8. The empirical resuls show ha he muual effecs of he Taiwan and he Korea s exchange rae markes may consruc in bivariae IGARCH (, ) model. The empirical resul also shows ha here exiss he posiive relaions beween Taiwan and Korea s exchange rae markes - namely wo exchange rae marke reurn s volailiy are synchronized influenced, and he average esimaion of he DCC coefficien of wo exchange rae markes equals o.473. The Japan s exchange rae reurn s volailiy will also affec he variaion risk of he Taiwan s exchange rae marke, bu he Japan s exchange rae reurn s volailiy will no affec he variaion risk of he Korea s exchange rae marke. Furhermore, Taiwan and Korea's exchange rae markes do no have he asymmerical effec in he research period. Keyword Exchange rae marke reurns, DCC, bivariae IGARCH model, Suden s disribuion, asymmerical effec.. 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 exchange rae marke a relaed ascension. Taiwan's economical physique belongs parly o an island economy, where posiive includes o he foreign rade unfolds where ies beween Korea and Japan are close. We know ha Korea is one of Asian four dragons, also Korea economy of growh in 6 is 7.9%, and he forecas of he grow rae is % in he fuure. And Japan is also he Asia main financial cener, is foreign exchange marke is he fourh big rading marke in he world. We also know ha Also, Taiwan is geographically close o Korea, herefore he relaion beween Taiwan and Korea exchange rae 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 (98) proposes he auoregressive condiionally heeroskedasiciy (ARCH) model and Bollerslev (986) 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 (99) 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, bu canno change along wih he posiive and negaive marks. To improve his flaw, Nelson (99) proposes he so-called exponenial GARCH model and Glosen, Jaganahan and Runkle (993) propose he so-called hreshold GARCH model. For he research of asymmeric problems, one may also refer o Horng and Lee (8), Poon and Fung (), Chrisie (98), French, Schwer and Sambaugh (987), Campell and Henschel (99), Koumos and Booh (995), and Koumos (996). Aferwards, 7

2 A DCC Analysis of Two Exchange Rae Marke Reurns Volailiy wih an Japan Dollars Facor: Sudy of Taiwan and Korea s Exchange Rae Markes 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 (99) 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., 974) 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 Japan s exchange rae reurn on he Taiwan and Korea s exchange rae markes. This paper is organized as follows. Secion descibes he daa characerisics of Taiwan s and Korea s exchange rae and he volailiy of heir reurns, and he daa characerisics of Japan s exchange rae; 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 Taiwan s and Korea s exchange rae reurns; Secion 5 gives he empirical resuls of he proposed model; Secion 6 gives he conclusions.. Daa characerisics. Basic saisics and rend chars The research sample period was from January 3, o July 3, 8, and he maerial origin akes from Taiwan economy journal (TEJ), a daabase in Taiwan. Among hem, he Taiwan s exchange rae price is he Taiwan dollars (US dollars) in New York marke, he Korea s exchange rae price is he Korea dollars (US dollars) in he New York marke. The Japan s exchange rae price is he Japan dollars (US dollars) in he New York marke. In he daa processing aspec, he markes do no do business on respecive Taiwan s and Korea 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 75 from now on. The Taiwan s exchange rae marke reurn ( ) for every day closing price naural logarihm difference, rides again, his namely = (log( TER / TER )), in which TER represens he -h dae he Taiwan s exchange rae closing price; The Korea s exchange rae marke reurn ( RKER ) for every day closing price naural logarihm difference, rides again, his namely RKER = (log( KER / KER )), in which KER represens he -h dae of he Korea s exchange rae closing price. ; The Japan s exchange rae marke reurn ( ) for every day closing price naural logarihm difference, rides again, his namely = (log( JER / JER )), in which JER represens he -h dae of he Japan s exchange rae closing price. In Figure, he Taiwan s and Korea s exchange rae reurn volailiy shows he clusering phenomenon, so ha we may know he Taiwan exchange rae marke and Korea s sock marke have cerain relevance. And reurn rae of Japan s exchange rae can also affec he exchange rae marke. By he uni roo es as below, he reurn rae of he Taiwan s exchange rae, he reurn rae of he Korea exchange rae, and he reurn rae of he Japan s exchange rae are all saionary sequences. The basic saisics of hese sequences are saed in Table. From Table, he average reurn rae of he Taiwan s exchange rae is -., he average reurn rae of he Korea s exchange rae is -.54, and he average reurn rae of he Japan s exchange rae is.8. The variaion risk of he Taiwan s exchange rae reurn rae is.999, he variaion risk of he Korea s exchange rae reurn rae is.477, and he variaion risk of he Japan s exchange rae reurn rae is.666, and herefore he variaion risk of he Japan s exchange rae reurn rae is he highes. According o Table, 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. 8

3 RKER 5 5 Figure. Tend chars of Taiwan s and Korea s exchange rae reurn rae, and he reurn rae of Japan s exchange rae. Table. Basic saisics of he research daa Saisics TER KER RKER Mean Sandard deviaion J-B (p-).68 (.) 7774 *** (.) 45. (.) 547 *** (.) Sample Saisics JER Mean Sandard deviaion J-B (p-) 53.8 (.) (.) Sample Noe: () J-B denoes he normal disribuion es of *** Jarque-Bera. () levelα =%. denoes significance a. Uni roo es and Co-inegraion es This paper furher uses he uni roo ess of ADF (Dickey and Fuller, 979 and 98) and KSS (Kapeanios e al., 3) o deermine he sabiliy of he ime series daa. The ADF and KSS examinaion resuls is lised in Table. I shows ha he reurn rae of he Taiwan s exchange rae, he reurn rae of he Korea s exchange rae, and he reurn rae of he Japan s exchange rae do no have he uni roo characerisic- namely, he hree markes are saionary ime series daa, under α =% significance level. Table. Uni roo es of ADF and KSS mehods ADF RKER Saisic Criical (α =%), -3.4 (α =5%) KSS RKER Saisic Criical -.8 (α =%), -. (α =5%) ADF Saisic Criical (α =%), -3.4 (α =5%) KSS Saisic Criical -.8 (α =%), -. (α =5%) *** Noe: denoes significance a he % level. By he coinegraion es of Johansen (99), we know ha he saisics of λmax is no significan under he level α = 5% in Table 3. This demonsraes ha hose hree markes of he he reurn rae of he Taiwan s exchange rae, he reurn rae of he Korea s exchange rae, and he reurn rae of he Japan s exchange rae do no have co-inegraion of heir relaions. Therefore, we are no considered he model of error correcion in his paper. In Table 4, hese hree exchange rae markes can really affec one anoher. Therefore, we go a sep furher o undersand he ineracions of he hree exchange rae markes. Table 3. Johansen co-inegraion es (VAR lag=) Null H λ max Criical None A mos A mos Noe: The lag of VAR is seleced by he AIC rule (Akaike, 973). The criical is given under he 5% level. 9

4 A DCC Analysis of Two Exchange Rae Marke Reurns Volailiy wih an Japan Dollars Facor: Sudy of Taiwan and Korea s Exchange Rae Markes Table 4. Uncondiional correlaion marix Coefficien RKER RKER ARCH effec es Based on he formula () and () as below, we uses he mehods of LM es (Engle, 98) and F es (Tsay, 4) o es he condiionally heeroskedasiciy phenomenon. In Table 5, he resuls of he ARCH effec es show ha hese wo markes have he condiionally heeroskedasiciy phenomenon exiss. This resul suggess ha we can use he GARCH model o mach and analyze i. The deail is omied here. Table 5. ARCH effec es Engle LM es Tsay F es Saisics *** *** (p-) (.) (.) RKER Engle LM Tsay F es es Saisics ***.695 *** (p-) (.) (.) Noe: *** denoes significance a levelα =%. 3. Asymmeric es of he bivariae ARCH model wih a DCC The bivariae IGARCH(, ) model wih a DCC can be consruced in he nex secion. The asymmeric es mehods (Engle and Ng, 993) are used he following wo mehods as: negaive size bias es and join es. Table 6 asymmerically examines he resul for he Taiwan s exchange rae marke as: () The posiive size bias es does no reveal (α =%). () The join es does no reveal ( α =%). Table 6 asymmerically examines he resul for he Korea s exchange rae marke as: () The posiive size bias es does no reveal ( α =%). () The join es does no reveal (α =%). The resuls of asymmeric es sugges ha he proposed model does no need o use he asymmeric GARCH model. Table 6. Asymmeric es of he bivariae IGARCH Asymmeric Posiive size Join es bias es es F saisic (p-) (.49) (.468) RKER Asymmeric es Posiive size bias es Join es F saisic (p-) (.34) (.5379) Noes: p- <α denoes significance. (α =5%) 4. Proposed model A dynamic condiional correlaion (DCC) and he bivariae GARCH(, ) model wih a facor of Japan exchange rae reurn is proposed in his secion, is model may be expressed as = RKER 3 a (), RKER = RKER 3 a (), ' a = ( a,, a, ) ~ Tv (,( ν ) H / ν ) (3) h α α a β h q h, =,, η (4), = α α a, β h, γ η (5) γ ρ γ = a, a, / h, h, ρ exp( q ) /(exp( q ) ) (6) = h, = 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 (). 5. Empirical resuls Table 7 shows he esimae resuls for he Taiwan s exchange rae reurn rae and Korea s exchange rae reurn rae by he DCC and he bivariae IGARCH(, ) model. we know ha he esimaed of is coefficien wheher remarkable, examines each

5 coefficien significance by he P-. In selecs in sample period, he Taiwan s exchange rae reurn receives he previous one periods impac of he Taiwan s exchange rae reurn ( =-.745), he Taiwan s exchange rae reurn receives he previous one periods impac of he Korea s exchange rae reurn ( =.5), and i also receives he previous one periods impac of he Japan s exchange rae reurn ( 3 =.397); The Korea s exchange rae reurn receives he previous one periods impac of he Korea s exchange rae reurn ( =-.97), and i also receives he previous one periods impac of he Taiwan s exchange rae reurn( =.37). The Korea s exchange rae reurn also receives he previous one periods impac of he Japan s exchange rae reurn ( 3 =.8). On he oher hand, he average ρˆ esimaion ( =.473) of he DCC coefficien of he Taiwan s exchange rae reurn and he Korea s exchange rae reurn volailiy is significan, and shows he Korea s exchange rae reurn he volailiy is a posiive influence on Taiwan s exchange rae reurn volailiy. The synchronized muual influence, when variaion of risk of he Korea s exchange rae reurn increases, enables he money marke invesor o see risk of he Taiwan s exchange rae reurn also increase; likewise, when variaion of risk of he Korea s exchange rae reurn reduces, he invesor sees he risk of he Taiwan s exchange rae reurn reduce as well. In addiion, esimaed of he degree of freedom for he Suden's disribuion is , under he significance level α =%. This is remarkable, and shows his research maerial has he hick ail disribuion. Moreover, Taiwan s exchange rae reurn condiional variance and he Korea s exchange rae reurn condiional variance all can affec he Taiwan s and Korea s exchange rae reurn volailiy. Also models seen in Table 6 ha, in he condiional variance equaion, we have α β η = and α β η = wih boh equals o, conforms o parameer of he IGARCH model condiion supposiion. And he Japan s exchange rae reurn s volailiy ( η =.4) will also affec he variaion risk of he Taiwan s exchange rae marke, bu he Japan s exchange rae reurn s volailiy will no affec he variaion risk of he Korea s exchange rae marke. This also demonsraes he bivariae IGARCH(, ) model wih a DCC may cach beween he Taiwan s exchange rae reurn and he Korea s exchange rae reurn volailiy process. Table 7. Parameer esimaion of he DCC and he bivariae IGARCH(, ) model Parameer Coefficien (p-) (.84) (.3) (.343) Parameer 3 Coefficien (p-) (.) (.6) (.) Parameer 3 Coefficien.37.8 (p-) (.) (.) Parameer α α β Coefficien (p-) (.) (.) (.) Parameer η α α Coefficien (p-) (.66) (.) (.) Parameer β η Coefficien (p-) (.) (.463) (.) Parameer γ γ γ Coefficien (p-) (.) (.) (.6) Parameer ρ min ρ max ρ Coefficien (p-) (.) Noe: p-<α denoes significance. ( α =%, α =5%, α =%); α is he significance level. min ρ denoes he minimum of max ρ denoes he maximum of ρ. ρ and To es he inappropriaeness of he DCC and he bivariae IGARCH(, ) model, he es mehod of Ljung and Box (978) is used o examine ν

6 A DCC Analysis of Two Exchange Rae Marke Reurns Volailiy wih an Japan Dollars Facor: Sudy of Taiwan and Korea s Exchange Rae Markes 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(, ) model are more appropriae. 6. Conclusions The empirical diagnosis resul shows ha regarding Taiwan s and Korea s exchange rae reurn volailiy, he reciprociy may consruc in he bivariae Suden's disribuion and he bivariae IGARCH(, ) model wih a DCC; his model also passes hrough a sandard residual error relevance and ARCH effec examinaion showing he use of bivariae IGARCH(, ) model wih a DCC, which evaluaes wo exchange rae markes reurn he volailiy processes is appropriae. The empirical diagnosis resul also shows ha he average ρˆ esimaion ( =.473) of he DCC coefficien of wo exchange rae markes reurn is he posiive relaion- he Korea s exchange rae reurn volailiy is affecing he Taiwan s exchange rae reurn, also he Taiwan s exchange rae reurn volailiy is affecing he Korea s exchange rae reurn, bringing forh a synchronizaion. The empirical resul also shows ha Taiwan s and Korea s exchange rae marke reurn volailiy receives he impac of he Japan s exchange rae reurn volailiy. The empirical resuls presen ha he volailiy process do no have asymmerical in he Taiwan s and Korea s exchange rae markes. The empirical resuls also show ha he Taiwan exchange rae reurn rae s volailiy rae ruly has an affec on he Korea s exchange rae marke reurn rae s volailiy. And he Japan s exchange rae reurn s volailiy will also affec he variaion risk of he Taiwan s exchange rae marke, bu he Japan s exchange rae reurn s volailiy will no affec he variaion risk of he Korea s exchange rae marke. 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 a beer explanaory abiliy compared o he radiional bivariae GARCH model wih a CCC. 7. References [] 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, 973, 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, 974, pp [3]T. Bollerslev, Generalized Auoregressive Condiional Heroskedasiciy, Journal of Economerics, 3, 986, pp [4] A.A. Chrisie, The Sochasic Behavior of Common Sock Variances: Value, Leverage and Ineres Rae Effecs, Journal of Financial Economics,, 98, 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, 3, 99, pp.8-38 [6] T. Bollerslev, Modeling he coherence in shor-run nominal exchange raes: a mulivariae generalized ARCH model, Review of Economics and Saisics, 7, 99, 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, 979, pp [8]D.A. Dickey, and W.A. Fuller, Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica, 49, 98, pp [9] R.F. Engle, Auoregressive condiional heeroskedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 5, 98, pp [] R.F. Engle, and V.K. Ng, Measuring and Tesing he Impac of News on Volailiy, Journal of Finance, 48(5), 993, pp [] R.F. Engle, Dynamic condiional correlaion- a simple class of mulivariae GARCH models, Journal of Business and Economic Saisics,,, pp [] S. Johansen, Esimaion and hypohesis esing of coinegraion vecor in Gaussian vecor auoregressive models, Economerica, 59, 99, pp [3] G. Kapeanios, Y. Shin, and A. Snell, Tesing for a uni roo in he nonlinear STAR framework, Journal of Economerics, (), 3, pp [] C. Kearney, The causes of volailiy in a small, inernaionally inegraed sock marke: Ireland, July June 994, Journal of Financial Research,, 998, pp [] G.M. Ljung, and G.E.P. Box, On a measure of lack of fi in ime series models, Biomerika, 65, 978, pp [] 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, 4,, pp [3] D.B. Nelson, Saionariy and persisence in he GARCH(,) model, Economeric Theory, 6, 99, pp

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