Dynamic Relatedness Analysis of Three Exchange Rate Markets Volatility: Study of Korea, Taiwan and Thailand

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1 Inernionl Conference on Advnced Compuer Science nd Elecronics Informion (ICACSEI 3) Dynmic Reledness Anlysis of Tree Excnge Re Mrkes Voliliy: Sudy of Kore, Tiwn nd Tilnd Wnn-Jyi Horng, Tien-Cung Hu, Deprmen of Hospil nd Hel Cre Adminisrion, Ci Nn Universiy of Prmcy & Science, Tinn 77, Tiwn Deprmen of Memics, Nionl Tsing Hu Universiy, Hsincu 3, Tiwn nd negive vlues do no respond o is influence on e condiionl vrince equion. Te condiionl vrince only cnges long wi e error erm s vlue cnge, nd cnno go long wi e error erm s posiive nd negive cnges. To improve is flw, Nelson9 presens n exponenil GARCH model nd Glosen, Jgnn, nd Runkle give GJR-GARCH model. Tese model re e so-clled e models of symmeric GARCH. Tere re mny reserc sudies on e symmeric problem, suc s Brooks, Poon nd Fung, Cmpell nd Henscel6, Koumos nd Boo4, nd Koumos5. Tese sudies expnd e reserc meods of e reurn voliliy beween sock mrkes. For semens on e mulivrie GARCH model, scolrs suc s Yng4, Yng nd Doong3, Grnger, Hung nd Yng, Wng nd Brre () nd Bollerslev4 proposes e bivrie GARCH model. Te min gol of is pper is o discuss e ssociion of e Kore, e Tiwn, nd e Tilnd s excnge res voliliy. Te pper consrucs e DCC nd e rivrie GARCH eoreicl model nd exmines weer or no ere is n symmericl influence beween e mrkes. We undersnd ere possibly crees n influence on e ree excnge re mrkes, by using e mulivrie Norml disribuion for e socsic error erm. We lso use e mximum likeliood lgorim meod of BHHH (Bernd e. l. 5) o esime e prmeers of e proposed model. Te orgnizion of is pper is s follows. Secion ses e d crcerisics. Secion 3 provides e proposed model nd e empiricl resuls. Secion 4 provides e symmericl es of e proposed model nd e ls secion gives e conclusion. Absrc - Tis pper sudies e ssociion nd e model consrucion of e Kore s, e Tiwn s nd e Tilnd s excnge re mrkes. In is pper we cn consruc dynmic condiionl correlion (DCC) nd rivrie IGARCH (, ) model o evlue e ssociion nd ere re no exis n symmericl effec mong e ree excnge re mrkes. Te empiricl resuls of correlion nlysis lso sow Kore excnge re mrke posiively ffecs e Tiwn s nd e Tilnd s excnge re mrkes, nd e voliliy of e ree excnge re mrke inerc wi one noer. Furermore, for exmple, e vriion risk of e Kore excnge re mrkes voliliy ffecs e vriion risks of e Tiwn nd Tilnd excnge re mrkes. Te empiricl resul suggess e invesors or inernionl fund mngers of e excnge re mrkes mus evlue eir mrkes on e previous of e excnge re invesmen decision. Tey lso need o consider e risk nd relionsip of e ree excnge re mrkes voliliy. Index Terms - excnge re mrke, symmericl effec, DCC, rivrie IGARCH model. I. Inroducion We know Kore's economicl pysique belongs prly o n islnd economy, were posiive includes o e foreign rde unfolds were ies beween Tilnd nd Tiwn re close. We know Kore is one of Asin four drgons, lso Kore economy of grow in 6 is 5%, nd e forecs vlue of e grow re is 4.3% in e fuure. We lso know Tilnd is lso e mjor economicl finncil sysem in e Associion of Sou-es Asi Nions. Tilnd nd Tiwn ve close relionsip wi e Kore bsed on e rde nd e circulion of cpil, nd e Tilnd is e mos powerful globl economic nion in e Associion of Soues Asi Nions. Terefore, ow ese ree sock mrkes impc one noer is cerinly wor furer discussion. Among e finncil ime series non-lineriy reserc lierures, Engle9 proposes e uoregressive condiionlly eeroskedsiciy (clled ARCH) model nd Bollerslev3 offers e generlizion uoregressive condiionlly eeroskedsiciy (clled GARCH) model. Tese wo models cn cc e finncil properies wen e condiionl vrince is no fixed prmeer. Nelson8 looks sock price cnges nd discovers ey ve bo posiive nd negive relionsips wi e fuure sock price voliliy. II. D Crcerisics A. D Sources Tis reserc discusses e excnge re reurns in e Kore, e Tiwn, nd e Tilnd nd weer ere is n ssociion of e ree excnge re mrkes voliliy on ec oer. In e smple selecion, is reserc uses e Kore excnge re, Tiwn excnge re, Tilnd excnge re s e smple. We selec e smple period from Jnury, o December, 9 nd use e excnge re prices for ll e des. Te d origine from e DSrem, lrge dbse in Tiwn. Te GARCH model supposes seled ime condiionl vrince for e preceding issue of condiionl vrince nd n error erm squre funcion. Terefore, e error erm s posiive 3. Te uors - Publised by Alnis Press B. Voliliy Re Clculion nd Trend Crs In order o compue e excnge re voliliy res, is 393

2 pper dops e nurl logrim of e excnge re for every excnge re mrke smple ( KER, TWER, THER ) wi one sep difference nd en muliplied by - nmely, for e Kore s excnge re mrke, e excnge re voliliy res re *[ln( KER ) ln( KER )]. For e Tiwn s excnge re mrke, e excnge re voliliy res re *[ln( TWER ) ln( TWER )]. Finlly, for e Tilnd s excnge re mrke, e excnge re voliliy res re RTHER *[ln( THER ) ln( THER )] KER 5 5 THER TWER RTHER 5 5 Figure. Trend crs of e Kore, Tiwn nd Tilnd s excnge res, nd rend crs of e Kore, Tiwn nd Tilnd s excnge re voliliies. From Figure, we my see e Kore, e Tiwn nd e Tilnd s excnge res presens obviously e sme direcion of rend. From Figure, we lso know e voliliy of ese ree excnge re mrke reurns ve voliliy clusering penomenon. We my lso know e Kore excnge re mrke, e Tiwn excnge re mrke nd e Tilnd excnge re mrke ve cerin relevnces on eir reurn voliliy processes. Tis lso mens ere re e muul relions mong ese ree excnge re mrkes. Tis is lso minly e min moivion for discussing e relionsips mong e Kore, e Tiwn nd e Tilnd s excnge re voliliies. C. Bsic Sisics nd Some Tess Te reurn res of e excnge res in e Kore, e Tiwn nd e Tilnd sow sionry se sequence. Tble sows some bsic sisicl nlysis: men vlue, sndrd deviion, kurosis coefficien, skewed coefficien, nd norml disribuion exminion. From Tble, e verge re of reurn of e Kore s excnge re is -.35, e verge re of reurn of e Tiwn s excnge re is -.4, nd e verge re of reurn of e Tilnd s excnge re is -.. Te vriion risk of e Kore s excnge re reurn re is.7768, e vriion risk of e Tiwn s excnge re reurn re is.77, nd e vriion risk of e Tilnd s excnge re reurn re is.4834, nd erefore e vriion risk of e Kore s excnge re reurn re is e iges. From e Jrque-Ber sisics, under e null ypoeses of e norml disribuion, we discover e ree excnge re reurn res do no sow norml disribuion. Moreover, e kurosis is bigger n 3, nd is demonsres e d ve e penomen of evy il disribuion. Wen e smple size is lrge enoug, e evy il disribuion will pproxime e norml disribuion. Tble. D Sisics Sisic RTHER Men S-D Skewed Kurosis J-B N (p-vlue) 95.3 (.) (.) 38.4 (.) smple Noes: () S-D denoes e sndrd deviion of d. () J-B N denoes e norml disribuion es of Jrque-Ber. (3) p-vlue <denoes significnce (=%,=5%,=%). In order o mc e suible model, firs one my deermine e sbiliy of e ime series d, s well s void e non-sionry se of e ime series sequences nd reduce e miske of e empiricl resul. To do so, is pper uses e uni roo ess of ADF (Dickey-Fuller 7-8 ) nd KSS (Kpenios e l. 6 ). Te ADF nd KSS exminion resuls re omied ere. I sows e Kore, Tiwn nd Tilnd s excnge res do ve sionry se sequences. Under e co-inegrion es of Jonsen 3, we know mx nd e Trce sisics re no significn under e level 5%, e deil is omied. Tis demonsres e excnge res of e ree excnge re mrkes do no ve coinegrion relionsip logeer. Terefore, e Kore, e Tiwn nd e Tilnd s excnge re mrkes do no ve e long-erm co-inegrion relionsip, ese ree mrkes cn relly ffec one noer. Empiricl resul lso sows Kore, Tiwn nd Tilnd excnge re mrkes ve relionsip, bsed on e uncondiionl correlion coefficien. Terefore, we go sep furer o undersnd e inercions of e ree excnge re mrkes. D. Arc Effec Tes Tis pper furer uses e ARCH effec es o deermine e sock reurn voliliy nd weer ere is e condiionlly eeroskedsiciy penomenon. Tis reserc implemens e Ljung-Box 7 es meod, e Lgrnge Muliplier (LM) es meod of Engle 9, nd e F disribuion es meod of Tsy o furer confirm e vrince of e residul error sequence nd weer ere is n ARCH effec, nd en if ere is n ARCH effec we use e GARCH model o mc i suibly. Te ARCH effec es kes e residul error squre of e ps q periods o crry on e regression 394

3 nlysis. Te ARCH effec es is bsed on e AR model in e nex secion. We nex implemen e LM, F, nd Ljung-Box (L-B) es meods o exmine e excnge re reurns nd o deermine weer ere is condiionlly eeroskedsiciy penomenon. Te resuls of e ARCH effec es for e ree excnge re mrkes re lised in Tble. Te resuls sow e ree excnge re voliliy res ve e condiionlly eeroskedsiciy penomenon. Tis suggess i mces suibly nd i could use e GARCH model o nlyze e d. Tble. ARCH Effec Tes for Kore Tiwn nd Tilnd Excnge Re Mrkes (lg=3) Engle LM es Tsy F es L-B es LB () LB (3) Sisic (p-vlue) (.) (.) (.) (.) Engle LM es Tsy F es L-B es LB () LB () Sisic (p-vlue) (.) (.) (.) (.) RTHER Engle LM es Tsy F es L-B es LB () LB (4) Sisic (p-vlue) (.) (.) (.) (.) Noes: p-vlue <denoe significnce (=%,=5%,=%). III. Proposed Model Tis secion uses e rivrie GARCH model- nmely, i kes e ()-(3) ype o discuss e Kore, e Tiwn nd e Tilnd s excnge re voliliies reledness nlysis. Te prmeers esimion firs considers generl model nd is bsed on e esimed resuls. We en delees some no so significn consn iems. Finlly, we obins simplificion model for e Kore, e Tiwn nd e Tilnd s excnge re voliliies reledness nlysis. From e empiricl dignosis resuls, we know e Kore, e Tiwn nd e Tilnd s excnge re voliliy res my be consruced on e rivrie GARCH(, ) model wi DCC, e esime resuls re sed in Tble 3. Te proposed model is given s follows: RTHER RTHER, () RTHER, () RTHER 3, (3) (4),,, (5),,,, (6) 33, 3 3, 33, q c c c,,,, /,, q d d d 3, 3,, 3, /, 33, q e e e 3, 3,, 3, /, 33,, exp( q, ) /(exp( q, ) ) (7) 3, exp( q3, ) /(exp( q3, ) ) (8) 3, exp( q3, ) /(exp( q3, ) ) (9),,,,, () 3, 3,, 33,, () 3, 3,, 33,, () (,,,, 3, ) obeys e rivrie norml disribuion- nmely, N, H ), mong (,,) nd (,,, H,,,,,, 3, 3,,, 3, 3, 33, 3, 3,. (3) Te probbiliy densiy funcion of of Tsy (4). Here cn refer e book is e dynmic condiionl, is e, correlion (DCC) coefficien of nd, 3, DCC coefficien of, nd 3,, 3, is e DCC coefficien,, of nd 3. By e esimed resuls of e rivrie GARCH(, ) model wi DCC in Tble 3, we es e esimed vlue of e prmeers coefficien o be significn or no wi P- vlue. In e smple period, e Kore s excnge re voliliy receives e previous one dy s influence from e Kore s excnge re mrke ( =-.76). Te Kore s excnge re voliliy receives e previous one dy s impc from e Tiwn s excnge re mrke ( =.933). Te Kore s excnge re voliliy receives e previous one dy s impc from e Tilnd s excnge re mrke, 395

4 ( =.899). Te Tiwn s excnge re voliliy receives e previous one dy s influence from e Kore s excnge re mrke ( =.594). Te Tiwn s excnge re voliliy does no receive e previous one dy s influence of e Tiwn s excnge re mrke. Te Tiwn s excnge re voliliy lso receives e previous one dy s influence from e Tilnd s excnge re mrke ( =.3). Te Tilnd s excnge re vpliliy receives e previous one dy s influence of e Kore s excnge re mrke ( =.63), e Tilnd s excnge re voliliy receives e previous one dy s influence of e Tiwn s excnge re mrke ( =.798), nd i receives e previous one dy s influence of e Tilnd s excnge re mrke ( =-.785). From e empiricl resuls s bove, we lso know ese ree excnge re mrkes do ve e relionsips. On e oer nd, e DCC verge esimion vlue of e Kore nd e Tiwn excnge re voliliies is ˆ significn ( =.4475). Tis resul mens e Kore excnge re s voliliy s posiive influence o e Tiwn excnge re s voliliy, nd ey re precisely syncronized muul influence. Wen e vriion risk of e Kore excnge re voliliy re increses, e invesor s risk in e Tiwn excnge re mrke is ble o increse. Likewise, wen e vriion risk of e Kore excnge re voliliy re flls, e invesor s risk in e Tiwn excnge re mrke is lso ble o be reduced. Similrly, e DCC verge esimion vlue of e Kore nd e Tilnd excnge re voliliies is significn ( 3 =.348). Te DCC verge esimion vlue of e Tiwn nd e Tilnd excnge re voliliies is lso significn ( 3=.98). As n exmple, for e Kore excnge re mrke, e risk of is excnge re receives e influence from e Tiwn excnge re mrke nd e influence is e bigger n of e Tilnd mrke. Te observed condiionl vrince equion of e esimed coefficien, under e % significnce level, demonsres ll e condiionl vrince esimed coefficiens re significnce in Tble 3. Tis resul works wen e excnge re voliliy re of e Kore, e Tiwn, nd e Tilnd re differen o e rdiionl GARCH model wi consn condiionl correlion. Te previous one dys residul error squre iem nd e previous one dy s condiionl vrince will ffec e Kore, e Tiwn, nd e Tilnd s excnge re voliliy re voliliies nd lso cn produce e differen vriion risks, mong wic,,, nd., ˆ ˆ Also,, nd conforms o e prmeer of e IGARCH model s condiionl supposiion. Te empiricl resul lso sows e voliliy of vriion risk is e lowes ( ) for e Tiwn s excnge re mrke. Te single vrible GARCH nd bivrie GARCH models re unble o respond o is informion, bu e DCC nd e rivrie GARCH(, ) model mig ruly cc e Kore, e Tiwn, nd e Tilnd s excnge res voliliy process. Terefore, e explnory biliy of e rivrie GARCH(, ) model wi DCC is beer n e rdiionl models of e single vrible nd e bivrie GARCH. Tble 3. Prmeer Esimion of e Trivrie IGARCH(, ) Model wi DCC Prmeer Coefficien (p-vlue) (.) (.56) (.) (.) Prmeer Coefficien (p-vlue) (.885) (.) (.7) (.78) Prmeer Coefficien (p-vlue) (.3) (.) (.) (.) Prmeer Coefficien (p-vlue) (.) (.) (.79) (.) Prmeer 3 c Coefficien (p-vlue) (.) (.) (.) (.) Prmeer c c d d Coefficien (p-vlue) (.) (.) (.) (.) Prmeer d e e e Coefficien (p-vlue) (.) (.) (.) (.) Prmeer, min, mx, 3, Coefficien (p-vlue) (.) (.) Prmeer mx 3, 3, min 3, mx 3, Coefficien (p-vlue) (.) Noes: () p-vlue<denoes significnce (=%,=5%,=%). () Te min denoes e minimum vlue of DCC coefficien, nd e mx denoes e mximum vlue of DCC coefficien. Te rivrie GARCH model is pproprie o exmine e sndrd residul error nd sndrd residul error squre series by e es meod of Ljung-Box 7 o see weer ere sill exiss uo-correlion. Empiricl resul sows e dignosis presens e DCC nd e rivrie GARCH(, ) model lredy s no uo-correlion of e sndrd residul error. Te DCC nd e rivrie GARCH(, ) model lredy does no ve n ARCH effec of e sndrd 396

5 residul error squre series. Terefore, is model mces quie suibly nd is pproprie. IV. Asymmeric Tes Of Te Trivrie Grc Model Becuse of e prmeer esimion nd e sndrd residul error dignosis in e bove, e exminion only cn ceck if e model mces up wi e suible quliy, bu i cully is unble o look up weer e model s n symmericl penomenon. Terefore, Engle nd Ng develop dignosis es in order o exmine weer e model s symmericl risk or no. Tis reserc uses is dignosis es o crry ou e exminion. Te exminion meod of e model ypoeses s e following four exminion meods: () sign bis es () negive size bis es (3) posiive size bis es (4) join es. Te es resuls re sed in Tble 4. Tble 4. Asymmeric Tes of e Trivrie GARCH Model Kore Sign bis Negive size Posiive size Join es es Bis es Bis es F sisic (p-vlue) (.3) (.5759) (.55) (.38) Tiwn Sign bis Negive size Posiive size Join es es Bis es Bis es F sisic (p-vlue) (.789) (.659) (.47) (.75) Tilnd Sign bis Negive size Posiive size Join es es Bis es Bis es F sisic (p-vlue) (.39) (.3374) (.598) (.356) Noes: p-vlue<denoes significnce (=%,=5%,=%). From e posiive size bis es nd e join es, we know e excnge re mrkes of e Kore, e Tiwn nd e Tilnd do no ve n symmericl penomenon in e smple period. V. Conclusions Tere re mny fcors my influence excnge re mrke, suc s e overll economic gens nd overll currency supplies, ineres res, prices, nd inflion res. Ec fcor cn ve n influence on e excnge re voliliies. Tis reserc discusses ree excnge re mrke voliliies influence of e Kore, e Tiwn nd e Tilnd. Te empiricl resul sows e Kore, e Tiwn nd e Tilnd s excnge re voliliies my be consruced in e rivrie IGARCH(, ) model wi DCC. Tis model lso psses sndrd residul error nd e ARCH effec es, demonsring e rivrie IGARCH(, ) model s fiings re pproprie. Te empiricl resul lso obins e verge esimion vlue of DCC coefficien ( ˆ =.4475) of e Kore nd Tiwn wo excnge re mrke voliliies is posiive, e verge esimion vlue of DCC coefficien ( ˆ =.348) of e 3 Kore nd Tilnd wo excnge re mrke voliliies is lso posiive, nd e verge esimion vlue of DCC coefficien ( ˆ =.98) of e Tiwn nd Tilnd wo 3 excnge re mrke voliliies is lso posiive. Tis resul demonsres e Kore excnge re voliliy ffecs e Tiwn nd Tilnd excnge re risks, nd e Tiwn excnge re voliliy lso ffecs e Kore nd Tilnd excnge re risks. Te empiricl resul lso discovers e Kore, e Tiwn nd e Tilnd s excnge re mrke voliliies do no ve e symmericl penomenon in e smple period. Te eories nd e models discussing on e reurn re nd e voliliy properies of finncil commodiies re counless, nd is reserc only uses e rivrie GARCH model o discuss e ree excnge re mrkes of e Kore, e Tiwn nd e Tilnd. Te ree excnge re mrkes voliliy re lso sows e relionsips. For fuure reserc, we sugges e oers mulivrie GARCH models cn be used for furer nlysis. References [] H. Akike, Informion Teory nd n Exension of e Mximum Likeliood Principle. In d. Inernionl Symposium on Informion Teory, edied by B. N. Perov nd F. C. Budpes: Akdemii Kido (973), [] C. Brooks, A Double-Tresold GARCH Model for e Frenc Frnc/Deuscmrk Excnge Re, Journl of Forecsing, 35 (). [3] T. Bollerslev, Generlized uoregressive condiionl eroscedsiciy, Journl of Economerics, 37 (986). [4] T. Bollerslev, Modeling e coerence in sor-run nominl excnge res: mulivrie generlized ARCH model, Review of Economics nd Sisics 7, 498 (99). [5] E. K. Bernd, B.H. Hll, R.E. Hll, nd J.A. Husmn, Esimion nd inference in nonliner srucurl models, Annls of Economic nd Socil Mesuremen 4, 653 (974). [6] J.Y. Cmpell nd L. Henscel, No news is good news: n symmeric model of cnging voliliy in sock reurns, Journl of Finncil Economic, 8 (99). [7] D.A. Dickey nd W.A. Fuller, Disribuion of esimes for uoregressive ime series wi uni roo, Journl of e Americn Sisicl Associion 74, 47 (979). [8] D.A. Dickey nd W.A. Fuller, Likeliood Rio Sisics for Auoregressive Time Series wi Uni Roo, Economeric 49, 57 (98). [9] R.F. Engle, Auoregressive condiionl eeroscedsiciy wi esimes of e vrince of Unied Kingdom Inflion, Economeric 5, 987 (98). [] R.F. Engle nd V.K. Ng, Mesuring nd esing e impc of news on voliliy, Journl of Finnce 45, 749 (993). [] C.W. Grnger, J.B. Hung nd C.W. Yng, A bivrie cusliy beween sock prices nd excnge res: evidence from recen Asin Flu, Te Qurerly Review of Economics nd Finnce 4, 337 (). [] L.R. Glosen, R. Jgnnn nd D.E. Runkle, On e relion beween e expeced vlue nd e voliliy on e nominl excess reurns on socks, Journl of Finnce 48, 779 (993). [3] S. Jonsen, Esimion nd ypoesis esing of coinegrion vecor in gussin vecor uoregressive models, Economeric 59, 55 (99). [4] G. Koumos nd G.G. Boo, Asymmeric voliliy rnsmission in inernionl sock mrkes, Journl of Inernionl Money nd Finnce 4, 747 (995). [5] G. Koumos, Modeling e dynmic inerdependence of mjor Europen sock mrkes, Journl of Business Finnce nd Accouning 3, 975 (996). 397

6 [6] G. Kpenios, Y. Sin nd A. Snell, Tesing for uni roo in e nonliner STAR frmework, Journl of Economerics (), 359 (3). [7] G.M. Ljung nd G.E.P. Box, On mesure of lck of fi in ime series models, Biomerik 65, 97 (978). [8] D.B. Nelson, Sionriy nd persisence in e GARCH(,) model, Economeric Teory 6, 8 (99). [9] D.B. Nelson, Condiionl eeroscedsiciy in sse reurns: A new Approc, Economeric 59, 347 (99). [] W.P.H. Poon nd H.G. Fung, Red cip or H sres: Wic Cinbcked securiies process informion e fses?, Journl of Mulinionl Finncil Mngemen, 5 (). [] R.S. Tsy, Anlysis of Finncil Time Series, New York: Jon Wiley & Sons, Inc (4). [] K.L. Wng nd C.B. Brre, A new look e rde volume effecs of rel excnge re risk, Working pper in Cornell Universiy (). [3] S.Y. Yng nd S.C. Doong, Price nd voliliy spillovers beween sock prices nd excnge res: empiricl evidence from e G-7 counries, Inernionl Journl of Business nd Economics 3(), 39 (4). [4] S.Y. Yng, A DCC nlysis of inernionl sock mrke correlions: e role of Jpn on e Asin Four Tigers, Applied Finncil Economics Leers (), 89 (5). 398