Links between the Indian, U.S. and Chinese Stock Markets

Transcription

1 Deparmen of Economics Working Paper No hp://n2.fas.nus.edu.sg/ecs/pub/wp/wp0602.pdf Links beween he Indian, U.S. and Chinese Sock Markes by Heng Chen, Beno J. Lobo and Wing-Keung Wong 2005 Heng Chen, Beno J. Lobo and Wing-Keung Wong. Views expressed herein are hose of he auhor/s and do no necessarily reflec he views of he Deparmen of Economics, Naional Universiy of Singapore.

2 Links beween he Indian, U.S. and Chinese Sock Markes Heng Chen Naional Universiy of Singapore Beno J. Lobo Universiy of Tennessee a Chaanooga Wing-Keung Wong Naional Universiy of Singapore January 2006

3 Links beween he Indian, U.S. and Chinese Sock Markes Absrac: This sudy examines he bilaeral relaions beween hree pairs of sock markes, namely India-U.S., India-China and China-U.S. We use a Fracionally Inegraed Vecor Error Correcion Model (FIVECM) o examine he coinegraion mechanism beween markes. By augmening he FIVECM wih a mulivariae GARCH formulaion, we sudy he firs and second momen spillover effecs simulaneously. Our empirical resuls show ha all hree pairs of sock markes are fracionally coinegraed. The U.S. sock marke plays a dominan role in he relaions wih he oher wo markes, whereas here is an ineracive relaionship beween he Indian and Chinese sock markes. In paricular, he Indian sock marke dominaes he firs momen feedback wih he Chinese marke, while he laer dominaes he second momen feedback wih he former. Keywords: Sock marke, Coinegraion, Fracionally Inegraed Vecor Error Correcion Model, Mulivariae GARCH

4 I. Inroducion Globalizaion has been gaining momenum in recen years. Financial markes are a he forefron of his process. The las wo decades have winessed rapid inernaional capial mobiliy in he form of boh direc and indirec invesmens. This phenomenon is a resul of he increasing ineracion of world economies, boh developing and developed. The liberalizaion of capial markes and he increasing variey of financial insrumens and advances in informaion echnology have also conribued o his rapidly moving process. This paper aims o conribue o our undersanding of he globalizaion and inegraion of sock markes. Sudies of sock marke inegraion have aken many pahs. For insance, diversificaion heory assumes ha relaions among prices of differen financial markes could help o reduce risks and increase revenue of invesmen porfolios. Since he work of Grubel (968) on he benefis of inernaional porfolio diversificaion, he relaionships among financial markes have been widely sudied. Sock markes, however, appear o be unique in ha hey serve as economic baromeers because hey faciliae direc financing which is a significan engine of growh for he economy. Movemens in sock markes appear o reflec no only domesic economic condiions, bu also he level of confidence ha domesic and foreign invesors have in an economy. The ever closer relaions among inernaional sock markes have imporan implicaions for macroeconomic policies and oucomes. The inegraion of global sock markes has spurred changes in naional exchange rae and rade sraegies and domesic moneary and fiscal policies. Given he grea imporance of sock markes, researchers now view he relaions among sock markes as a proxy for he relaions among economies. Therefore, sudies on he inegraion and co-inegraion of sock markes have blossomed, and advances in economeric echniques have caalyzed his research. 2

5 This paper examines bilaeral relaions of hree pairs of sock markes, namely India-U.S., China-U.S., and India-China. We probe he riangular relaions of hese hree sock markes because he U.S. marke is he leading developed marke, whereas he oher wo are key developing markes. India and China have been named as he mos promising emerging markes due o heir susained and rapid economic growh in he pas wo decades or so. During his period, he rade volume, capial flows and muual invesmens among he hree counries have also increased rapidly. Therefore, i is of grea academic and pracical imporance o undersand he links beween hese hree criical global markes. This paper applies a Fracionally Inegraed Vecor Error Correcion Model (FIVECM) o deec he co-movemens of he pairs of sock markes. The FIVECM is superior o he sandard VECM because i reveals no merely long-run equilibrium relaions and shor-run dynamics among co-inegraed variables, bu also accouns for he possible long memory in he coinegraion residual series which may oherwise skew he esimaion. Moreover, we augmen he FIVECM wih a mulivariae GARCH represenaion o conrol for he condiional auocorrelaions in he second momens of he series. The FIVECM-GARCH model is relaively novel in his line of research. Wihin his modeling framework, empirical lead-lag relaions in he level as well as volailiy of series are simulaneously sudied. Our empirical resuls show ha he hree markes are fracionally co-inegraed wih each oher, whereas only one sock index series seems o be bound by he long run equilibrium implied by coinegraion. We also find ha he U.S. marke leads he Indian marke in informaion spillover and leads he Chinese marke in reurn ransmission, bu no vice versa. The Indian and Chinese markes are found o be more ineracive. Specifically, we find ha while he Chinese marke leads he Indian marke in reurn ransmission, he laer leads he former in informaion spillover. Therefore, economerically speaking, he wo neighboring emerging markes appear 3

6 o be more closely linked o each oher relaive o he U.S. The res of he paper is organized as follows: Secion II offers a review of he lieraure and moivaion for his paper; Secion III describes he daa and mehodology; secion IV presens he empirical resuls and implicaions. Finally, secion V concludes. II. Lieraure Review and Moivaion As skeched in he inroducion, he relaionship among various sock markes is a ho research opic among academicians for boh micro- and macro-reasons. The research daes back o he early 970 s and has burgeoned since lae 980 s. Early sudies by Ripley (973), Lessard (976), and Hilliard (979) generally find low correlaions among naional sock markes, which validae he benefis of diversificaion in inernaional porfolio managemen. However, his alleged low correlaion was found o ech up afer he U.S. marke crash in Ocober 987. Lee and Kim (994), for insance, find ha naional sock markes became more inerrelaed afer he crash. Applying a VAR and impulse response funcion analysis, Jeon and Von-Fursenberg (990) also show a sronger co-movemen among inernaional sock indices afer he 987 crash. Similar conclusions are reached for Asian sock markes afer he Asian financial crisis in 998. I seems ha crises have drawn sock markes closer o each oher. Sudies also verify he co-movemen beween he U.S. marke and oher markes. For example, Eun and Shim (989) find evidence of co-movemens beween he U.S. sock marke and oher world equiy markes. Cheung and Ng (992) invesigae he dynamic properies of sock marke reurns in Tokyo and New York and find ha he U.S. marke o be a dominan global force from January 985 hrough December 989. However, no all research suppors inegraion among inernaional sock markes. Koop (994) uses Bayesian mehods o conclude ha here are no common sochasic rends in sock prices across seleced counries. In a similar vein, Forbes and Rigobon 4

7 (2002) claim ha recen currency crises (saring from he U.S. marke crash in 987) do no increase he inegraion among sock markes afer correcing for one heoreical flaw which engenders overesimaion of correlaion coefficiens The majoriy of empirical financial research pivos on he Norh American, European and Japanese markes, namely he mos developed markes in he world. This paper ries o examine a special riangular relaion among he Indian, Chinese and U.S. markes. The following observaions moivaed us. Firsly, China and India ogeher accoun for over 40% of he world s populaion, and heir huge domesic markes form he basis for heir rising global prominence. In he pas wo decades or so, he wo mos populous counries have grown rapidly and are expeced o be significan global economic powers in he years ahead. These wo economies have simulaed fas evolving sock markes wihin each counry. Ineresingly, alhough he Indian sock marke has a much longer hisory han is Chinese counerpar, i was no ill early 99 ha financial liberalizaion reforms commenced, a roughly he same ime ha he Chinese sock marke ook birh. Wih he help of a series of reform measures, he Indian sock marke has become more efficien and ransparen. Meanwhile, he Chinese sock marke has kep evolving during is 5 year hisory, hanks o coninuing reform and liberalizaion measures. The Chinese deregulaion of financial markes picked up seam afer China joined he WTO lae 200. Moreover, he wo emerging powers have elevaed heir inegraion recenly by opening up rade borders. By he end of 2004, India s rade volume wih China was $3.6 billion, second only o is rade volume wih he U.S. China could conceivably replace he U.S. as India s principal rading parner in he near fuure. A deeper undersanding of he links beween he Indian and Chinese sock markes could shed ligh on he exen o which hese economies are inegraed. Secondly, he influence of he U.S. economy and sock marke on global markes is pervasive and well documened. In addiion, he dominan role of he U.S. dollar in he inernaional moneary sysem has also enhanced he cenral posiion of he U.S. 5

8 sock marke on he global sage. The wo emerging economies rely heavily on he U.S. marke. The U.S. is he bigges rade parner and larges foreign invesmen source o boh India and China. As of 2004, he rade volume beween India and he U.S. was $22. billion, whereas ha of he U.S. and China was abou $70 billion, around 0% of China s GDP. Also, India and China are imporan expor desinaions for he U.S., and boh counries finance a significan porion of he U.S. budge defici by buying U.S. Treasury bonds wih heir fas growing foreign exchange reserves. Given he close economic ies among he U.S., China and India, his sudy seeks o explore he degree of inegraion and bi-direcional informaion spillover beween he hree markes. Furhermore, as widely-known, he capial asse pricing model (CAPM) across counries hinges largely on he relaions among inernaional sock markes. In a recenly discussion abou asse pricing peraining o emerging markes, Harvey (2005) poins ou ha marke inegraion plays a criical role in he performance of heoreical models. Boh of he wo developing counries, namely India and China, have been experiencing gradual financial liberalizaions during he pas decade. Thus, he coinegraion relaions among he ypical developing and developed markes revealed in he curren paper could provide some hins for academician researchers on asse pricing models as well as praciioners like inernaional porfolio managemens. Anoher major moivaion for his paper sems from economeric consideraions. This paper invesigaes he bilaeral relaions beween sock markes by employing a bivariae coinegraion echnique. As usual, he coinegraion sudy is conduced wihin a VECM framework (see Engle and Granger, 987). However, he disequilibrium error used in he VECM (also ECM) applied on financial series is ofen neiher I() nor I(0), bu raher a fracionally inegraed process, I(d), where 0.5 < d < 0.5. Wihou accouning for he long memory (when d<0.5) feaure of he disequilibrium error, he rue relaions among coinegraed variables may well be disored. Therefore, his paper employs a Fracionally Inegraed VECM (see Baillie, 6

9 996) o sudy he co-movemen of he pairs of markes. Furhermore, since condiional heeroskedasiciy is ofen observed in high-frequency ime series, his paper augmens he FIVECM model wih a bivariae GARCH represenaion of he volailiy process o capure he second momen auocorrelaions in he reurn series. In paricular, we employ he BEKK (,) model proposed by Engle and Kroner (995) o model he evoluion of condiional variances. Since here are no resricions imposed on he coefficien marices of he condiional mean and variance, lead-lag relaions in he firs as well as second momens are simulaneously revealed in his model. Of course, he benefis of a FIVECM-BEKK model come a he cos of more complicaed compuaions. We propose a muli-sep procedure o esimae his complex model, he deails of which are discussed in he nex secion. III. DATA AND METHODOLOGY 3. Daa descripion This paper uses weekly sock index daa from January 2, 99 hrough December 29, We use he Bombay Sock Exchange Naional index for he Indian sock marke, he All Shares Index from he Shanghai Sock Exchange for China, and he S&P 500 index for he U.S. marke. All daa are from Daasream. We use weekly daa in order o alleviae he effecs of noise characerizing daily or higher frequency daa. Furher, o avoid he so called day-of-he-week effec, we use Wednesday-close indices, since sock markes are said o be more volaile on Monday and Friday (Lo and MacKinlay 988). The oal number of observaions is 73. Some feaures of he daa are Long memory ime series models augmened by GARCH have been adoped in he lieraure o model a variey of economic and financial siuaions. For example, Baillie e al (996) analyze inflaion series of en counries using a fracionally inegraed ARFIMA-GARCH model; Lien and Tse (999) apply a FIVECM-GARCH(,) model o evaluae he performance of fuures hedge raios. Few sudies, however, examine sock marke co-movemens using FIVECM-BEKK model. 7

10 described in Table. Logarihms of he sock indices for he Indian, Chinese and U.S. markes a ime are noaed IND, CHN, and US, respecively. 3.2 Mehodology Firsly, o esablish he coinegraion relaion beween sock indices, we employ a Granger wo-sep procedure. In he firs sep, we fi he following dynamic ordinary leas squares model (DOLS) o he pairs of sock indices: y p = α + βy2 + ω Δ j y2 j + η () j= p where y y2, are pairs of sock indices involving IND, CHN and US ; he esimae βˆ is shown by Sock and Wason (993) o be super-consisen as well as efficien. Then he esimaed coinegraing residual is consruced as follows: ˆ = ˆ. (2) z y β y2 In he second sep, we es for long memory, using a R/S es (cie reference) o he ẑ series. If he coinegraing residual is confirmed o follow a long memory (I(d), -0.5<d<0.5) process, hen y y2, are said o be fracionally coinegraed wih each oher, and we proceed o fi an auoregressive fracionally inegraed moving average (ARFIMA) model o each residual series in he form: d ( B ) Φ( B) ( B) z = a Ψ ˆ (3) where, Ψ(B) and Φ(B) are MA and AR polynomials, B is a backward shif operaor, a is an i.i.d. noise and will be inerpreed o be he disequilibrium error in he error correcion model o follow. Once he coinegraion relaions among variables are esablished, Engle and 8

11 Granger (987) show ha coinegraion leads o he Vecor Error Correcion Model (VECM) which is exremely powerful in modeling he long-run as well as shor-run dynamics among he coinegraed variables. We expand he VECM o a FIVECM by accouning for he fracional inegraion propery in ẑ series using he ARFIMA model (3). The bivariae FIVECM will hen ake he form: m m d i i α ( ) ( )( ) ˆ i 2 2 i ε i= i= m m d i i ( ) ( ) ˆ α 2 i 22 2 i ε2 i= i= Δ y = c + Ψ B Φ B B z + Δ y + Δ y + Δ y = c + Ψ B Φ B ( B) z + Δ y + Δ y +. where Δ = ( Δy Δy ) y, 2 is he differenced series vecor or reurn vecor of ( ΔIND, Δ ) US or ( ΔIND, Δ ) CHN or ( ΔCHN, Δ ) US. z is esimaed from model () fied o respecive sock index vecors. Noe ha we employ VAR(m) srucure for he VECM model, in paricular m= in his paper. ( ε,ε ) = α,α 2 error vecor. The coefficiens ( ) ˆ = 2 (4) ε is he α capure he reacion of he series when hey deviae from he long-run equilibrium; he magniudes of he αi ' s represen he speed of he adjusmen. The lag erms in (4) accoun for he AR srucure of he Δ y series, while heir coefficiens reflec he reurn ransmissions beween differen markes. Because i is ofen observed ha he condiional volailiies of financial reurn series exhibi ime varying characerisics, we employ a mulivariae GARCH (MGARCH) model o capure he heeroskedasiciy in he series. In oher words, we model he condiional mean and condiional variance of he reurn series simulaneously. To do so, le ( ) cov 2 22 σ σ 2 σ σ ε denoe he variance-covariance 9

12 marix of ε condiional on pas informaion. The mos general and flexible MGARCH model is he BEKK model proposed by Engle and Kroner (995) in he following form: = A p q + ( ) + 0 A0 Ai iε i Ai B j j B j i= j= ε (5) where A 0 is a lower riangular marix, A i ' s and B j ' s are unresriced coefficien marices, is symmeric and posiive semi-definie. Usually, p= and q= suffice for modeling volailiy in financial ime series. Wih his formulaion, he dynamics of are fully displayed in he sense ha he dynamics of he condiional variance as well as he condiional covariance are modeled direcly, hereby allowing for volailiy spillovers across series o be observed. The volailiy spillover effec is indicaed by he off-diagonal enries of coefficien marices A and B. This can be clearly seen from he expansion of BEKK(,) ino individual dynamic equaions: σ σ σ 22 2 [ ] [ σ ] ( A0 ) + [ A ε + A ε 2 ] + ( B ) σ + 2B B σ + ( B ) σ ( A ) + ( A ) + [ A ε + A ε ] + ( B ) σ + 2B B σ + ( B ) ( B B + B B ) σ + B B σ = = = A 0 0 A A A 2 ε 2 + ( A A 22 + A 2 A 2 ) ε ε 2 + A 2 A 22 ε B B 2 σ (6) + The above equaion sysem is much more complicaed han a univariae GARCH model because of ineracions among he wo condiional variances and residuals. The ime-varying correlaion coefficien can be obained from he condiional variances and covariances afer he model is esimaed. Since here are no resricions on he coefficiens, esimaion of he BEKK model involves more compuaion han oher MGARCH models. The saionariy condiion for he volailiy series in a BEKK (,) model is ha he eigenvalues of marix A A + B B are all less han uniy in modulus. 2 2 For condiions for he general BEKK model, see Proposiion 2.7 in Engle and Kroner,

13 By esimaing joinly he FIVECM-BEKK model (i.e. sysems (4) and (6)), he coefficien esimaes would be more efficien, and he relaions among he series would be delineaed more accuraely. IV. Empirical Resuls and Inerpreaions 4. Coinegraion seup The firs necessary sep in coinegraion sudy is o es he non-saionariy of he involved series. Therefore, we es for non-saionariy by applying he ADF and PP uni roo ess, o he logarihms of IND, US and CHN. The resuls conained in Table 2 show ha all he indices are found o be I() processes under boh ess, which are consisen wih resuls in he finance lieraure. Nex, we es he possible coinegraing relaions beween he hree pairs of sock indices ( IND, ) US, ( IND, ) CHN, and ( CHN, ) US by fiing he DOLS model in () wih lag lengh p=2. The esimaed model coefficiens are lised in Table 3, in paricular, all he esimaed βˆ for he hree regressions are highly significan. In order o confirm he coinegraion relaion beween series in each pair, we have o es he saionariy of coinegraion residuals by firs consrucing he ẑ series according o (2) for each pair of series using he esimaed coinegraing coefficien βˆ from he corresponding DOLS model. These consruced disequilibrium error series are denoed as z ind us, z and z chn respecively (where superscrip sands ind chn us for dependen variable, subscrip for independen variable). The R/S es for long memory is applied o hese hree residual series. The resuls, presened in Table 4, confirm ha all he hree residual series have long memory. Therefore, we proceed o

14 fi an ARFIMA model o each of he series. The choice of ARFIMA order is based on he ACF and PACF of residual series. 3 The fied resuls are shown in Table 5. I is noeworhy ha all he esimaed values of d in he hree ARFIMA models fall ino he range 0.5 < d < 0. 5, and esimaed coefficiens for he AR erms also produce hree saionary series, alhough he serial correlaions of he hree series are persisen. In paricular, he hree d-values are all posiive and less han 0.5, confirming ha he coinegraing variables follow long memory saionary processes. Thus, we conclude ha he hree sock markes are fracionally coinegraed wih each oher. Nex, we proceed o fi a FIVECM-MGARCH model o he reurn series daa. Specifically, we fi he FIVECM-BEKK(,) model o he hree pairs of log-differenced index series, i.e. ( ΔIND, ΔUS ), ( ΔIND, ΔCHN ) and ( ΔCHN, ΔUS ), wih he firs variable in each pair being he dependen variable. The AR() srucure is chosen in he FIVECM condiional mean equaions based on he examinaion of ACF and PACF of he series. The error srucure in each model follows a bivariae suden -disribuion because he normaliy es applied o he reurn series shows srong non-normaliy in he series. 4.2 India-U.S. sock marke resuls The esimaes of parameers for he bivariae FIVECM in (4) for he Indian and U.S. sock markes are presened in Panel A of Table 6. To inerpre he resuls of he FIVECM model in (4), we firs focus on he condiional mean equaions, c i (i=,2), he consan erms in he condiional mean equaions, i j,k (i=, j=,2, k=,2) and he adjusmen speed parameers, α i (i=,2) where i j, k sand for he AR erm 3 Deails are no repored here bu are available upon reques. 2

15 coefficiens., and α i, i=,2, represen he adjusmen speed parameers. Boh c and c 2 are saisically significan, implying ha he long-run uncondiional means of boh he Indian BSE index reurn, Δ IND and S&P 500 index reurn Δ US, are posiive. The significan and 22 erms verify he serial dependence in he index reurns. The nonsignificance of boh 2 and 2 erms indicae ha here is no reurn ransmission from he U.S. marke o he Indian marke, or vice versa. In oher words, he U.S. sock marke does no Granger-cause or lead he Indian sock marke, and vice versa. In addiion, as expeced, α is significanly negaive, indicaing ha he Indian marke adjuss when i drifs away from long-run equilibrium. However, α 2 is no saisically significan. This suggess ha he coinegraing relaion beween he wo markes does impose cerain resricions on he movemen of he Indian sock marke, bu no on he US sock marke. Secondly, he esimaes for he condiional variance equaions in (5) reveal more abou he relaionship beween he wo markes. A(i, j) are he elemens of he consan marix A 0 in he variance equaion (5). The saisical significance of he diagonal elemens of he consan marix shows ha he uncondiional variances of he wo index reurn series are posiive. The firs-order ARCH(i,j) and GARCH(i,j) erms are he elemens of he ARCH and GARCH coefficien marices A and B, respecively. The diagonal elemens of he ARCH and GARCH marices are highly significan, indicaing ha he ARCH and GARCH effecs are subsanial in boh index reurn series, and supporing he noion ha GARCH modeling is appropriae for our daase. The significan off-diagonal elemens ARCH(,2) and GARCH(,2) indicae ha here is unidirecional informaion ransmission from he U.S. sock marke o he Indian sock marke. These off-diagonal esimaes also indicae ha he ime varying correlaion coefficien beween he wo series is deermined by lagged values of volailiies and residuals respecively, which can be seen from he equaion 3

16 sysem (6). In shor, our resuls poin o unidirecional volailiy spillover from he U.S. o he Indian marke. The srong influence of he U.S. sock marke on he Indian sock marke is expeced, since he former is he larges sock marke buil upon he mos influenial economy in he world and he U.S. is he mos imporan rading parner and expor desinaion for Indian goods and services. The model diagnosics are lised in Panel B of Table 6 including he hree es saisics and heir corresponding p-values applied o he individual residual series separaely. Specifically, he Jarque-Bera Normaliy ess are conduced on he wo residual series; Ljung-Box ess of whie noise are applied o sandardized residuals and squared residual series o es for serial correlaion in he firs and second momens of residuals. Since all he p-values of Ljung-Box ess for boh sandardized residuals and squared residual series in Table 6 are larger han convenional levels, we can conclude ha he fied model is adequae and successful in capuring he dynamics in he firs as well as second momens of he index reurn series. Finally, he eigenvalue moduli of Aˆ Aˆ ˆ ˆ + B B (where, Â and ˆB are esimaed ARCH and GARCH coefficien marices respecively) are 0.988, 0.956, 0.944, Since hey are all less han uniy, we conclude ha he condiional volailiies of he wo sock reurn series are saionary China-US sock marke resuls The esimaes for he FIVECM-BEKK model fied on he China-U.S. pair of sock reurns are repored in Panel A of Table 7. Firsly, we find ha he significan c 2 indicaes ha he long-run mean of Δ US is posiive, whereas ha of Δ CHN is zero as shown by he non-significan c, which is consisen wih he finding in Table 4

17 6. The significan and erms indicae ha serial dependence in Δ CHN and 22 Δ US is non-rivial. The cross erms in he AR srucure show an ineracive relaionship beween he wo series. Paricularly, he highly significan 2 poins o reurn ransmission from he U.S. marke o he Chinese marke. The negaive sign indicaes ha he Chinese marke does no follow he U.S. marke, bu moves in he opposie direcion. In addiion, he non-significan 2 implies ha he reurn ransmission is unidirecional from he U.S. marke o he Chinese marke. The coinegraion beween he wo markes is indicaed by he adjusmen speed coefficien α which is significanly negaive. Is close-o-one magniude implies ha he disequilibrium beween he wo markes will likely be correced wihin one period, namely one week in his paper. The non-significance of α 2 shows ha he U.S. marke is no bound by he coinegraion relaionship. Secondly, he resuls for he condiional variance equaions show a simple relaion beween he volailiies of he wo index reurn series. Again, he highly significan diagonal elemens in he ARCH and GARCH marices confirm he srong dependence in heir condiional volailiies. However, no feedback relaions beween he condiional variances of series ( ΔCHN, ΔUS ) are deeced, because none of he off-diagonal erms in he ARCH and GARCH marices is significan. In oher words, here is no informaion ransmission beween he wo markes. Finally, posiive and significan A(,) and A(2,2) sugges nonzero uncondiional variances for he wo reurn series. The diagnosic es saisics for his FIVECM-BEKK model are repored in Panel B. The adequacy of he model used is suppored by he es resuls. The moduli of he four eigenvalues of Aˆ Aˆ ˆ ˆ + B B for his model are 0.996, 0.977, and 0.976; all are less han uniy. Therefore, he condiional volailiies of he 5

18 ( ΔCHN, ΔUS ) series are deemed o be saionary. 4.4 India-China sock marke resuls The esimaes for he FIVECM-BEKK model fied on he India-China pair of sock reurns are repored in Panel A of Table 8. The coefficiens are noaed as in Table 6. Firsly, we find ha he significan c indicaes again ha he long-run mean of Δ IND is non-zero, whereas, he non-significan c 2 suggess ha he long run mean of Δ CHN is no differen from zero. The significan and 22 erms indicae ha serial dependence in Δ IND and Δ CHN is subsanial. I is noeworhy ha 2 is marginally significan wih a p-value of , which poins o reurn ransmission from he Chinese marke o he Indian marke. This fac, coupled wih he non-significan 2, implies ha he Chinese marke Granger-causes he Indian marke, bu no vice versa. The adjusmen speed parameer α is significanly negaive, which implies ha when he relaionship beween he wo markes srays from equilibrium, IND will decrease o resore he long-run equilibrium. The oher adjusmen parameer α 2 is no significan, hough i has he expeced sign. Secondly, he esimaes for he condiional variance equaions show an ineresing relaionship beween he volailiies of he wo index reurn series. Again, he highly significan diagonal esimaes of he ARCH and GARCH coefficien marices show ha he ime varying feaures of he second momens of he individual series are pronounced. A he same ime, he diagonal elemens of he consan marices A(,) and A(2,2) are significanly posiive, suggesing nonzero uncondiional variances for 6

19 he wo reurn series. The significan ARCH(2,) and GARCH(2,) erms show ha here is volailiy spillover from he Indian marke o he Chinese marke, and he spillover appears o be unidirecional since he oher wo off-diagonal coefficien esimaes are insignifican. In oher words, he Indian marke leads he Chinese marke in he ransmission of shocks. In sum, he overall picure revealed by he model esimaes suggess ha he Chinese marke passes reurn realizaions (firs momen) o he Indian marke, while he laer leads in he ransmission of informaion (second momen). Model diagnosics for he FIVECM-BEKK model on ( ) ΔIND, ΔCHN lised in Panel B indicae he adequacy of our model in capuring he dynamics of condiional means and condiional variances. Also, he four eigenvalues of Aˆ Aˆ ˆ ˆ + B B for his model are 0.979, 0.940, and which are all less han uniy. Therefore, he condiional volailiies of ( Δ ΔCHN ) However, he Ljung-Box es for whie noise on invesigae he dynamics of he Chinese marke 4. IND, series are deemed o be saionary. Δ CHN poins o he need o furher V. Conclusion This paper employs a fracionally inegraed vecor error correcion (FIVECM) model o invesigae he bilaeral relaions beween he Indian, U.S. and Chinese sock markes. By augmening he FIVECM model wih a mulivariae GARCH (BEKK, in paricular), he coinegraing relaions among he index series, and he dynamic dependence and lead-lag relaions in he firs and second condiional momens of he index reurn series are revealed simulaneously. 4 We ried oher specificaions for mean equaion of Δ CHN, he resuls do no improve. 7

20 The esimaion resuls confirm our conjecure ha here is fracional coinegraion or long-run equilibrium beween he hree pairs of sock markes, namely India-U.S., China-U.S., and India-China. In each of he hree models, only one marke is found o adjus o resore equilibrium. In paricular, he Indian marke adjuss in response o disequilibrium wih boh he U.S. and Chinese markes; he Chinese marke adjuss disequilibrium condiions wih he U.S. We also find ha while he U.S. marke does no Granger-cause or lead he Indian marke wih respec o reurn (firs momen) ransmission, i does lead he Chinese marke in his respec. However, while here is unidirecional volailiy (second momen) ransmission from he U.S. marke o he Indian marke, no such feedback is observed beween he U.S. and Chinese markes. The Indian and Chinese markes are found o be more ineracive. In addiion o being fracionally coinegraed, here are ineresing lead-lag relaions beween he wo markes. Specifically, we find ha he Chinese marke leads he Indian marke in reurn ransmission, whereas he laer leads he former in informaion spillover. Furher research may exend he FIVECM model wih a bivariae GARCH model employed in our paper o he mulivariae GARCH model o sudy all hree counries simulaneously. In his paper, we only apply he FIVECM model wih a bivariae GARCH o sudy he relaionship beween wo counries o avoid from overhauling boh he srucure and argumen when we pu all hree markes wihin one model framework. However, we noe ha i is possible o exend he approach employed in our paper o he mulivariae GARCH model o sudy all hree counries simulaneously hough he esimaion will become difficul as one has o overhaul he complicaed srucure and argumen if one pus all hree markes wihin one model framework. Finally, no ha we invesigae he relaions among sock markes by employing only index daa, bu we bear in mind ha cerain macroeconomic variables like bilaeral rade and foreign exchange may have cerain influences on he co-movemens of sock markes. Incorporaing macro variables ino coinegraion 8

21 sudy would yield insighful resuls, provided he difficuly of obaining high frequency macro daa is appropriaely ackled. 9

22 References Baillie, R. (996), Long Memory Processes and Fracional Inegraion in Economerics, Journal of Economerics, 73,,996, pp.5-59 Cheung, Y. and K. Lai (993), A fracional coinegraion analysis of purchasing power pariy, Journal of Business and Economic Saisics, Vol., pp Cheung, Yin-Wong and Lilian K. Ng (992), Sock price dynamics and firm size: an empirical invesigaion, The Journal of Finance, Vol. 47, pp Chou, W. and Y. Shih, (997), Long-run purchasing power pariy and long-erm memory: evidence from Asian newly indusrialized counries, Applied Economics Leers, Vol. 4, pp Corhay, A., A. Rad and J. Urbain (995), Long-run behavior of Pacific-Basin sock prices, Applied Financial Economics, Vol. 5, pp.-8. Dickey, D.A. and W.A. Fuller (979), Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion, Vol. 74, pp Dickey, D.A. and W.A. Fuller (98), Likelihood raio saisics for auoregressive ime series wih a uni roo, Economerica, Vol. 49, pp Engle, R. and C.W.J. Granger (987), Coinegraion and error correcion: represenaion, esimaion and esing, Economerica, Vol. 55, pp Eun, C. S. and S. Shim (989), Inernaional ransmission of sock marke movemens, Journal of Financial and Quaniaive Analysis, Vol. 24, pp Geweke J. and S. Porer-Hudak (983), The esimaion and applicaion of long memory ime series models, Journal of Time Series Analysis, Vol. 4, pp Granger, C. W. J. (98), Long memory relaionships and he aggregaion of dynamic models, Journal of Economerics, Vol. 4, pp Granger, C. W. J. (988), Some recen developmen in a concep of causaliy, Journal of Economerics, Vol. 39, pp Granger, C. W. J., B. N. Huang and C. W. Yang (2000), A bivariae causaliy beween sock prices and exchange raes: evidence from recen Asian flu, The Quarerly Review of Economics and Finance, Vol. 40, pp

23 Grubel, Herber G. (968), Inernaionally diversified porfolios: welfare gains and capial flows, American Economic Review, Vol. 58, no. 5, pp Hilliard, J. (979), The relaionship beween equiy indices on world exchanges, Journal of Finance, (March 979), pp Hsiao, C. (979), Auoregressive modeling of Canadian money and income daa, Journal of he American Saisical Associaion, Vol. 74, pp Hsiao, C. (98), Auoregressive modelling of money income causaliy deecion, Journal of Moneary Economics, Vol. 7, No., pp Hung, B. and Y.L. Cheung (995), Inerdependence of Asian emerging equiy markes, Journal of Business Finance & Accouning; Vol. 22, Jeon, Bang and Von Fursenberg (990), Growing inernaional co-movemen in sock price indexes, Quarerly Review of Economics and Finance, Vol. 30, No. 30, pp Johansen, S. (988a), The mahemaical srucure of error correcion models, Conemporary Mahemeics, Vol. 8, pp Johansen, S. (988b), Saisical analysis of coinegraion vecor, Journal of Economic Dynamics and Conrol, Vol. 2, pp Johansen, S. (995), Likelihood-inference in coinegraed vecor auo-regressive models, Oxford: OUP. Koop, Gary. (994), An objecive Bayesian analysis of common sochasic rends in inernaional sock prices and exchange raes, Journal of Empirical Finance, Vol., pp Lee, S.B., and K.J. Kim (994), Does he Ocober 987 crash srenghen he co-movemen in sock price indexes, Quarerly Review of Economics and Business, Vol.3, No.-2, pp Lessard, D. R. (976), World, counry and indusry facors in equiy reurns: implicaions for risk reducions hrough inernaional diversificion, Financial Analyss Journal, Vol. 32, pp Lo, A. W. and A. C. MacKinlay (988), Sock marke prices do no follow random walks: evidence from a simple specificaion es, Review of Financial Sudies, Vol., pp

24 Phillips, P.C.B. and Perron, P. (988), Tesing for a uni roo in ime series regression, Biomerika, Vol. 75, No. 2, pp Rao, B.S.R. and Umesh Naik (990), Iner-relaedness of sock marke specral invesigaion of USA, Japan and Indian markes noe, Arha Vignana, Vol. 32, No. 3&4, pp Ripley, Duncan M. (973), Sysemaic elemens in he linkage of naional sock marke indices, Review of Economics and Saisics, Vol. 55, No. 3, pp Sharma, J.L. and R.E. Kennedy (977), Comparaive analysis of sock price behavior on he Bombay, London & New York Sock Exchanges, Journal of Financial and Quaniaive Analysis, Sep 977, pp Sims, C. and J. H. Sock (990), Inference in linear ime series models wih some uni roos, Economerica, Vol. 58, pp Sock, J.H. and M.W.Wason (993). A simple Esimaor of Coinegraing Vecors in Higher Order Inegraed Sysems, Economerica, 6, pp Whie, H. (980), A heeroskadesiciy-consisen covariance marix esimaor and a direc es for heeroskedasiciy, Economerica, Vol. 48, pp Wong W K and G Bian, (2000), Robus Bayesian inference in asse pricing esimaion, Journal of Applied Mahemaics & Decision Sciences, Vol. 4, No., pp

25 Table. Descripive saisics Saisics IND CHN US Mean Median N Sd Dev SE Mean Skewness Kurosis Noe: The indices are he Bombay Sock Exchange Naional index (IND ), he S&P 500 index (US ), and all Shares Index of Shanghai Sock Exchange (CHN ). The Kurosis here compued wih S-PLUS is he excess kurosis. Table 2. Uni roo ess Tes ADF PP Index -saisic p-value -saisic p-value IND CHN US Noe: The indices are he Bombay Sock Exchange Naional index (IND ), he S&P 500 index (US ), and All Shares Index of he Shanghai Sock Exchange (CHN ). The ADF ess applied on IND and US are wih consan and one lag, he ADF es on CHN is wih consan, rend and one lag. The corresponding PP ess have he same srucure wihou lag erms. 23

26 Table 3. Dynamic OLS Esimaes Saisics (IND, US ) (CHN, US ) (IND, CHN ) Esimae P-value Esimae P-value Esimae P-value Esimaes αˆ βˆ ˆ ω 2 ˆ ω ˆω 0 ˆω ˆω Noe: The dependen variable in each model is marked in bold. Table 4. Saionariy ess on coinegraion residuals Tes Range Over Sandard Deviaion (R/S) es Index Tes saisic P-value <0.0 ind z us chn z us ind z chn < <0.0 Noe: The residual series are consruced using Equaion (2) in he ex based on he corresponding DOLS model in Table 3. Table 5. ARFIMA fi resuls Esimaes Parameers chn z us Value P-value Value P-value Value P-value d AR() AR(2) NA NA ind z us ind z chn Noe: Series z chn us, z and z ind are consruced wih equaion (2) in he ex wih superscrip ind us chn sands for dependen variable, subscrip for independen variable, using esimae βˆ obained from DOLS models in Table 3. Selecion of AR (lag) erms is based on he examinaion of ACF and PACF. 24

27 Table 6. FIVECM-BEKK(,) fied on ( ) ΔIND, ΔUS c c 2 2 Panel A. Model Esimaes Parameers Esimae Sd. Error value Pr(> ) α α A(,) A(2,) A(2,2) ARCH(,) ARCH(,2) ARCH(2,) ARCH(2,2) GARCH(,) GARCH(,2) GARCH(2,) GARCH(2,2) Panel B. Model Diagnosics Tes Normaliy es (Jarque-Bera) Whie noise es (Ljung-Box) GARCH effec es (Ljung-Box) Series saisic p-value saisic p-value saisic p-value ΔIND ΔUS Noes: The esimaed model is FIVECM-BEKK(,) (Equaion sysems (4) + (6)); he dependen variable is ΔIND ; he error srucure is bivariae -disribuion, he esimaed degrees of freedom are 9.42 wih sandard error.895. The use of an an ARFIMA (2,d,0) model reduces he acual sample size o 727. The number of lags in he wo Ljung-Box ess are 2, hus he es saisics follow a Chi-square disribuion wih 2 degrees of freedom. 25

28 Table 7. FIVECM-BEKK(,) fied on ( ) ΔCHN, ΔUS c c 2 Panel A. Model Esimaes Parameers Esimae Sd. Error value Pr(> ) α α A(,) A(2,) A(2,2) ARCH(,) ARCH(,2) ARCH(2,) ARCH(2,2) GARCH(,) GARCH(,2) GARCH(2,) GARCH(2,2) Panel B. Model Diagnosics Tes Normaliy es (Jarque-Bera) Whie noise es (Ljung-Box) GARCH effec es (Ljung-Box) Series saisic p-value saisic p-value saisic p-value ΔCHN ΔUS Noes: The esimaed model is FIVECM-BEKK(,) (Equaion sysems (4) + (6)); he dependen variable is ΔCHN ; he error srucure is bivariae -disribuion, he esimaed degrees of freedom are 6.86 wih sandard error.005. The use of an an ARFIMA (2,d,0) model reduces he acual sample size o 728. The number of lags employed in he wo Ljung-Box ess are 2, hus he es saisics follow a Chi-square disribuion wih 2 degrees of freedom. 26

29 Table 8. FIVECM-BEKK(,) fied on ( ) ΔIND, ΔCHN Panel A. Model Esimaes Parameers Esimae Sd. Error value Pr(> ) c c α α A(,) A(2,) A(2,2) ARCH(,) ARCH(,2) ARCH(2,) ARCH(2,2) GARCH(,) GARCH(,2) GARCH(2,) GARCH(2,2) Panel B. Model Diagnosics Tes Normaliy es (Jarque-Bera) Whie noise es (Ljung-Box) GARCH effec es (Ljung-Box) Series saisic p-value saisic p-value saisic p-value ΔIND ΔCHN Noes: The esimaed model is FIVECM-BEKK(,) (Equaion sysems (4) + (6)); he dependen variable is ΔIND ; he error srucure is bivariae -disribuion, he esimaed degrees of freedom are 6.36 wih sandard error The use of an an ARFIMA (2,d,0) model reduces he acual sample size o 727. The number of lags employed in he wo Ljung-Box ess are 2, hus he es saisics follow a Chi-square disribuion wih 2 degrees of freedom. 27