Multivariate GARCH modeling analysis of unexpected U.S. D, Yen and Euro-dollar to Reminibi volatility spillover to stock markets.

Transcription

1 Mulvarae GARCH modelng analyss of unexpeced U.S. D, Yen and Euro-dollar o Remnb volaly spllover o sock markes Cng-Cun We Deparmen of Fance, Provdence Unvesy Absrac Te objecve of s paper, by employng e Consan Condonal Correlaon(CCC) and Dynamc Condonal Correlaon(DCC) MGARCH-M model usng e unexpeced excange rae sock o measure e mpac effec of e U.S.D, Yen and Eurodollar excange rae sock mean and volaly spllover o sock markes. Te emprcal resuls of e CCC-MGARCH sows e negave correlaon beween e unexpeced U.S.D-RMB a Cna sock markes ndcae a unexpeced sock wll ave a negave effec o e Cna sock markes. Te posve correlaon of New York Dow Jones and wo Cna sock markes sow a e ncrease of New York sock marke ndex wll ncrease e Cna sock marke ndex. From e DCC-MGARCH(1,1) model, e posve and sgnfcan value of \ and ] sow ARCH and GARCH effec exs. Te DCC parameers are nsgnfcanly and e sum value of e parameers s less an one, sow a model s mean reverng. Caon: We, Cng-Cun, (008) "Mulvarae GARCH modelng analyss of unexpeced U.S. D, Yen and Euro-dollar o Remnb volaly spllover o sock markes." Economcs Bullen, Vol. 3, No. 64 pp Submed: Aprl 4, 008. Acceped: Ocober 10, 008. URL: p://economcsbullen.vanderbl.edu/008/volume3/eb-08c30065a.pdf

2 1. Inroducon Te relaonsps beween socks and e foregn excange markes ave been dscussed by prevous auors. For example, Jonson and Soenen (1998) fnd evdence of correlaon beween USD and Japanese Yen, and e sock markes n some pacfc-basc counres. Meanwle, Abd e al (003) nvesgaed e correlaons wn emergng sock markes and found a volaly spllover occurs n bo drecons. On e oer and, several papers ave nvesgaed e ransmsson mecansm of nnovaon and volaly sock across nernaonal sock markes. For nsance, mean and volaly spllover across nernaonal sock markes ave been suded by Hamao e.al (1990), Koumos (1996a, 1999b), and Jeong (1999). Numerous sudes ave aemped o model e dynamcs of e excange rae process and e ransmsson of excange rae volaly across markes wn a gven excange rae sysem. Tese sudes nclude a carred ou by Kearney and Paon (000) wo used mulvarae EGARCH modelng of excange rae volaly ransmsson n e European Moneary Sysem, and e one carred ou by Najand and Yung (1997), wo suded e ransmsson of volaly n e foregn excange fuures markes. Granger, Huang, and Yang (000) adoped a seres of co-negraon models w srucural breaks o examne e relaonsp beween sock reurns and currency markes. However, ey dd no fnd sgnfcan evdence regardng causaly beween e wo varables. Ts fndng s no suppored by Baarumsan e al. (00). Pylaks and Ravazzollo (005) used co-negraon models o denfy a sgnfcan relaonsp beween sock reurns and currency markes. Troug co-negraon analyss and error correcon models, Ajay and Mougoue (1996), meanwle, found evdence of dynamc lnkage beween sock prce and excange raes n eg ndusralzed counres. Tasam (006) sowed a e condonal correlaon beween e excange rae and U.S. sock reurn dsplays a g exen of me varaon, wle Kanas (000) found evdence of volaly spllover from sock reurns o excange rae canges n fve of e sx ndusralzed counres. He sowed a all sock reurns spllovers are symmerc, ndcang a e effec of bad news s e same as e effec of good news on e excange rae. On e oer and, Zapaero (1995) sowed a ere s an explc lnkage beween e volaly of sock prce and e volaly of e excange rae n fully negraed fnancal markes. Aloug numerous sudes ave been devoed o analyzng e mpac of excange rae canges on sock prces (Gao, 000), lle as been done o nvesgae e neracon beween unexpeced excange rae sock and nernaonal sock markes. Tus, e objecve of s paper s o use e error erm (.e., e erm wc dervaes from e GARCH (1,1) model o become e proxy varable of e unexpeced excange rae sock) o measure e mpac of e USD-, Yen- and Eurodollar-Remnb (RMB) excange rae sock mean and volaly spllover o e wo Cna sock markes by employng e Consan Condonal Correlaon(CCC) and Dynamc Condonal Correlaon (DCC) MGARCH-M models. One advanage of e MGARCH specfcaon s a

3 perms me-varyng condonal varance as well as smple varance, ereby allowng for possble neracon wn e condonal mean and e varance of wo or more fnancal seres. Te remander of s paper proceeds as follows: Secon descrbes e deals of our economerc meods; Secon 3 provdes a descrpon of e daa, fundamenal sasc and volaly measuremen, and e emprcal analyss before fnally dscussng e resuls. Secon 4 concludes e paper.. Meodology.1 Consan Condonal Correlaon (CCC) MGARCH model One advanage of e MGARCH specfcaon s a ey perm me-varyng condonal varance as well as varance; us allow for possble neracon wn e condonal mean and varance of wo or more fnancal seres. Insead of modelng condonal covarance marx drecly, some oer researc model H ndrecly roug condonal correlaon. Te frs model of s ype s e Consan Condonal Correlaon (CCC) model of Bollerslev(1990). He proposed a class of MGARCH models n wc e condonal correlaons are consan and us e condonal varances are proporonal o e produce of e correspondng condonal sandard devaons. Te resrcon gly reduces e number of unknown parameers and s smplfes esmaon. Te CCC model s defned as: H D RD e j jj (1) were D dag / 1/ nn symmerc posve defne marx w e j =1,, can be defned as any unvarae GARCH model, and R=(e j ) s a and R s e marx conanng e condonal correlaon e j. Te orgnal CCC model as a GARCH(1,1) specfcaon for eac condonal varance n D : W, 1, 1,=1 N () were H s posve defne f and only f all e N condonal varances are posve and R s posve defne. Ts model gves posve defne and saonary condonal covarance marx provded a e j make up a well-defned correlaon marx and e parameers are all nonnegave. Te esmaon s done by maxmzng e quas-lkelood, assumng condonal normaly.. Dynamc Condonal Correlaon (DCC) MGARCH model 1

4 In e CCC model, e assumpon a e condonal correlaons are consan may seem unrealsc n many emprcal applcaons. Engle (00) propose a generalzaon of e CCC model by makng e condonal correlaon marx me dependen. Te model s en called a dynamc condonal correlaon (DCC) model. Te DCC model belongs o e famly of mulvarae GARCH models. Developmens n mulvarae GARCH modelng are drven by e need o reduce compuaonal requremens wle smulaneously ensurng a covarance marces reman posve defne roug suable parameer resrcons. To undersandng e DCC-MGARCH model, we wre e condonal varance covarance marx as below: 1 0 r ~ N, H H D R D were H s e condonal covarance marx; R s e nxn me varyng correlaon marx, were D dag s a nxn dagonal marx of me-varyng sandard devaon from unvarae (3) (4) GARCH models; and R e j wc s a correlaon marx conanng condonal correlaon coeffcens. Te elemens n D follow e unvarae GARCH(p,q) process n e followng: W p p1 p p q q1 q, 1, n (5) Dvdng eac reurn by s condonal sandard devaon,, we ge e vecor of sandardzed reurns D 1 r, were ~~ N(0, R ). We wre Engle s specfcaon of a dynamc correlaon srucure as below: R Q Q Q Q 1 1 ' m n Q m m m nqn 1 m n m n (6) (7) were Q s a dagonal marx conanng e square roo of e dagonal enres of Q, Q s e condonal varance-covarance marx Q s obaned from e frs sage of equaon. Were, e covarance marx, Q, s calculaed as a weged average of Q, Te uncondonal covarance of e sandardzed resduals; m, ' m, a lagged funcon of e sandardzed resduals; and Q n e pas realzaon of e condonal covarance. In e DCC(1,1) specfcaon only e frs lagged

5 realzaon of e covarance of e sandardzed resduals and e condonal covarance are used. Ts requres e esmaon of wo addonal parameers, m and n. Q s a dagonal marx wose elemens are e square roo of e dagonal elemens of Q. Te DCC-MGARCH model s esmaed usng e maxmum lkelood meod n wc e log-lkeood can be wren as: 1 L were ' T ' 1 nlog() log D log R R 1 s e sandardzed resdual derved from e frs sage unvarae GARCH esmaon, wc s assumed o be n..d. w a mean zero and a varance, s also e correlaon marx of e orgnal zero mean reurn seres. (8) R. Hence, e varance marx, R, Te DCC model s desgned o allow for e wo-sage esmaon of e condonal covarance marx H, e frs sage unvarae volaly models are fed for eac of e asses and esmaes of are obaned. In e second sage, e marke reurns are ransformed by er esmaed sandard devaons resulng from e frs sage and are used o esmae e parameers of e condonal correlaon. Te H marx s generaed by usng unvarae GARCH models for e varances, combned w e correlaons produced by e. 3. Emprcal Resuls In order o nvesgae e mean and volaly spllover of e unexpeced excange rae o e Cnese sock markes, e daa used consss of e daly daa culled from fve sock marke ndexes and ree excange raes from e Tawan Economc Journal (TEJ) daa bank. Tese are e New York Dow-Jones ndex (NYD), e Japan Nkke 5 ndex (J5), e European Amserdam AEX Sock ndex (AEX), e Cna Sanga Compose ndex (SHC), and e Senzen Compose ndex (SJC), as well as e respecve excange raes of e U.S. Dollar (CAR), Japan Yen (CJR), and Eurodollar (CUR) o Cna RMB from July 1, 005 o January 4, 007. Reurns n eac marke are calculaed as e frs dfference n e naural logarms of e sock marke ndexes. Table 1 presens e descrpve sascs for eac varable seres. From e able we can see a e skewness sascs sugges lack of normaly n e dsrbuon of e reurn seres, wle e value of kuross ndcae a eac of e reurn seres s more peaked an n e normal dsrbuon. Te Jarque-Bera (JB) normaly es rejecs e null ypoess of normally. Te sgnfcan value of e LB-Q sascs for e squared reurns suggess e presence of auocorrelaon n e square of sock reurns. Te ARCH-LM s sascally sgnfcan a 1% level, ndcang e exsence of ARCH penomena for all varable seres. Tere are dfferen approaces o proxy excange rae uncerany. Here, we use e GARCH meod error erm as e proxy for One approac s o use e varance of e excange rae reurn (Goldberg and KolsadK, 1995). Anoer approac s usng e esmaed sandard 3

6 measurng excange rae uncerany or socks. Due o e fac a e calculaed ADF sascs are consdered less an e crcal value only for frs dfference of varables, could be concluded a all varables ave dfferences n erms of saonary. 3.1 Te Consan Condon Correlaon (CCC) MGARCH Model Table sows e parameer esmae of e CCC-MGARCH model for e effec of e USD-RMB unexpeced excange rae sock on e Cna sock marke. Teα and βvalues of e unexpeced excange rae sock on e Cna SHC sock markes are posve and sgnfcan a and 0.95, respecvely. Te α and β values of e unexpeced excange rae sock o e Cna SJC sock markes are and , respecvely. Bo are consdered posve and sascally sgnfcan a 1% level. Te posve and sgnfcan ARCH erm and GARCH erm sow a e ARCH and GARCH effecs exs n ese models. Te repored resuls demonsrae a, n fac, all seres exb me-varyng condonal volaly, wc can be successfully modeled usng e GARCH (1,1) models. Te correlaon beween unexpeced USD-RMB socks o e Cna sock markes s negave (.e., for e SHC sock marke and for e SJC sock marke). Ts ndcaes a e ncrease of e unexpeced excange rae sock wll reduce e sock marke ndex reurns. Table 3 presens e effec of e Yen-RMB unexpeced excange rae sock o e sock markes. Te unexpeced excange rae sock o e Cna sock markes sow posve and sgnfcan α and β values. Te unexpeced excange rae sock o e Cna sock marke sows a negave correlaon ( for SHC and for SJC) and a posve correlaon ( for SHC and for SJC) beween e NYD and Cna sock markes, respecvely. Table 4 sows e parameer esmaes of e unexpeced Eurodollar-RMB excange rae o e sock markes. Emprcal resuls presened n e able sow posve and sgnfcan α and β values. Based on e consan correlaon esmae, e correlaon values of e unexpeced excange rae sock o e Cna sock marke are posve (0.014 for SHC and for SJC), w a correspondng posve correlaon ( for SHC and for SJC) beween e AEX and Cna sock markes. 3.. Te Dynamc Condonal Correcon (DCC) MGARCH Model Table 5 repors on e parameer esmaes for e DCC-MGARCH model for e USD-RMB excange rae volaly o e Cna sock markes. Te respecve values of α sows a e sor run perssence n volaly are posve and sascally sgnfcan ( and ). Panel B of Table 5 sows e esmaons of e posve and sgnfcan parameers of e B value a DCC (1.1). If e sum of e DCC (1.1) parameer s less an one, s mples a e model s GARCH model o oban a condonal measure of volaly. GARCH meods ave been used o derve measures of uncerany (Engle, 198). 4

7 srcly mean reverng. Table 6 dsplays e unexpeced RMB-Yen excange rae sock o e sock markes w posve and sgnfcan α and β values. Te DCC parameers are nsgnfcan and e sum of e parameers s less an one, mplyng a e model s mean reverng. Lasly, e unexpeced Eurodollar-RMB excange rae sock o e sock marke s presened n Table 7, w posve and sascally sgnfcan α and β values a 1% level for e wo Cna sock markes. Te DCC parameers are nsgnfcan and e sum value of e parameers s less an one, mplyng a e model s mean reverng. 4. Concluson Accordng o e CCC-MGARCH (1,1) model, e α and β values of e ree unexpeced excange rae socks o e Cna sock markes are posve and sascally sgnfcan a 1% level. Te consan correlaon esmae marx of bo e USD-RMB and e Yen-RMB unexpeced excange rae socks o e wo Cna sock markes are negavely correlaed, wle a for e Eurodollar-RMB unexpeced excange rae sock s no. From e DCC-MGARCH (1,1) model, we can see e posve and sgnfcan values of α and β n e ree unexpeced excange markes. Based on e DCC (1,1) parameer able, e coeffcen value of e parameers are nsgnfcan wn e ree unexpeced excange rae markes. Moreover, e sum of e DCC (1,1) parameer sow a models are mean reverng. Based on emprcal resuls, e negave correlaon beween e unexpeced excange rae sock and sock markes ndcae a e unexpeced sock wll ave a negave effec on e Cna sock markes. Terefore, Cna needs o face e unexpeced excange rae ransmsson effec from oer counres because s gradually openng and dependng. Ts s especally rue for e USD-RMB excange rae marke. Moreover, e volaly ransmed effecs o e sock markes ave been found n e ree unexpeced excange rae markes. 5

8 References Abd H. and H. Asraf. (00) Sock Marke Volaly and Weak-Form Effcency: Evdence From an Emergng Marke Sae Bank of Paksan Workng Paper. Ajay, R.A., and M. Mougoue, (1996) On e Dynamc Relaon beween Sock Prces and Excange Raes Te Journal of Fnancal Researc, Baarumsa, A. Z., A, M.A. Mas and M.A. Zal (00) Te Sock Marke and e Rngg Excange Rae: A Noe Journal of e World Economy 14, Gao T. (000) Excange Rae Movemens and e Profably of U.S. Mulnaonals Journal of Inernaonal Money and Fnance 19, Hamao Y.R. R.W. Masuls and K.Ng (1990) Correlaon n Prce Canges and Volaly across Inernaonal Sock Markes Revew of Fnancal Sudes 3, Jeong J.G.. (1999) Cross-border Transmsson of Sock Prce Volaly: Evdence from e Overlappng Tradng Hours Global Fnance Journal 10, Jonson, R., and L. Soenen (1998) Sock Prce and Excange Rae: Emprcal Evdence from e Pacfc Basn Journal of Asan Busness 14, Kanas, A. (000) Volaly Spllovers beween Sock Reurn and Excange Rae Cange: Inernaonal Evdence Journal of Busness Fnance & accounng 7, Kearney, C. and A.J. Paon (000) Mulvarae GARCH Modelng of Excange Rae Volaly Transmsson n e European Moneary Sysem Fnancal Revew, 41, Koumos, G.. (1996a) Modelng e Dynamc Inerdependence of Major European Sock Markes Journal of Busness Fnance and Accounng 3, (1999b), Asymmerc Prce and Volaly Adjusmens n Emergng Asan Sock Markes Journal of Busness Fnance and Accounng, 6, Najand M. and K. Yung (1997) Prce Dynamcs among Excange Raes Sock Index and Treasury Bonds n Fuure Markes Advances n Invesmen Analyss and Porfolo Managemen 59, Pylaks, K. and F. Ravazzdol (005) Sock Prces and Excange Rae Dynamcs Journal of Inernaonal Money and Fnance 4,

9 Daa Summary Sascs Table 1 CAR CJR CUR NYD J5 AEX SHC SJC Mean Medam Maxmum Mnmum Sd.Dev Skewness Kuross Jarque-Bera ARCH-LM(1) LB(1) LB (1) Te sgnfcan value of e LB-Q sascs for e squared reurns suggess e presence of auocorrelaon n e square of sock reurns. ARCH-LM sascs proposed by Engle (198) amed o deec ARCH. In fac e values of ARCH-LM (1) are all sgnfcan a 1% level, ndcang e exsence of ARCH penomena for all varable seres.., and ndcaed a leas sgnfcan a 1%, 5%, and 10 % level. 7

10 Table Parameer esmaes for e CCC-MGARCH (1.1) model for U.S.D-RMB volaly spllover o NYD and Cna Sock Markes H D RD e j jj W, 1, 1, =1 N Panel A:Varance Equaon DLNYD DLSHC G1 DLNYD DLSJC G1 ω 1.30e-05.44e e e e e-11 (-4.04e-06) (-1.71e-06) (-3.38e-1) (-7.97e-07) (-.87e-06) (-6.00e-1) (-0.031) (-0.017) (-6.99e-03) (-0.003) (-0.018) ( ) β ( ) ( ) ( ) ( ) (-0.017) (-0.054) Panel B:Consan Correlaon esmaes DLNYD DLSHC G1 DLNYD DLSJC G1 DLNYD DLNYD e03 (-0.048) ( ) ( ) ( ) DLSHC DLSHC ( ) ( ) G1 G1 Log-lke: Log-lke: Te sasc repored n e pareness s e robus sandard errors.. DLNYD, DLSHC and DLSJC are e dfference log of e New York Dow-Jones sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G1 s e U.S.D-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4., and ndcaed a leas sgnfcan a 1%, 5%, and 10% level. 8

11 Table 3 Parameer esmaes for e CCC-MGARCH (1.1) model for Yen-RMB volaly spllover o J5 and Cna Sock Markes H D RD e j jj W, 1, 1,=1 N Panel A:Varance Equaon DLJ5 DLSHC G DLJ5 DLSJC G ω 1.041e e e-11.15e e e-1 (-9.13e-06) (-8.39e-08) (-1.07e-1) (-1.31e-06) (-.77e-06) (-3.9e-11) α ( ) (-6.1e-03) (-0.07) (-0.596) (-0.03) (-0.061) β (-0.55) (-6.5e-03) (-6.76e-04) ( ) ( ) (-0.033) Panel B:Consan Correlaon esmaes DLJ5 DLSHC G DLJ5 DLSJC G DLJ DLNYD ( ) ( ) ( ) ( ) DLSHC DLSHC (-0.050) ( ) G G Log-lke: Log-lke: Te sasc repored n e pareness s e robus sandard errors.. DLJ5, DLSHC and DLSJC are e dfference log of e Japan Nkke 5 sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G s e Yen-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4.,, ndcaed a leas sgnfcan a 1%,5%, and 10% level. 9

12 Table 4 Parameer esmaes for e CCC-MGARCH model for Eurodollar-RMB volaly spllover o AEX and Cna Sock Markes H D RD e j jj W, 1, 1,=1 N Panel A: Varance Equaon DLAEX DLSHC G3 DLAEX DLSJC G3 ω 5.480e e e e-06.81e e-10 (-1.60e-06) (-.38e-06) (-4.48e-11) (-1.65e-06) (-9.75e-07) (-6.18e-11) α (-0.03) (-7.81e-03) (-0.017) ( ) ( ) (-0.077) β (-0.064) ( ) ( ) (-0.054) ( ) ( ) Panel B: Consan Correlaon esmaes DLAEX DLSHC G3 DLAEX DLSJC G3 DLAEX DLNYD ( ) ( ) (-0.047) ( ) DLSHC DLSHC ( ) (-0.055) G3 G3 Log-lke: Log-lke: Te sasc repored n e pareness s e robus sandard errors.. DLAEX, DLSHC and DLSJC are e dfference log of e Amserdam sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G3 s e Eurodollar-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4.,, ndcaed a leas sgnfcan a 1%,5% and 10% level. 10

13 Table 5 Parameer esmaes for e DCC-MGARCH model for U.S.D-RMB excange rae volaly o NYD and Cna Sock Marke 1 0 r ~ N, H Panel A:Varance Equaon H D R D 1. Te sasc repored n e pareness s e robus sandard errors.. DLNYD, DLSHC and DLSJC are e dfference log of e New York Dow-Jones sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G1 s e U.S.D-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4.,, ndcaed a leas sgnfcan a 1%,5% and 10% level. W p p1 p p q q1 q, 1, n DLNYD DLSHC G1 DLNYD DLSJC G1 ω e-05.07e e e e e-11 (-1.87e-06) (-9.18e-06) (-.4e-1) (-1.59e-06) (-1.01e-05) (-1.98e-1) α e (-0.03) (-0.04) (-.60E-03) (-0.0) (-9.4e-03) (-7.64e-04) β (-0.04) (-0.04) (-0.01) (-0.03) (-0.0) (-7.5e-03) Panel B:DCC (1.1)parameer ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 5.56e e (-1.57e-03) (-0.08) (-4.37e-03) (-0.10) Log-lke: Log-lke:

14 Table 6 Parameer esmaes for e DCC MGARCH model for Yen-RMB volaly spllover o J5 and Cna Sock Markes 1 0 r ~ N, H H D R D 1. Te sasc repored n e pareness s e robus sandard errors.. DLJ5, DLSHC and DLSJC are e dfference log of e Japan Nkke 5 sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G s e Yen-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4.,, ndcaed a leas sgnfcan a 1%, 5% and 10% level. W p p1 p p q q1 q, 1, n Panel A:Varance Equaon DLJ5 DLSHC G DLJ5 DLSJC G ω e e e e e e-11 (-1.18e-05) (-.6e-05) (-7.0e-1) (-1.13e-06) (-1.67e-05) (-.98e-1) α (-0.03) (-0.03) (-0.04) (-0.0) (-0.06) (-0.0) β (-0.0) (-0.05) (-0.10) (-0.01) (-0.04) (-0.04) Panel B:DCC(1.1)parameer ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ e e (-0.03) (-0.08) (-0.0) (-0.05) Log-lke: Log-lke:

15 Table 7 Parameer esmaes for e DCC-MGARCH model for Eurodollar-RMB volaly spllover o AEX and Cna Sock Markes 1 0 r ~ N, H H D R D 1. Te sasc repored n e pareness s e robus sandard errors.. DLAEX, DLSHC and DLSJC are e dfference log of e Amserdam sock ndex, Sanga compose sock ndex and Senzen compose sock ndex. 3. G3 s e Eurodollar-RMB unexpeced excange rae sock wc derved from GARCH(1.1) error erm. 4.,, ndcaed a leas sgnfcan a 1%, 5%, and 10% level. W p p1 p p q q1 q, 1, n Panel A:Varance Equaon DLAEX DLSHC G3 DLAEX DLSJC G3 ω 1.694e-05.13e e e-05.19e e-10 (-1.35e-06) (-1.76e-06) (-6.04e-11) (-3.73e-06) -1.41e e-11 α (-0.0) (-0.01) (-0.0) (-0.0) (-0.03) (-0.0) β (-0.0) (-0.01) (-0.04) (-8.54e-03) (-0.04) (-0.04) Panel B:DCC(1.1)parameer ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ e e (-0.96) (-0.64) (-0.0) (-0.13) Log-lke: Log-lke: