Equity Diversification in Two Chinese Share Markets: Old Wine and New Bottle. Abstract

Transcription

1 Equiy Diversificion in wo Chinese Shre Mrkes: Old Wine nd New Bole sngyo Chng Depren of Finnce, Feng Chi Universiy, ichung, iwn Yng Cheng Lu Depren of Finnce, Ming Chun Universiy, ipei. iwn Absrc his sudy provides evidence h here exis long run benefis for invesors fro diversifying in wo Chinese shre rkes over he period Jnury 5, o Deceber 3, 5. he evidence is bsed on ess for pirwise coinegrion beween he Shnghi nd Shenzhen s A shre nd B shre sock price indexes, using five coinegrion ess, nely PO, I, JJ, KSS, nd BN pproches. he resuls fro hese five ess re robus nd consisen in suggesing h hese wo Chinese shre rkes re no pirwise coinegred wih ech oher. hese findings could be vluble o individul invesors nd finncil insiuions holding long run invesen porfolios in hese wo Chinese shre rkes. Ciion: Chng, sngyo nd Yng Cheng Lu, (6) "Equiy Diversificion in wo Chinese Shre Mrkes: Old Wine nd New Bole." Econoics Bullein, Vol. 7, No. 4 pp. 7 Subied: Februry, 6. Acceped: April 3, 6. URL: hp:// 6GA.pdf

2 Equiy Diversificion in wo Chinese Shre Mrkes: Old Wine nd New Bole ABSRAC his sudy provides evidence h here exis long-run benefis for invesors fro diversifying in wo Chinese shre rkes over he period Jnury 5, o Deceber 3, 5. he evidence is bsed on ess for pirwise coinegrion beween he Shnghi nd Shenzhen s A-shre nd B-shre sock price indexes, using five coinegrion ess, nely PO, I, JJ, KSS, nd BN pproches. he resuls fro hese five ess re robus nd consisen in suggesing h hese wo Chinese shre rkes re no pirwise coinegred wih ech oher. hese findings could be vluble o individul invesors nd finncil insiuions holding long-run invesen porfolios in hese wo Chinese shre rkes. Key Words: Chinese Shre Mrkes, Equiy Diversificion, Nonliner, Coinegrion ess JEL Clssificion: C3, F

3 . INRODUCION his sudy is o explore wheher here exis ny long-run benefis fro equiy diversificion for invesors who inves in wo Chinese shre rkes, nely hose of Shnghi nd Shenzhen Sock Exchnges. Recen epiricl sudies hve eployed coinegrion echniques o invesige wheher here exis such long-run benefis fro inernionl equiy diversificion (see ylor nd onks, 989; Chn e l., 99; Arshnplli nd Douks, 993; Roger, 994; Chowdhury, 994; Kwn e l., 995; Msih nd Msih, 997; Liu e l., 997; Kns, 999 nd Chng nd Cudill, 6). According o hese sudies, sse prices fro wo differen efficien rkes cnno be coinegred. Specificlly, if pir of sock prices is coinegred hen one sock price cn be forecsed by he oher sock price. hus, hese coinegrion resuls sugges h here is no gin fro porfolio diversificion. In his sudy, we es for pirwise long-run equilibriu relionships beween wo Chinese shre rkes by eploying five echniques of coinegrion ess, nely PO, I, JJ, KSS nd BN pproches. he findings of our five ess ll sugges h he wo Chinese shre rkes re no priwise coinegred wih ech oher. he finding of no coinegrion cn be inerpreed s evidence h here were no long-run linkges beween hese wo Chinese shre rkes nd hus, here exis poenil gins for invesors fro diversifying in hese wo Chinese shre rkes. hese resuls re vluble o invesors nd finncil insiuions, holding long-run invesen porfolios in hese wo Chinese shre rkes. he jor oivions for his sudy re hree folds. Firs, Chin is rpidly expnding eerging rke nd he rpid growh of he Chinese econoy hs rced he enion of inernionl invesors. Second, he governen policy of grdul relxion of resricions on foreign invesens in Chinese shre rkes hs furher enhnced he ipornce of he Chinese shre rkes o inernionl equiy invesors. hird, he ls decde hs seen significn increse in he inegrion of world cpil rkes. In ligh of pressure for incorporing developing econoy sock rkes ino globl invesen sregies, sudies on hin securiy rkes hve incresed in ipornce. Epiricl resuls fro sock rkes such s he Chinese shre rkes re of gre ipornce o globl fund invesors who y, be plnning o inves in hese wo Chinese shre rkes. he reinder of his sudy is orgnized s follows. Secion describes he d used. Secion 3 presens he ehodologies eployed nd discusses he findings. Finlly, Secion 4 concludes. PO, I, JJ, KSS nd BN re bbreviions for five ypes of coinegrion ess of Phillips nd Ouliris s (99) ulivrie rce sisic, rris nd Inder s (994) KPSS uni roo-bsed, Johnsen nd Juselius (99) xiu likelihood nd Kpenios, Shin nd Snell s (3) Nonliner uni roo-bsed pproches, nd Bieren s (997) nonpreric pproch, respecively.

4 . DAA Dily closing price indexes for A-shre nd B-shre fro boh Shnghi nd Shenzhen Sock Exchnges re used in his sudy nd he period exends fro Jnury 5, o Deceber 3, 5. D re colleced fro he Core Pcific Securiies Invesen rus Co. Ld, iwn. All series re esured in nurl logs. We firs exine how hese four sock rkes re correled wih ech oher. he sury sisics nd correlion rices for hese four sock rke index reurns (or log price chnges) cn be visully pprecied in ble. he rke s verge dily index reurns re.%,.5%,.4% nd.6% for Shnghi A-shre, Shnghi B-shre, Shenzhen A-shre nd Shenzhen B-shre, respecively, over his epiricl sple period. Regrding he sndrd deviion, we find h he Shnghi A-shre hs he highes dily sndrd deviion of 4.%, wheres he Shnghi B-shre hs he lowes 3.65% over he sple period. ble lso shows h index reurns for ech rke re lepokuric since he relive lrge vlue of he kurosis sisic (lrger hn hree) suggess h he underlying d re lepokuric, or hevily iled nd shrply peked bou he en when copred wih he norl disribuion. he Jrque-Ber es lso leds o he rejecion of norliy in he d ses of hese our rkes dily reurns d ses. Regrding he correlion rix, we find h ll he correlions re posiive nd significn. he highes coneporneous correlions re shown beween he Shnghi A-shre nd Shenzhen A-shre, while he lowes re shown for he Shnghi A-shre nd Shenzhen B-shre. Inser ble bou here 3. MEODOLOGY AND EMPIRICAL RESULS 3.. Uni Roo ess Sudies hve found h ny croeconoic nd finncil ie series, including sock price series, conin uni roos doined by sochsic rends (see Nelson nd Plosser, 98; Lee nd Jeon, 995). A necessry bu no sufficien condiion for coinegrion is h ech of he sock price index should be inegred of he se order (see Grnger, 986). In order o fully invesige he sionry propery of ech sock index, his pper pplies hree uni roos echniques, which include ADF (Dickey nd Fuller, 98), KPSS (Kwikowski e l., 99) nd PP (Phillips nd Perron, 988) ess. Pnel A, B nd C in ble repor he resuls of non-sionry ess for Shnghi s A-shre nd B-shre nd Shenzhen s A-shre nd B-shre sock price indexes using ADF, KPSS nd P-P ess, respecively. Ech sock price index is he null for KPPS is I(), wheres i s I() for oher wo ess, ADF nd PP.

5 nonsionry in levels nd sionry in firs differences, suggesing h he sock price indexes re inegred of order one, I(). On he bsis of hese resuls, we proceed o es wheher hese wo Chinese shre rkes re coinegred using he Mulivrie rce $P z es, rris-inder es, he Johnsen ehod nd he KSS s (Kpenios, Shin nd Snell, 3) pproch. 3.. esing For Coinegrion 3... PO Coinegrion es bsed on he Mulivrie rce Sisic $P z Following Phillips nd Ouliris (99), we consider he following bivrie coinegring regression X = + bx + Z () where Z re he residuls of he coinegring regression fro Equion (), nd nd re he wo shre price indexes o be esed for coinegrion, According o X X Phillips nd Ouliris (99), he $Pz sisic ess he null hypohesis of no coinegrion, nd is clculed s where Ω p $Pz = rce[ω p X X ] k = Z Z + W ( Z Z + Z Z ) sk s+ s s () for soe choice of lg window such s Wsk = ( s/( k + ))(see Phillips nd Ouliris, 99), is he sple size, X = ( X, X, nd re he wo shre price indexes o be ) X Z esed for coinegrion, nd X re he residuls fro esiing Equion () wih orhogonl les squres. According o Phillips nd Ouliris (99, ble IV), he 5% criicl vlue for he $P z sisic for one explnory vrible is 55.. If he copued vlue of he sisic is greer hn 55., hen we rejec he null hypohesis of no coinegrion. ble 3 repors he $P es resul. he copued sisics for ech pir of shre price indexes re ll lower hn he criicl vlue of 55., hus he null hypohesis of no coinegrion cnno be rejeced. z <Inser ble 3 bou here> 3.. I Coinegrion es bsed on KPSS Uni Roo rris-inder pproch is bsiclly n exension of he es proposed by Engle nd 3

6 Grnger (987) ixed wih he KPSS uni roo es. According o rris nd Inder (994), he es is specified s Y = X β + δ + ε, ε ~ IN(, σ ) (3) X = X + v (4) δ = δ + w (5) Where Y is he dependen vrible, X is vecor of nonsionry explnory vribles nd δ is rndo wlk in he residuls of he coinegrion Equion (3). If he Equions (3) o (5) re he rue d genering processes, hen he presence of he rndo wlk coponens in he residuls will ensure Y nd X no o be coinegred. owever, if he vrince of he rndo wlk coponen ( σ w ) is resriced o zero hen he rndo wlk coponen reduces o consn for ll. In his cse, Equion (3) will represen coinegring relionship beween nd wih consn nd sionry residuls. As indiced by rris nd Inder (994), esing he null hypohesis of σ w = gins he lernive σ w > will es he null hypohesis of coinegrion gins he lernive of no coinegrion. In he cse of rris-inder es, he firs sep is o esie Equion (3) by OLS o obin he error er, nd hen he KPSS es is pplied o check for uni roos in he residuls. ble 4 repors he resuls fro rris-inder es indicing he null hypohesis of coinegrion re rejeced for ll cses. Y X <Inser ble 4 bou here> JJ Coinegrion ess bsed on Mxiu Likelihood Rio Following Johnsen nd Juselius (99), we consruc p-diensionl ( x ) vecor uoregressive odel wih Gussin errors, expressed by is firs-differenced error correcion for s ΔY = ΓΔY + ΓΔ Y Γk ΔY k+ ΠY + μ + ε (6) where Y re shre price indexes sudied, ε is i.i.d. N(, Σ ), Γ i = I + A + A Ai, for i=,,...,k-, nd Π = I A A... A k. he Π rix conveys inforion bou he long-run relionship beween vribles, nd he rnk of Π is he nuber of linerly independen nd sionry liner cobinions of vribles sudied. hus, esing for coinegrion involves esing for he rnk of Π rix r by exining wheher he eigenvlues of Π re significnly differen fro zero. Johnsen nd Juselius (99) propose wo es sisics for esing he nuber of coinegring vecors (or he rnk of Π), nely, he rce ( ) nd he xiu eigenvlue (L-x) sisics. he Johnsen ehod pplies he xiu likelihood procedure o deerine he presence of coinegring vecors in r Y 4

7 nonsionry ie series. I is well known he coinegrion ess re very sensiive o he choice of lg lengh. Schwrz Crierion (SC) ws used o selec he nuber of lgs required in he coinegrion es. A VAR odel is firs fi o he d o find n pproprie lg srucure. ble 5 presens he resuls fro he Johnsen nd Jueslius (99) coinegrion es. As shown in his ble, boh sisic nd L-x sisic sugges h he null hypohesis of no coinegrion cnno be rejeced. r <Inser ble 5 bou here> KSS Coinegrion ess bsed on Nonliner Uni Roo Incorporing wih he non-liner uni roo es, he Kpenios e l. s (3) pproch is lso n exension of he Engle nd Grnger (987) coinegrion es. According o Kpenois e l. (3), he es is specified s Y = X β + δ + ε, ε ~ IN(, σ ) (7) Δε = γε + ν { exp( θε )} (8) where Y is he dependen vrible, X is vecor of nonsionry explnory vribles nd < γ <. We re now ineresed in esing he null hypohesis of θ = gins he lernive θ >. Under he null ε follows liner uni roo process (no coinegrion), wheres i is nonliner sionry ESAR process under he lernive (non-liner coinegrion). owever, he preer γ is no idenified under he null hypohesis. Following Luukkonen e l. (988), Kpenios e l. (3) use firs-order ylor series pproxiion o { exp( θε he null ) } under θ = nd pproxie Equion (8) by he following uxiliry regression: k 3 + iδε i +, =,,., (9) i= Δε = ξ + δε b ν hen, he null hypohesis nd lernive hypoheses re expressed s δ = (no coinegrion) gins. δ < (non-liner ESAR coinegrion). he siuled criicl vlues for differen K re buled KSS s ble of heir pper. ble 6 repors he resuls fro he KSS es nd furher deonsre he null hypohesis of no coinegrion cn no be rejeced for ll six cses. <Inser ble 6 bou here> Bierens (997) Non-Preric Approch Siilr o he properies of he Johnsen nd Jueslius pproch, he Bierens es sisic is lso obined for he soluions of generlized eigenvlue proble nd, 5

8 on he oher, he hypoheses esed re he se. he in difference is h, in he nonpreric pproch, he generlized eigenvlue proble is foruled on he bsis of wo rndo rices which re consruced independenly of he DGP. hese rices consis of weighed ens of he syse vribles in levels nd firs differences nd re consruced such h heir generlized eigenvlues shre siilr properies o hose in he Johnsen nd Juselius pproch. he Bierens nonpreric coinegrion es considers he generl frework s: z π + + () = π y Where π ( qx ) nd π ( qx) re opil en nd rend ers, nd y is zero-en unobservble process such h Δ y is sionry nd ergodic. Apr fro hese regulriy condiions, he ehod does no require furher specificion of DGP for, nd in his sense, i is copleely nonpreric. z he Bierens ehod is bsed on he generlized eigenvlues of rices A nd ( B c A ), where A nd B re defined in he following + rices: 8π A = k ( cos(kπ (.5) / ) z )( cos(kπ (.5) / ) z ) () k = = = B = Δ Δ ( cos(kπ (.5) / ) z )( cos(kπ (.5) / ) z ) () k = = = Which re copued s sus of ouer-producs of weighed ens of z nd Δz, nd is he sple size. o ensure invrince of he es sisics o drif ers, he weighed funcions of cos( kπ (.5) / ) re recoended here. Siilr o he properies of he Johnsen nd Juselius likelihood rio ehod, he ordered generlized eigenvlues of his nonpreric ehod re obined s soluion o he proble de[ P λ Q ] = when he pir of rndo rices P = nd A Q = ( B + c A ) re defined. hus, i cn be used o es hypohesis on he coinegrion rnk r. o esie r, Bierens (997) proposed wo sisics. One is he λ in es, which corresponds o he Johnsen s xiu likelihood procedure, o es for he hypohesis of ( ) gins ( r ). he criicl vlues for his es re r + buled in he se ricle. Second is g (r) es, which is copued fro he Bierens s generlized eigenvlues: 6

9 n ˆ ( Cλk, ), if... r = k = n r n g r = ˆ r ˆ( ) ( ˆ Cλk, ) ( Cλk, ), if... r =,..., n (3) k = k = n r+ n n ˆ Cλk,, if... r = n k = his sisic eploys he buled opil vlues (see Bierens, 997, ble ) for r, provided r > n, nd = n is chosen when n = r. hen ˆ ( r) converges in probbiliy o infiniy if he rue nuber of coinegring vecor is unequl o r, nd g ˆ ( r) = O hve p () if he rue nuber of coinegring vecor is equl o r. herefore, we li n ( ˆ P r = r) =, when rˆ rg in { ˆ = r< n g ( r)}. hus, his sisic is useful o double-check on he deerinion of r. As poined by Bierens (997), one of he jor dvnge of his non-preric ehod is h is poenil superioriy deecing coinegrion when he error correcion echnis in non-liner. ble 7 repors he resuls fro he Bierens nonpreric coinegrion es nd he resuls furher deonsres he null hypohesis of no coinegrion cn no be rejeced for ll six cses. We only repor he resuls of he λ in es nd he resuls of g (r), no repored here o sve spce, bu re vilble upon reques. hese λ in es resuls sugges h here ws no long-run relionship beween hese wo Chinese shre rkes nd hus confir our conclusions fro he Mulivrie rce g Sisic $P z, he rris-inder es, he Johnsen s ess, nd he KSS es. he lck of long-run relionship suggess h here exis long-run diversificion benefis for invesors who inves in hese wo Chinese shre rkes. <Inser ble 7 bou here> 4. CONCLUSION his sudy hs provided evidence h here exis long-run benefis for invesors fro diversifying in wo Chinese shre rkes over he period Jnury 5, o Deceber 3, 5. he evidence is bsed on ess for pirwise coinegrion beween he Shnghi nd Shenzhen s A-shre nd B-shre sock price indexes, using four coinegrion ess, nely PO, I, JJ, KSS nd BN pproches. he resuls fro hese five ess re robus nd consisen in suggesing h hese wo Chinese shre rkes re no pirwise coinegred wih ech oher. hese findings could be vluble o individul invesors nd finncil insiuions holding long-run invesen porfolios in hese wo Chinese shre rkes. 7

10 REFERENCES Arshnplli, B., nd Douks, J. (993) Inernionl sock rke linkges: evidence fro he pre- nd pos-ocober 987 period, Journl of Bnking nd Finnce, Bierens,. J. (997) Nonpreric coinegrion nlysis, Journl of Econoerics, 77, Bierens,. J. (4) EsyReg Inernionl, Depren of Econoics, Pennsylvni Se Universiy, Universiy Prk, P.A. USA. Cpbell, J nd Perron, Peer. (99) Wh croeconoiss should know bou uni roos, edied by O. Blnchrd nd S. Fish, NBER croeconoics nnul, MI Press, Cbridge, MA. Chn, K. C., Gup, B. E., nd Pn, M. S. (99) An epiricl nlysis of sock prices in jor Asin rkes nd he Unied Ses, he Finncil Review, 7, Chng, sngyo nd Cudill, B. Seven (6) A noe on he long-run benefis fro inernionl equiy diversificion for iwn invesor diversifying in he US equiy rke, Inernionl Review of Finncil Anlysis, 5, Chowdhury, A. R. (994) Sock rke inerdependencies: evidence fro he Asin NIEs, Journl of Mcroeconoics, 6, Engle, Rober nd Grnger, C. W. J. (987) Coinegrion nd error correcion: represenion, esiion, nd esing, Econoeric, 55, Grnger, C.W.J. (986) Developens in he sudy of co-inegred econoic vribles, Oxford Bullein of Econoics nd Sisics, 48, 3-8. Grnger, C.W.J. (988) Soe recen developens in concep of cusliy, Journl of Econoerics, 39, 99-. rris, Dvid nd Inder, Bre. (994) A es of he null hypohesis of coinegrion, in Nonsionry ie Series Anlysis nd Coinegrion, edied by Colin rgreves, Oxford: Oxford Universiy Press, Johnsen, S., nd Juselius, K. (99) Mxiu likelihood esiion nd Inference on Coinegrion - Wih Applicions o he Dend for Money, Oxford Bullein of Econoics nd Sisics, 5,69-. Kns, Angelos. (999) A noe on he long-run benefis fro inernionl equiy diversificion for UK invesor diversifying in he US equiy rke, Applied Econoics Leers, 6, Kpenios, George,. Shin, Yongcheol nd Snell, Andy. (3) esing for Coinegrion in Nonliner SAR Error Correcion Models, Working Pper, Queen Mry, Universiy of London. Kwn, Andy C. C., Si, Ah-Boon nd Cosoiis, John A. (995) he cusl 8

11 relionships beween equiies on world exchnges, Applied Econoics, 7, Kwikowski, Denis, Phillips, Peer, Schid, Peer nd Shin, Yongcheol. (99) esing he null hypohesis of sionriy gins he lernive of uni roo: how sure re we h econoic ie series hve uni roo? Journl of Econoerics, 54, Lee, Bong-Soo nd Jeon, Bng N. (995) Coon sochsic rends nd predicbiliy of inernionl sock prices, Journl of he Jpnese nd Inernionl Econoics, 9, Liu, Xiing., Song, iyn., nd Roilly, Peer. (997) Are Chinese sock rkes efficien? A coinegrion nd cusliy nlysis, Applied Econoics Leers, 4, Msih, Abul M. M. nd Msih, Rui. (997) A coprive nlysis of he propgion of he rke flucuions in lernive odels of dynic cusl linkges, Applied Finncil Econoics, 7, Nelson, Chrles R nd Plosser, Chrles I. (98) rends nd rndo wlks in croeconoic ie series, Journl of Monery Econoics,, Newey, Whiney nd Wes, Kenneh. (987) A siple, posiive sei-definie, heeroskedsiciy nd uocorrelion consisen covrince rix, Econoeric, 55, Oserwld-Lenu, M. (99) A noe wih quniles of he sypoic disribuion of he xiu likelihood coinegrion rnk es sisics, Oxford Bullein of Econoics nd Sisics, 54, Phillips, Peer C. B. nd Perron, Pierre. (988) esing for uni roo in ie series regression, Bioerik, 75, Phillips, Peer C. B. nd Ouliris, S. (99) Asypoic properies of residul bsed ess for coinegrion, Econoeric, 58, Roger, John. (994) Enry brriers nd price oveens beween jor nd eerging sock rkes, Journl of Mcroeconoics, 6,, -4. ylor, M. P. nd onks, I. (989) he inernionlizion of sock rkes nd he boliion of UK exchnge conrol, Review of Econoics nd Sisics, 7,

12 ble. Sury Sisics nd Correlion Coefficiens Pnel A. Sury Sisics of Sock Price Index Reurns RSA RSB RSZA RSZB Men.%.5%.4%.6% Sd Dev 4.% 3.65% 3.79% 3.7% Miniu -.4% -9.% -.6% -9.7% Mxiu 34.8% 6.3% 3.6% 4.3% Skewness Kurosis J-B 9,84.3* 48.4* 5,436.5* 5,886.4* L-Q(6).98* 49.7* 33.3* 98.7* L-Q() 37.86* 68.47* 38.86*.7* L-Q(6) 6.56* 4.76* 5.36* 4.78* L-Q() 78.6* 6.4* 6.59* 64.33* Pnel B. Correlion Mrix of Sock Price Index Reurns (or log price chnges) RSA RSB RSZA RSZB RSA RSB RSZA RSZB Noe: * indices significnce he 5% level.

13 ble. Uni Roo ess for Shnghi nd Shenzhen Sock Price Indexes Pnel A Pnel B Pnel C ADF KPSS Levels PP η u Lsh (4) 4.45 [4]*.467 [4]* -.9 [] Lshb.955 (4) 3.98 [4]* 3.74 [4]*. [] Lsz -.88 (4). [4]* 3.77 [4]* -.45 [] Lszb. (4) 4.3 [4]* 3. [4]*.657 [] η Firs-differences Dlsh (4)*.7 [4].47 [4] []* Dlshb -6.3 (4)*.37 [4].7 [4] []* Dlsz (4)*.98 [4].8 [4] []* Dlszb (4).3 [4].37 [4] []* Noes:. Lsh, Lshb, Lsz, nd Lszb represen Shnghi nd Shenzhen s A- nd B-shres, respecively, in he logrih for.. D- iplies differencing in ech vrible. 3. he nuber in he prenhesis indices he seleced lg order of he ADF odel. Lgs were chosen bsed on Cpbell nd Perron s (99) ehod.. he nuber in he brcke indices he lg runcion for Brle kernel suggesed by Newey-Wes es (987). 3. * indices significnce 5% level. ble 3. PO Coinegrion es bsed on he Mulivrie rce Sisic Pˆ Z Mrkes $ P sisic z SA-SB.33 SZA-SZB 5.78 SA-SZA SB-SZB SA-SZB 7.57 SZA-SB.546 Noe: he repored $P z sisic is bsed on lg window of 6. Alernive lg windows of,, 3, 5, nd 6 yield quliively siilr resuls. he 5% criicl vlue for he $Pz sisic for one explnory vrible is 55. (Phillips nd Ouliris, 99, ble IV).

14 ble 4. I Coinegrion es bsed on KPSS Uni Roo η u 6 lgs 9 lgs η SA-SB 7.4*.48* 5.79*.994* SA-SZA 9.39*.8* 6.8*.598* SB-SZB 7.345*.48* 5.79*.993* SA-SZB 3.35*.3*.95*.* SZA-SB 9.3*.99* 7.655*.79* SZA-SZB 8.*.83* 5.87*.63* Noes:. * indices significn 5% level.. Criicl vlues re ken fro Kwikowski e l. (99) 3. he KPSS es bsed on lg windows of 6 nd 9 lgs yields quliively siilr resuls. η u η ble 5. JJ Coinegrion es bsed on Mxiu Likelihood Rio rce es 5% criicl vlue L-x es 5% criicl vlue SA-SB (VAR lg = 4) : r : r SZA-SZB (VAR lg = 5) : r : r SA-SZA (VAR lg = 7) : r : r SB-SZB (VAR lg = 5) : r : r SA-SZB (VAR lg = 5) : r : r SZA-SB (VAR lg = ) : r : r Noes:. Criicl vlues re ken fro Oserwld-Lenu (99).. r denoe he nuber of coinegring vecors. 3. Schwrz Crierion (SC) ws used o selec he nuber of lgs required in he coinegring es. he copued Ljung-Box Q-sisics indice h he residuls re whie noise.

15 ble 6. KSS Coinegrion ess bsed on Nonliner Uni Roo Counries Sisic on δˆ SA-SB -.3 SZA-SZB -.39 SA-SZA SB-SZB -.6 SA-SZB -.57 SZA-SB -.7 Noe: he criicl vlues for sisic on δˆ re buled KSS s (3) ble of heir pper. ble 7. Coinegrion es bsed on Bierens Nonpreeric Approch λ in es es 5% criicl vlue es % criicl vlue SA-SB Conclusion r = : r = : r =.986 (,.7).58 (,.5) : r = : r = -- (,.54) -- (,.) SZA-SZB Conclusion r = ) : r =.84 (,.7).6 (,.5) : r = : r = : r = -- (,.54) -- (,.) SA-SZA Conclusion r = : r = : r =.8 (,.7).64 (,.5) : r = : r = -- (,.54) -- (,.) SB-SZB Conclusion r = : r = : r =.83 (,.7).7 (,.5) : r = : r = -- (,.54) -- (,.) SA-SZB Conclusion r = : r = : r =.554 (,.7).33 (,.5). : r = : r = -- (,.54) -- (,.) 3

16 SZA-SB Conclusion r = : r = : r =.5 (,.7).65 (,.5) : r = : r = λ in -- (,.54) -- (,.) Noes:. he es is bsed on he generlized eigenvlues of rices of A nd [ B + ca ], where A nd B re copued s sus of ouerproducs of weighed ens of y nd Δy, y is uni roo process, is he sple size, nd c is posiive consn. he vlue of c is, s suggesed in Bierens (4).. he criicl vlues re fro Bierens (4). If he vlue of he λ in sisic is ouside he criicl region, hen we do no rejec he null hypohesis. If he vlue of he λ in sisic is wihin he criicl region, hen we rejec he o. If boh he null hypoheses re rejeced hen we conclude h r =, i.e. here is no coinegrion (Bierens, 4) (r denoes he nuber of coinegring vecors) 4