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LondonSouthBank UniversityFaculty of Business, Computing & Information M anagement

EfficientM arket Hypothesis:An empirical analysisofforecasting share returns and volatility on Chineaes t o c k market

I3y

U i w m t i o n submitted in partial fulfillment o f t h e requirement forth e degm ofM sc Financc& Accounting

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ContentsCHAPTER 1 Intmduction 1,

CHAPTER 2 Ch.ineaeS t m k M arket2.1, ,H,iswricnlbackground and development2.2 Structural,m d 1:nstitutional Characteristics2.3 The'llmfilcs

C,HaPTER3 Literature 'Review3. ,, :EmergingM,arkr?&3.2 Random NMks3.3 ,E:EficicntM arket Hypothesis3. 4 Volatility

C W E H Time-Serieo ,EmnometrimMethaddolop5.1 Objective5.2 %st ing forStationary

5.2.'1 StochasticF mess and :Distri,buti,on5.2.2 Inteegrated Processes en d 'Differencing5.2.3 Tcsti,ngor Autocorrelation

5. 2. 3. 1 TheCormlogram

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5.2.3.2 T he Box-,PierceT W & the : I ju,ng-,Box s t5. 2. 3. 3 T h e Lagrangc M ultiplier ' k s t & the P%st

5.2.4 Unit Root b s t5.2.4.'1, Introd uctim5. 2. 4. 2 TheDkkcg- Ful l erQ6t5. 2. 4. 3 ThcAugmented Dickey-Fuller lkst5.2 .44 ' T heA I C & theSB C

5.3 'Forecastingwi,thA R I A U M odels

CHAPTER6 Empirical bsu:lta6. 1, , Empi r i calDistribution of lbhms6.2 Carrelatian Coefficient of Re t u r ns6. 3 1:nregratcd Pr a~ssesnd Differencing For

ShnrePrice Indims &Retwns6. 4' TheCo,rrclogram or Shnre Price I'ndices& Returns6.5 TheQ & the Q %st ,fmReturns6. 5 The IAfl & the F lkst for Return66.7 ' Uni tRoot Ikst

6. 7. 16. 7. 2Formast i ng Re t u r ns with ARMA Mo d e l0.8.1,6.8.2 M odeli,ngA , W pcci.fimti,ons6. 8. 3 Formasting '&turns

Unit Root Tcs t for Share Pri,ce1,ndicesUnit b o t %st. for 'Returns

6. 8I dentification d t h c value ofp &.q

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CHAPTER 8 Cancluaion

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Acknowledgements

I would like to cxpress m y si ncere gratitude t o ,my supervisor,Dr ,Howard G r i f i t h s , for his guidance nnd encouragementtowards my rompletion of this thes,is. This thesis woul d noLharebeen possible without:hishelp.

I wou l d HISOike t o thank those who have ki ndl y given mern1,unblehdp,i.n hc development [and completion o f my thesis.

Finnlly, 'I amparti,cularly grateful t o my pamnts and rng sistc,rfor their support and encouragement throughout my studies.

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SynopsisThisthesisexamimswhcthcr or not: the behaviour of the Chineses w , k rnn,rkcts(CShfld appear to be e f i c i , e n tbased on econometr i cstime-series rnethod,ol,ogics.

T h e first part o:fthis study shows. by nmalysing iheir ermr serialcorrelations basedon the SACIP and ,theUni,tRoot tests , theCshls'rcturns a,renot stat ionaxy tirne.sePiesduri.ngthe period October1992 to September 2003,.I n thesemnd l s ~ r tf this thcsis, acmrdi.ngta theappemance o:fthestationary time-series,w e model the return processes vin ARWlA,speci,fi,cation,s i t h :Fmedcm,Eficien,tsestimated from p w t d a h , toforecnst the CSAls' Future return processes.The last: pnrt of this thesis is mnclerned with volatilitymeasurement, si,ncethe classicnl assumption o f errors having aconstantvariancecannothe indicttied. We examinerdntility usingmodels of thc G,A.R-C,HI :family nnd more spccifically theG'A.RC,H(I,,I,)models mgctrhcr with compar i son tn the ARhtAl'I,.'l)tXIodcls.

Our main :6,ndi,ngi sthat the historical rcturns can he used t r oforecast: stock 'returns n short, horizon in the CSAls, especially ,i.nthe Shengwn-A L5ZAI stock market. The existing potentialpred'ictability implies that theCSMs arePn'r fromthe weak form oftheemcient rnerk,echypothesi,s EMHI.,Furthermom, w e a h ,nnlysed the correlat ion hetween the CSMsthemselves and the Nikkci 225. W e dkmvered that thecombination of theemerging CSMs an d the well developed Nikkei225 would be a good strategicplay tu avoi,drisk,

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NotationAkHike lnformnbion C rilxrionAugmented 'Dickey FullerChina Securities Rep latmy CommissionChineseStock M arketsDickey FullerDOWJ ones Chi.na88Efficient M a.rket HypothesisInitial Public Of f er i ngsJ arquc-BeraL agrange M ultiplierbIa.xirnurnCikelihoodRenminbiRmtMcan Squa.reErrorSampleAutocorrelation FunctionSchwa,rx Bayesian Criteri,onShmghai Stock ExchmgcShenzhen Stock ExchangcShanghai-AStwk ExchangeShanghai-BStock 'ExchangeShenzhen-AStwk E x c h m g cShenzhen-B Stwk ExchangeWorld TradeOrpniztitiun

AICADFCSRCCSMsDFD588EMH11'0sJ BLMA4LRRmRi iKESACFSBGSHSESZSESHASHBSZASZBWTO

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Listof TablesTeble 5. 2. 3. Shtiona,ry or Non-stationary: i, ecision r deTable 5. 2. 3. 2Table5.2.4.1,Ta,ble5.2.4 .2 .aThe ' DF nit mot kstingp:rmdurcTabl,e5.2.4.2.b Stntionary or ' Non- st at i onary:hc I lF est: decision ruleTable 5.2.4.3.a h e ADF unit motkstingpmcdure'11~1Iilc5.2.4'.3.b tationnry or Non-stationary:The,ADF s t decision rulem i l e 6.1, ,Uistci,butionof returnsstntisticsTable 6.2 Estimated cmrelstion coefficientsof the retu,rnSTnhle6 .5 Surnmarkd Q & Q statistiicsof :returnsTabh 6. 6 Serin1correlation of return$ tcsidual,~Table6. 7. ,, H:U,F :1,2)est For 'theshamprice ind'icesTable6. 7. 2~ I ' F 1,2)ksc for cheS:HA& theS%Areturns -1,Table G.7.2.b A.DP k s t Tor the SHA& the SZA retu,rns-2Table S.7.2.c I W test for theSH ' H & theSZ:H returns'lhblc 6.8.1, Estimating the A .R nM (l,q)modelsTable 6.8.2.a li'he 01123esti,mationsof the partmetcrsTnble 6.8.2.h EstirnntedA,'KMAmodelsTabk 6. 8. 3 &SUI,& f forecastsTablc7.2Table '7.3Table 7.4TAble -7.5Table 7.5.a A s s u m k g n t-distribution

Stationary or Non-stetionmy: Q, p'decision rulcStationa,ry or Non-stationary: Unitmtd,ecision rule

ARCH:effect decision ru l esh s u l i s of thea:KC:nffectARCH effect decision ruleshsu l tsof Wf!%ent6 of GA:RCH(1,1,)models

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Table-7.5.bTable7.6.aTable7.G.b7'nblc 7.6.c'klble 7 .7

Assumi.ng a nor mal distributionForccasr ing vo~uti.l.ity ith lGARCHh,'l) model fur SHACornpari,n#est imarcd errors for SH.AForecastingvolatil.ity for S U

h~ :ca , su rcsf forecastperformances

Listof Fi gur esFigure 6.'l,,.bF,igure6. 3:F igure G.4,.a:Figure6.4.b'Figure6. 8. 3,Figure 7.7

Themflximum & rnin'imumstatistics of returnsPatterns oFshnre prim ind.icesAnd returnsCorrclogramo l share ppicc indices and returnsSampleautomrrclation,c o c f i c i e n u o f retu:rns'Ploto f ~ t u dnd forccnstsI!lot of actual nnd Forccas&

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CHAPTER 1Introduction

The purpose of thethesisMfeseek to build upon knowledgt? gs ined from the MSc Finance BrAccounti.ng ~ U P S C or g rca t~ rundershnding, both empiricallyand a.nalyticnlly of the Chi.nesesmk ma.rkets (CSMs) pricingeEciency.

The Chi.nesc stock, marke& are emerging market s and bad notbeen establ.ishcd,until htte 1,990. h ehaviour has not heenex,arnincd n detail up until temntly. T hemfore, our pu.rposesH.W:

1. 7b i.ndicatethe coml ati ons between the CSMs themelves andthe other biggest sbck market: in Asia , i.n pa:rticula.r theJ apancse stock market. Ni kkei 225.

2. To form a diversi:fiedpottiol.io o i.mproverisk-return trade-om.3. To exarni.newhether Che behnviour o f thc CSMs appears t o be

efficient.4. l b t e s t whether the CSMs wru,rns can be forccast and thei.r

volntilitics (risk) ca.n be mcasurcd based on econometricsmethodologies.

5. To learn mote about:emerging mnrkcts.1

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6 . 'Ib provide useful information for investors to understand thebchtlviour of the CSMs

'b achieve the above purpows, some spec& questions will beaddressed BW followe,

>' Can the investment risk be diversified away or reducedsi.grdicantlyby H portfolio?

4 !f the CSMs do nQt appear ta be eficient, how i,neEcientare they'?

> Ho w t o fQreCfi6tshare prim4 returns and measwe risk,hyusi.ngeconometrics mebhodoloigies?

3. What k.ind of models can be used IO do so, and ifany!whichmeasur ement will perfo,rmbetter?

Structureof the thesisThisthesis i s organized into the following chapk r s:

Ch~pter Presents the background, development, structural andinstitutional characteristics, the prof,leG, and lists some of theshortcomings of the CSMs.

Chapter 3 Reviews the most 'i:mpnrta:nt1,iteratureregarding t he'random w a l k s , the eficicnb market hypothesis and Ibrecastingvolatility ns well 8s the major a.rbicles regarding the emergingmarket$.

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Chapter 4 Describesthe appl.icationofor ighd dAta, logdata, logmtutnsnnd emnometticsofiwarepnckagcs.

Cha,pter6 I ntmd,uces the the-ser iesemnometrics met hodol ogi esused in this thesis. for testi .ng sbtionnry prowsses in the CSMs.Thesc approachesn.m- integrated processesand di,ffercncing- the correlogrm- thc ; I~OK - I ?~EPZCe s t & the ,Lju,ng-Rox&et,

the hgrmgc M ul~ipl iere s t & the ,F & s tuni,t oot bst including the IIF test i% the M3,F * ~ tthe ATC & theSRC selectioncrikrin

---- Forecastingwith ARI,MAmodels

Chapter b A.nalgse the empirical results. Out comes i.nclude 'thetnhlcs and Ggurcs.

Chapter 7hmily tcgethe'rwith mmpsrimnb theA:WAmodels.

Exa.mi,ncs volatility usi.ng mod& o t thc GA:RCH,

Cha,pter8 Concludes the m,ai.nti.ndi,ngsof this thesis and pointout the extension,of stud,ies.

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CHAPTER 2ChineseStock M arket

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2.1Historical backgroundand developmentI n the enrly 'halfofthe20thmntury, Shanghai wa s regarded,as thefa,r.cn$d fi.nn,ncislmnwr with n glorystock msrket. :However,nftcrR short period of rehlgcncc, this ever financial,center had been indrcariness u,ntil the middle 198Os, Chi.nescgovernment decided t r ~rebuild stock rna.rkc& which w as part o f the new policy o:f'eoonornic reform a,nd open-ouwide'. A t the ti.me, thc issues an dtrades were nll owr-the-cmners. Thc situation had not heenchnngcd until late 1, 440when Shanghai Stock 'Exdmnge(S:RSE)nnd Shenahen Stack Ewhmge (S7SK)were established.

b,ttho very bcgi.nni.ngof its est abl i shment , Chi.n,csesiock marketW A S H very small scale OF market;: 13 listed companies, several,bill.ion RMR of ma.rkctcapitdization, t housands i.nrresbors. t ens o:fbrokerage :fi.rmsan d werage one million :IZklB o f da:ily tradingvo lume. Along with the wide npplicntion of high-tech and h u gdemand o f market, the following one decode has b x n seen tz rapidprogress i.ntheC h e w stlock market.

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The growth ofthc stock mar,kctein thc last:1,3year5hnsbcen mostimpressive by any stnndmd. Theh6al rnN,rkctcapitalization ~t thcend of theyear 20)02was up to ovcr $4. 4' rillion ( RMB38 trillion).This made Chinese mwket th c second largest in Asia &er J apan.I n the market there are 1.238 lisbed companies, and over 69million i nvestors acmu.nts 12'1.

2.2 Structuraland Institutional CharacbrhticsOptions available to n company for a stlock exchange listinginclude:2 Domestic hti .ngofA:sha.ms;> DomesticListingof B-shares;> Overseas listi.ngof For ei gn 'I nvestmentShares;4 ,&d-chip 1,isti.ngwhich can take various forms.

A company could list itfi domestic investment shnres(i n theform ofAsbares)or foreign i.nvostmentshare3(in the form of B-shares) inShanghai or Shenzhen or its foreign invesLn ien t shares onexchanges which have signed H M emorandum of Understandingwith the CSRC or underttakeH red-chip listing.

AShams A-shares wrc diffcscnt fmm other categoriesufdomcsticinvestment shares such HY eta te -owned shwrm. A-Aharcs aredomestic investment shares ,issued by Chi nese companies which

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g.rc l i s k d on theS,HSE:and SZSE. A-sharesaresubscribed by nndtraded nmong Chinese ci ,t,hns nd/or enti ties.

,BShares Forei gn investment shn.res are h t e d as B.she:resonthe S:HSE or S E X T h e t ~r m B-shn.res.d,ornesticn.lly1,ist;cdforeign investment shares and spccin.1 , re,nminbi CmR) -denominated shA.resall refer fa the same thing-ordi.nn.rysharesofC hi .nee shnreholdi,ng compfinies that n.m d,enorni.natd .n RM Bbut: traded, i.n loreign currencies,such 8s US dallsrs, on a Chinese3ecu.rities e,xchn,nge. B-sha.rcs an n n l r be subscri,bcd by and,traded n.mong foreign cgd and naruralperwns m d ,other entities,legal nnd natural persons from Hang,Kong,M acau and Taiwan,nnd Chi.ncsecitimn who a.* resident: abroad.

0verSeasLis.fingof Forei gn Shems All Ibrci.gn l.istingmust beapproved by rhe CSRC nnd the Foreign stock exchange (andregulahry nuthmity+such EISthe SE C i.n the case of n US1isti.ng).:Foreign sha.rcs (such HS H:-sha.res)must be issued in rcgkteredform and denomi,nated i.n RMR e v m though they are traded, inForeign cur rencies. :IIcpository rewipw issued ovcr H-sharesarcnlso treated RS roreignshn.ri?s.

Red Chip fikting K ed-chip compnnies a.rc those i,ncorpora& d i.n:Ho,ng ong and listed on the Hong KoongStock Exchange but w i t hcontml1,ing shnreho1,ders rom mai.nh.ndChi.nesc entities.

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2.3 ThePmfdesThe stock mn.rkets have b e n d.ramaticn,lly gt%wi,n,g,cornpadwith its short history. Th e high emcient; tradi.ng system has m d eiis most i.mpressive profile. i.n berms OF central cleari.ng nndhmk.entry, market capitoliaacion, volume of rnising money,enln.rgementof i.nrrcstorbase, number of listed Eompanics, 8s well,a$ daily trnd'i.ngvolume cnm,pn.redw i t h any other markem in theworld,.

I ,n fiddi,tion, since its establiihrncnt, Chinesc stock rnnr,kct hasbeen on the trip o f glubnliaation, considering the Fnct that o lot ofChi,nesccornpnnies issued, ' Bha:resor I.iskd in H:ong,KongSt ockExchangc, Singnpore Stock %:xchAnge,Tbkyo Stock Exchange,kndon Stm'k, E:xchang!NASI?AQ and,NewYork, Sin& Exchange.Meanwhile, , Bhares n,ndo v ~ r w a s .istinghe1,ped themarket start:to norrndkc its practicc and systcrnof Inw and a,munti.ng n li.newiLh international, standa.rds. Even though, Chinew stock mn,rkethas been still sufferinga series of shortmmi.ng6AS followi.n@, duel o i,ts i:mmaturi,ty an d emnornic bacckgcound under Chi.nesetransitionnl s h p rom planed economy i.ntomn.rk,eremnomy.

3hoztcomi.nm> hfarket mechanism i s far fmmCQrnpleteness.3 Th e government somet i mes plays H role by changing pdicies. -

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CHAPTER 3

L ikratureReview31 EmergingM arketsAn mergi ng mark,& is one thst has publicly t raded secu.rities in EL lessdeveloped ma.rket. Broadly de cd. an emerging rnarkct isH country makinga.n e f f o r t t o change clnd i.mprovc its economy with the pal of raising itsperformance lo that of tbe worldsmow advanccd countries. k I ~ . u y ,hesernarkebogeratc in countries with IOWcr-capital i.ncome.Thecmergence ofcapital mar ket s in developi.n,gmuniirirics i s. pa.rt of a general process o fglobalization of capital rnarkee. Research on emerging markets hassuggeskd th.rce market features: high avera,gc retu.rns (cl+al of highp w t h economies), high, volAtility and low correlations both across thcemerging rnn.rketsand with developed markets.

These emerging rn~.rketsttract international i n v e s h ~ s ased in developedmuntries primwily because of the high potrntial for high rctu.ms in Brelatively shortpcriod of ti.me.These high return5ex i s t mai.nly because thecountries, newly i :ndustrisli-lk.d and developing countr ies, arc experiencingphenomenally high growth :rakes.This trendof h.igh ~ o w t hs expected tocontinuehence the high rawsof return, B R wdl ns the diversification benefitsit offers, ~ P , Dare expected t o perfiist. Rekacrt and Urias (1999) studied the

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rewards to be gained from ho1dingema:rgingmarket Rtockv i n R global equityportfolio. They used the mesn varitrnce a,nalgsic;: whereby covarianceestimate6were used to construct expectcd exccss ,returnsthat correspondedto ahypothetical efiicicnt portfo1:io.I nmost CAWS , the resultsshowed thatthe expected return for the emerging 'market smcka surpassed that of thedeveloped world equity market: :nde,x or opti.malportfolios,with at least 10%invested i n emerging markets.

Emerging market, returns are found t o be mow pmdict,tlble tha.n developedmarket returns. The sources of this predictability could be time varying riskexposures, timc-va.ryi.rig r isk premiums a.nd it could d s o be i nduced byfundamental inefficiencies. Beknert, Erb, Harvey and Viskanta (1996)establ.ished that as a mR.rk,echccomes more inwgrated into world capitalmarkets, it ismore hkely that w ~ l d ,nformation will have a great impacbonthe time varyi.ng mean rcturns. Most of the predictability is strong12influenced by local information, which isconsistent ai & the fact that someofthese countries arc s egment ed from world capital markeh. On the otherband, these high returns me also acwm,paniedby high volatility. There is ap a t deal of risk i n v o l v c d in investments in the emerging markets, becauseemerging rnarkcts a . ~ ,y d e h i t i o n , ,inH state of transition and a . ~ubjecttu unexpec ted political an d economic upheavals. The values of their stocks,bonds and currencycan chmgc d.casticnl.lyand without notice.

Divecha, Drnch and Stefck (1992)give some ofthereasons for this volatilityin H papcr.A few o f the e x p l n n a t i o n b this volfitility arepolitical instability,

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cumncp r i sks , i:ll.iq,uid'ity risks and high trwnsaction COS~S. Marketconcentration is suggcsted to be an i.mpottant: factor, w'hereby i.n thesemarkets, largcr stodk,srepresent a higher proportion rrl the overall marketcapitn1,izntion.This leads to a situationwherc them are fcwer opporcuni,tiesfor diversi.rIcation because the rcturns t o thcsc large stocks dominate theorernli rna,rkctreturn. Another k ey fncbr is that emergingmarkets tend tohave H strong ma.rket-relakd forcc that afleects a'I:Is b c k s withi.na rnawket,thu8 accentuatingvolatility.Thssis very much unl i ke the developed markets,where f orces afkfectthevarious scct~rsf theeconomy in difkrentways .

Bekaert and, 'Wtias (1999) a b xamined the risks involved 'from holdkgemerging rnsrket stock& AS part of an i.nternational portfoho. Their resulbdemonstrated that emergingmarketstmks, when8,ddedto H rnean-skandn.tddeviat ion dhgra.m. an e f i c i e n t frontier, the frontier either stayEd, thc sameor shifted ' tothe lek! i .e . the investor wi.ll &her b e i,nthe same, or h t k rposition as regn.rdsrisk. Also, tes ts t o hnd out whether thc 1efLwa.rds hi R i.nthe hontier w as signi:hcnntshowed that there wcre statistically signi:ficantdiversification benefits du.ring he tes t period.

Furthermore, even though,ernergkg rnn.rkets are risk,)? .ndividunU,y, lo woor rel at i ons b e t w e e n thcm and with developed, ma.rkets lead to risk,reduction Tor i.nvesmr8. Divccha,Drach a.odSbfek (1,9921,kkaertand Urias(1,999) an d Enker: Grant and, Wmdard (2000) all demonstrate that as ageneral rule, em,e tg ing rnn.rkew are much less oorrelakd wi , th one anotherthan n.re the developed mn. rke ts , with the exceptions M ng rnmkets in n

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specific region, for examp le Sou,thE ~s t s h . A,possible reason for thew lowmrrclations that exist: i s thnt theemergingmarket economcs are unrelated.Thi s i s as a resuk o f the few economic and trade links that emerging mnrke tshave w i t h ench other. Another 1.i.kolyPCHSOII that many of t h e emergingmarket econmnies have, or have had,, scvere restrictions on outsiderspa,rticipsting i.n thc:i:r narkek Thi s resu l t s in the emerging market s bei,nginsulated .Fromthe wo r l dw i d e , or even regional,, pa,tkrns i.n stock marketmtu.ms.Thus. contmry fa popular belief, R modest i.nvestmenr i.n emcrgi.ngmrukek will lead to .a d u c t i o n , rnther tha.n a.n incr ease, in portfolio risk foran i:nnvt.e.hx.

'Even a,br he two scvere fi.nancia1,an d economic crises that have afn.ictedth e emergi ng market s, che collnpse o f the M ex.imn peso :in 1994 and thecoUnpss orthe 'rhsi bath i,n1,9912//97, herea.rcstill diversi.ficatrion bCnefik6 tabe rcaped. 'Ibk,aertn,ndUrias (1,999) have identi.fied that:there is still a ' f reelunch' i.n the emerging ma.rket equities. They have shown that dircctexposure tn emergingmarkeL indices dmost always gives benefits at least 8sStrongns those Frommanngcd Funds. They ds o note that Iacbrs common COemerging markeh such 8,s poor l.iquidity amd currencyz as well HSmacroeeconomic i,nstabil.ity,which s f f e c b itsperformance, a.renot d l c c t m ! bybenchmark i.ndices. T hus, the performance of i,nvcstment in emergingma.rke& represented by benchrna:rk i.ndicesmay not:nlnnys be nchicvable.

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3. 2Random WalkeThe concept o:f market eficiency arose acccid,entally. Eu.rlyresewchers were concerned about the t h e series of changes i.nstock prices for prediction pur poses. T he first ,rcoordo f studies i.nthe change in stock, prices ca,n bc traced back t o 1,,990whenBachei.ier(1,901))oncluded that: the ptims i.n the llrench Hou,rscchmgeed in randomly fashion. His results w e l r ignored for manyyea rs and only in 1934, Working (1,,934) id 8 shi1a.r study on theUS sbk ma.rket.

The idea o f e K c i e n c y WM fi.rstmnccived a h r thework,ofK endnll(19531, w ho invcstigared, the chn.ngcs :i.nthe pr ices of the UKrnn.rket. We studied the wcekly chnngcs i.n the price indices for 23weeks . and,a.rrivedat theconclusion that they did not ,followH cycleor trend,and that the suwssive changes were i.ndepend,ent fcnchother, in other words, that they moved randomly and that thehistorical path provided no uscful i.nforma,tion. He added bhntinvestors made profits not: by lwrk,iagat past prices hut by luck,inside informa,tion, speed, o f reaction a.nd by the scale of theiroperations.Hs resulk!puzzled many fi.nancin1emnomists, 86 theyserried t o imply that the market: w as d.riven by animnl spi.ritswho followed no tulcs. Many ana l , ysk w e r e led t o behew that i.fprices rnovwl randomly, without much rationalle, the systcm wentugai.n6trill the pri.nci,p!esof classical economics.

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dlcxa,nder (J,,961,1, owever. showed that all that the rsndom,nessin price changes i.mpliedWEIS that prices adj u,sbd i.mmed,iakly .0new in:forrnation,which i.n Facc represented thc bl.issofcconomists.H'e found that ,fi.Iter kchniques did, not suoceed in beAting IIbuyhold strategyconsidering,becnuse of transaction and tn .xnt ionw s & . Athough the f i l ter techniques he used wcrc not exactly tlrandom ptoccss, he w as one OF rhe first to n c , k , n o w l d g e that a,random walk is not needed t ~ ensure et%?iiciencg;this concept of=fair game" rnther than ' randomwnlk W HS to devdoped hy Osborne( 1, 959nd Fnma (11913)years later.

Back in the US, 'Rober& 19SS'I mrnpn.red the movements of theDow index with H model b n s d on random chnngcs a.nd Found thn,tthe patkernswere si.mi.lnr,concludi,ngthat past i.nformstionwas ofno prcdicLive value. H'ewns also the first to classify the eficiencyofthc stock exchanges i.ntowcak and semi-stronga.ndsrrong.

'Fnrnn, ,Eugene (1,,9ti5)studied theserial correhtion o f the Dow 30'I ndustr,ial cornpan,iesfor A space o f : f ive years. :Hexmsidered thenatuml logarithm o f prices for up t ~ skLeen lam %.ndFound noevidcnce ofsuhstanti~l.i.ncnrdependence. :Headmitted thnt theremight: be non-linenr dependence which mighb hnve i.mpliedprofitnble tradi.ngsystem Pn,ma,alsostudied,thebehnviot o,fp,r icesi.n&rms of direction. H:econcluded that large daily price changes

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werc followed by si.m'ilarly mgc changes with 'rmdom sign. Thisalbeit not proper of A random wdk p m s s ,WAS ta'ken as R si.gnofmar ket eEc icncy . Hk explsined that these fl uctu,~tion ere rheresulr o:foveran d under Adj ust ment . ta 'new i,nforrnstian.

Niede,rhoEer and Usborne (I,,Ff66) tudied the s i g n of variations forthe WSE mncludi.ng how more I.i.kelyit is t o observc reversals(changes of sign>than mntinuations, and that theso wcm morehequent a:&r sir niht continuations. H,eexphi.ned this behaviorthrough the s tu d y of huy/scll orders to stockb,rokcrsand rhe likelyprofitabi1,ityo f unexecuted orders.

The work of British, resetircher, Dtgden (1970) yielded similarresuksof uncorlr lation for the 'L ondonStock 'Exchnngc.

3.3EfficientM arket HypothesisThe %MHWAS developed,as B result o f rescatxhes conducted byRenddl ( ' 1953)and, Cwtner (1,964) w ho bund tho,t it: W R Sexcess,ivelydi Ec ul t to 6:nd any predictn,blepatterns i,n he market.In pmticular 'Kcnd,aI.I,writes: "The series looks ,likeB wonde,ringone,aImust HS ,ifonceR wmk the ,Uc,moriof Chnncc drewH rnndomnumber fmrn a s,ymmetricdpapthtion of fixeddispersion andaddcdit tu the cu r ren t pricefaClekrmincthenmtweek2price.." lncssenmwhnt they had dcveloped w as the ,EMH where nn emcient

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m~.r k ets one which Al.rcndy reflects all available i.nformation.Ever since many academics havecmne up with mn,ny definitions ofmarketeficiency.

Th.reelevelsof eEfciency are usually considered,after the wor ks ofRoberts WX91 an d Fa.ma (1,965); thew are wen.k form eficiency,=mi-st rong form eficiency and s t rong 'Perm e,Eficicncy.These th:rceform d i . k .ntwms of thc typesof inforrnntion which arc used indewloping invcstrnent strategies.

> &rni:strong ' FormEmciencyw as the cumnt priw i.ncorporatcsa11 publicly available 'information including thRt o f thc we8.kfom.

> Strong II?ootm Efliciency w as the current price i.ncludes a'I:Iinformation i,ncludi,ngthat available to insiders.

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On the topic o f Chinesc stock ma.rkct efficiency, the literatu.rcisquite cxmf)icting. L aurence, Cai and Sun (1,997) i.ndbtlt.c that LhCex.irtence of tl weak-furm eE ciency i.n thc Chi.nesestock mn.rker(for A-sha:res), testi.ng the sample period 11,991-'1996. ang, pnyncan d Ferrg (1,,999)oxami.ned meuk is thnt Chinese s b k rnsrkotfollows H random willk,over the sample period of 1,992 o 1994,onthe wcekl,y bnse, by mcms of n wmianm-rntio methodology. Su,Dongwei (20031teskd Chi,nese B-share mntkcts a.m wcak-formefkient: fmm 1,4411,,a 1996.

Darrar and, Zhong (20001 provide a strong evidence for rejectingthe random-wdk hyprpothcsis i.n Chi.nesc smk m,a.tketsb y U6hgtw o difhrent nppmnches.They uti.l.hfid,daily date of theA-shn.msclosi.ng hdex prices of the SHEE from i t s i.nwptrion on 2 0 t h:December 1990 ta 1,9lh October '1,,498; nd of the SZSE fmm i,tsi.nmption on 4,Lh April 1,990in '1,WOctober 11,998.They used thestwndnrd, varinnce-rho kcst of Lo and M ~ncK i.nlny1,988) And a

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model-compariwn test thnt compa.rcsthe ex post fomcnsb From HN A h G (random wa1.k 'mdeU model w,ith thow obta,i,ned b r nseveral,alternative mode'lsOI.RIMA,GARCH and Arti:EicidNeumlNet.work-A:NNN).To ~ v d u a k x post forecasts, they ma.ke use ofscviynl prmdu'ms including RMSE, 'Wi, Theik I nequitybf ic i rnt , and encompassing tlcsts. Both approaches rcjccbd thehypothesis thac Chi:nese stock ma.rket is weak- f ormeEciency.Furthermom, compa.rcd with theva.riancc.rntio & s t , ,resulkj Emmthe model-comparison approach a.re qu,itcdecisive i.n rejecti.ngtherandom-walk hypopochesisin hoth Chi.nese$rock markets.

3.4 Volatility

M nndelbmt (1, 9631tated t h n t h,rgc changes (of either sign) tofol low lmgc changes a,nd,small changes (of either sign) to Followsma'll changes. This i s a v e r y fmnousdescription of the volrl,tilitycluster:i.ng.

Other i.mpoctant empi. t ica l regdariticrs are pmvidcd, by thepmsence of fat tails i,n the retu.rns, see among ochers the sameM nndelbrot (1, 963) s well as Fama (1,9911, by the existence offorecastable events such 8s thC presence of a high volatility beforecentrnl.bank decision, studied by lH,arvcyand h a n g 1,991)nnd bythe presence of non-trading period that: lad to volatility p ressmc,studied by A.ndcrsen and Rollerslev (1997).

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Thew relevant t esu l t s s ta te the i.mpotta,nceof modding not onlythe 6 r s t but also the second moment, w h i l e esplnini.ng thebchnriou.rof hnncial series. HIisimicdly, ir i s onl y since the en.r ly'80s that an etTective econometrically analysis ot it bas beendeveloped. T he first groundhreaki.ng paper must be attributed t oEngl e (1,982). Starti,ng from the bi l ineA:r model developed byGr anger a,nd Andersen (1978), he tried M capture the ch,ange inthe ~cond , oment o : f the M nditianal density function th.mughti.meby an autmcgressire process of the past-obwrved c~nditiondmoment values. The modcl cnn bc esti.mnted eficiently bymaximum l.i.keIlibaodas showed by themme 'Engle who defi.nedalso the cond'itions for the process tn be weakly stationa.ry andmeani.ngful.

All the peper. which have followed, can be seen HS a WRYi.mproveor CO ada,pt: he original one. The fi.rstand most i.mportantimprovement 'is given by the GA:RC,H, model devcloped byBollerslev (1986). The wnditiond variance in now cspresd asthe sum o f B moving average n.nd a n nubregressi,rreprwess. Thi spermits H mort pa.tsimonious reprcscntation, and a consequentesti.mntion, of themnditionlz'l wrin,nct?process in exnc t ly thesa.meWHY as an AHMA p'rocess encompasses R IMA or an A.R ones. Themme Bollerslcv defined the basic cond, i t ions for a menn,i.ngfulmodel 8s well R S the ones for H wcakly stationary process. T he

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I stkr is just given by the need for the cquivihent ARCHrepresentation to be ststionary. A deeper ~t.nalysisf themcan tiefound i.n Nel son andCHO1,992).

Rcga.rdi,ngaunivarhk approacb, w e review H GA, KCH(1, 1, )odel.The hrst mai.nextension of the hasic o.pproach w as fa move froman assumption of normality o : f he wnditional difitrihutionof thetmr, c1ea:rIynoc renlistic enough, to H diffcrent distribution. Thesn,me Bollerdev (1,987) applicd R tdistribution, Jorion ( 1, 988)norrnd-Poisson distribution, &eh (1889) n normal-lognormaldistribution, Nel son (1992) an exponentinl distribution and, :En&Gonzales-Rivera (1,991) H semi-pantmetric estimation o f thedistribution.

Othor e x k e n t i o w hwe mod,i:Ced he t y p e o f relationship betweenthe dependentv able a.nd the explanatoryonesto co,trcctspecificdrawbacks of the origi.nnl approach. Tnylor (1, 9861 nd Schwerr(1,9891 triedM modcl the conditional stnndard devin,tion with aoonseguent rcduction of the i.mportance of hrgc changes. Nelson(1,991)devcloped the %:GA:RC,HcxwnentialGARCHI model wherethe logarithmof the vn.rianccw as explai.ncdby an fiubregressivepart, a omstant and H non-symmetricnewseffect based on thenon-squn,red error term OF the previous :period,.Nion.symmetrypresent also in the GJ,Rmodel developcdby Closten, daga,nnathnnan d Run.kle(1, 993)S well as i.ntheQCkRC,H (Quad.raticCA:RCHj

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proposed,by Engle and Ng (1,993). he former obtains i c h o u g h adum.myvariable with n value o f I i.ncorrespondencewith negat i vepast e r r o r terms whereas Lhe latter subtrmt f l constnnt va lue &omthe p a s t error terms before 8qun.ring them. Higgins an d Bernt199!!) dehed the N CH' non-1.i.nea.rARCH) . which c m be seenas a mcipe for the th.me pmvious models, as w e l l 8 5 the GA.RCHitsclf.The Inst.covered extension o f the GA.RCH w i r h A univariaka p p r o ~ c h s given by the FIG'ARCH (Frncrionn.lly Inkgra tedGARCHI developed by ,Baillie. Bollerslev an d M ikkekon Iisssj.Th.is approach tries to solve the grnernl negative feature presentin,a.U the previous models of a fast&cay of persistence or, i,notherwords, H l ong temporal dependence ofvolati.l.ity.

Theabove su.rvey l i s t is publ.ished by BolIersIev and Kr oner ('14921i n Journal dEconamclrics; ARCH modeling in Pi.nnnce.

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CHAPTER 4

AppliedData

4.1 Data Description

M eanwhile, the Nh'ikhi,225 index is Used for oompmison. 'I'hereawn w h y wc choose Ui.k,,kci225, is thet i t is one o l Asia's, and,even thc wmld's major m,a,rketsand idseconomic fundamentals aresome of the st rongest : in the Asian rcgion. BIowcwr, benri.ng i.nmind that there a.- suspicions about: the bubbly dapanew stmkmarket. Thus data is downloaded from ht .e .~~: / /~t~t~~.eh~n~~at i .con~

I n addition. there are severd reasons supporting why w e chooseSASE & S7S, Endices. rather than an official nahnwide stockmarket index or Dow J ones China B8 tDJ88) i .ndex. ,Firstly.recalhg Chapter '1, w h e n China establ.ished n nationwide equityma.rket with two stock e x c h m g m l o c n k d , in Shanghai an dShenahcn.There WHS no of i ci d stock market index ,ee,flectingthe

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total,Chinese stock rnmket per f or msn~~.t pwsent this rem,ai.nsthesnme.

Secondly, although the cnmpositc s b k a p k k e d up by Dd88 ama,lrnostthose large-cap companies with rclntivc good pcrfo,rmanceof operation, they do not fi fl ~cthe truth OF tlhei.r smock, m,a.rketperformance. Furthermom! these 88 stocks' i.ncl,uded, r epresentonly 33. 22% of the total mnwkct cnpitdk ation and, about 30% ofthe tradable mn.rketcapitalization.

On t h e whole, w e mrrns,ider that SHA, SH& Sw \ & 52, Bndicesprescnt t,he whole set of stock,s, and we can be certain that ourresulb obtai.nedarc unbimscd.

1. DJ 88 io hnwd on thc following Fnctors: the mn,rketcapihl iz~tionf publictradablesmks, the cowmgc of the industrial scctoar~a,nd the liquidity orstocks. According fa the Irtest ediiion of th e components, then are 61mmpmics from SASE R p r c s e n h g 6i.1'996 of E w x ~ ~ A ~arkercapitdimtion in SHSE.Whi le 27 from%LSE. rcprc5cnt 32.51% of free-fiontmarket cnpitalizntion in .%SE. Them figures are obtaincd fromf ~- i n x-ml'u.tin htm

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I 4.2 Applicationof LogData& Log &turn3LQEdataFirstly, we take the logarithms of the original data as appliedshare indices, which is calculated a6 follow

P, = n X ,

Where X , denotes the ocigind share indices at time t andIn denotesthe natural logarithm.

h a eturasThen, we calculate returns from a series of 4 . There a.re twob,inds of farmat.ions of retu.rn8, wh.ich are sh p l e returns, al sok n o wn as change returns and continuously compounded returns,also known as log returns. : In th.is thesis, we employ the logreturns, which are shownaa follows,

Where Y( denotes themntinuously compoundedreturnat time t.

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4.3 EmonometricSoftware Package8

We use Microfit 4.1 for: our data processing, graphic display,estimation, hypothesistesting,etc.

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CHAPTER 5Time-Series EconometricsMethodology

5.1 ObjectiveIn this chapter. w e introduce some of the time-seriescwnornecricsmethodologies for th,isthesis. Section 5.2describes how t o test forstationary prmss. Foremstingwith A:RII:M:A,mod,el,ss i,ncluded,nSection 5. 3.

Be8.r i.nmnd, althvugh we are goi.ngt o &et.thecharacteristics ofboth the share price indices. e +and thcir rcmarns. V,, w e onlyrepresent d l equations on 1:. Obviously, thc testing processes ofp, a.rethesnme as I", .

5.2 Testi.ngfor Stationary

52.1 SbchaBticPmcessandDistributionStmhstictIrom&8Gujarnti (199, Sl states that B stochnst ic ppoccss is said bestationary i f i tsmaan an d variance apeconstant over time, an d thevalue o f covariance between t w o t h e per iods depends only on thedistnncc or lagbetween the tw o time periods nnd no t on the actual

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t h e at which themvaria,nm scom,puted.

'Inthe time series likmturc such H stO(;hRStic prowss is known HSa wctikly or wvfiri,am* stationary stochastic pmss. Note that Hwhite noise p,tocesshns constant mean and variance, and 7 ~ wcovminnm,except R E h gmw.

The properties of a stochflstic c mbe described by the moments,which am as follows.

Whcre cr' ,i sB mensure of the random variahle a,round i t s mean.T , ~s H meaeure of the covarianm between the values o f trnd,K e , nt 1,ag ,k . The first tr'nd,second rnomcnt equations I ll ,u,strakthat n stationary p:rwessshould have B Mnstn,,ntmean, H constant~ a r i n n c e , nd n constant covn,rin.nwstructu.rc.

D etributionThepricechanges and returns arenor ,mnl lydistrs,bukdove, t time.If transactions m e 'in sufic,iont number and evenly spread,acrosstime, pr im changesshould follow B norrnnl distribution.

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The third and fourth morncnL9 are used to measure prohabilityd.istdbution, ts skewnessh. ,ack of symmetry) and kurtosis (i.e.?~nllnessr flatness), re~pecciv

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Under the null hypothesis khat: is normdy distr ibubd, thedeckion role is that if the calcuhted v d ue of J B is pater thanthe critical 5% level in A chi-equarc (x ' ) distribution with 2degrees of freedom, which is 5.99, the null, hypothesis of 8 normaldistributionis rejected.

5.2.2 IntegratedProceasesandDifferencingI C is important t o hour for the time serieswhether ur not theunderlying stochastic proccss, that generated the series, c a n beaEsumed t o be invariant with respect t o the.

I f the characteristics o f thc s t m h s s t i c process changed or;er t i m eG.e., non-stationwy), it will often be dimcult t o represent the timeseries over past and future intervals of time b y a simplealgebraicmdel. On the other hand, if the stochastic process is f i x e d in timeL e.,stationary), h en we uin model the process via an equationwith Gxed coefficients that C H ~eestimated,frompast data.

Morwver, the statmnary d a t a knds t o return to i t s mean andfluctuation around it. On theother hand. H non-stationaryprocesswill havedifferent mean at different points i n time.

I n addition, running regre.ssiun on nun-stationan; data can g i v e24

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rise t o spurious v a h e s ol : K ' , Durbin-Watson (DW) test, and tstatistics causing ecunatnists wriously misleading t o conclude,that a metdngful relntionship o,xit;btr among the rcgressionvariables. Becausc nun-sta'cionriry variwldea have nn infini,tevariance, inferenw:usingOM s ,invalid.

A lthough it is difficult. o model non-strltiona.rypruceases, they canoften be transformed i nto stationary or approximately stationa.ryprocessesby integrated processes and differencing. For example,

#ere iiy isthefirst-di.ffemnceof Y, and K, isassu.med o be IIwhite noise pmess. The flhovc equation describes chat- the series

is mid t n be integrated of order one, denokd l r l j , becausetaking a first dimerence prod,uces B stationaq process. Anon-stationaryse r i e s is integrated of order d , denoted I(d! i.f itbecomes stationary after being f i r s t d.Secenced dtlme6.

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5-2-3 Testingfor Autocorrelation

5.2.3.1. TheComelogramThe oorrclogram is a plot o f 'theautocosrcletion function (ACF).TheACP provides t3 partinl descriptionof the ptocess for modeli.ngpurposes. I t tells us i f the true disturbances are nutommelatedand how much mrrelation there i,s between n,eighboring datnpoints i n 'thcwries 5, We define 'thenutoconeletion with lag k as

Where pr i s the autocorrelation coe:t%cientas a function of thelag k. ( p a is the wvarianrn betweea and

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n lficientsup t o the 12th lag, Far the share price index and its rcturns,respectivelj?

Secondly, we will plot the mrrelogrnms i n order Eo determinewhether th,eg depict the CO cients hI.l.ing off nurntiersinsigni.ficantIgdifXeren,tfrom 7xr0and f f uctuntingaround it, i f it i s,the series nppears to be stationary. Conversely, i.f they dccreasesl owy toward mro. the se,ries illustrates non-stationaryConsequentlyt for n strlti,onnr)l variable the correlogrnm shouldshow autooorrelations h a t dic out f d y quickly a5 k becomesl arge.

Thirdly, w e will conduct significancetests for the autocorrelationcwfficients,by constructi,ng rnnfidence interval for theestimatedautmorrela.tian coeficients tu determi,ne whether they aresignif i~nntly ifferent fromam rough 95%confidence htervnlwill be drawn at * I . S S / m . A t H gl,ance, .f bt fallsoutsidethisregion, then w e reject;the nu,U hypothesis that the true value of themffrcient: tit that lag k is ze,m.On the other hand, if w e cannotreject the null hypothesis, it implies that the ACF 'ie R zero

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mvarimce white noise process. By recnlhng t h e definition of theweakly or covariance stntionaq stochastic pnxess born Section52.1, w e can conclude that the mries Y expresses t o be astationruypmoss.

FindlJ : theSACF docisiu rulo is rmmlirimd in Table5.2.3.1.

Non-stationaryGm?

=0 dfnotes the value at the 95% confidence intendij,#0 denotes theva lue at the5% sigoificance level

It isworth noting that thc test : issubjective, because given the f i bof up to t he 12th lag is only for sampling. Therefore, one maycondude that the series iu $latAioaa,ry, hile others may considerthat it is a non-stationaryeeonom,ictimeseries.

However, t o tes t the joint,hypothesis that all the autceorrelationcoefficients are zero, w e use ihe Q statistic intruduced by B o xand Piem and the mod.ified statistic developed by L jung-Box inthe followingsection.

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5.2.3.2 T h e Box-PierceTeat theLjung-BoxTestTheBQX fierce 'CestBox and Pierce(1,!170) test the join,thypathmis that 811 lag kof theautacorrelation coefficients arc eimu,ltaneously equal t o zcm. TheQ test is carried out HS follow^

Where n is thenumber of observations nnd k isthe maximum laglea@. Q statistic is distributed RS ch.i s q u a r e with k degrees ofreedom, xi , under the null hypothesis that all k autxmrrelationmficientsare ' em

TheL ima - BQX eatAvar imt of theBox .Pierce test, hasbeen developed by LjungandB o x (1378). Si.nce the Box . Piercc test has poor small sampleproperties, implyi,ng that it mriy lead t o the wrong decisionfmquently for small sa,mples. :Ljunga.nd B o x show that the Q'test is as follows,

However , we forecast the tw o tests am equivalent. Because the34

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sample size is relatively large in this thesis, the (n+2) and (n-k)terms in the Ljung - Box formulation will not be significant.Therefore, the Q' test would be close to the Q test.Consequently, this test examines Y, 's correlations between theresiduals,E , , andk lagged values of the residuals.

Table5.2.3.2 StationaryorNon-stationzy.. Q,Q' decisionru1ee

1 I I1 Stationary 1 1 Nonxtationary 1Table 5.2.3.2 describes that if the calculated valueof Q& Q' aregreater than the critical 5% level in a x,' table, rewritten'asQ&Q' > x i , we can conclude that the null hypothesis ofnon-autocorrelation in E, is rejected. Note that rejecting thenullhypothesis, means accepting an alternative that at least oneautocorrelation is not zero. In other words, we reject the nullhypothesis that the time series is generated by a white noiseprocess (in which all autocorrelations should be zero), namely,rejecting stationary process. .

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5.2.3.3T he L agrange M ultiplier Test & theF TestThe Lagrange Multiplier testAn alternative approach to test if the true disturbances are serialcorrelation, is the Lagrange Multiplier (LM test introduced byBreusch and Godfrey (1978).

The test is the one in which the square of the OLS residual isregressed on an intercept and its lagged values, with the numberof observations,R, times the RZ. t isshownas follow

The LM statistic is distributed as chi square with k degrees offreedom, x i . Therefore, the decision role is that if LM > x i , wereject the null hypothesis of serial uncorrelation in E , , if otherwisewe do not reject it.

TheF testTesting for serial correlation of errors can also be done by using anF test to examine the coefficients of lagged OL S residuals, in aregression of the OLS residuals on the lagged OLS residuals andthe original regressors.

TheF test statistic isoperatedas follows,

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test stuti sti c = + F (k -1,n -k)RSS l (n - )

Where ESS is explained sum of square, RSS is residual sum ofsquares, n is the number of observations and k is the number ofregressors in unrestricted regression.

The decision rule is that if F >F ,,(k-1,n-k), we reject the nullhypothesisof serial uncorrelationin E , , and vice versa.

On the whole, the LM and the F statistics have the samedistribution asymptotically. However, in small samples the Fversion isgenerally preferable to the LM version. As our samplesare relatively large, we employ both of them in the thesis.

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5.2.4 UnitRoot Test

5.2.4.1 Introduction

The most common test of stationary isknownas the unit root test,introduced by David Dickey and Wayne Fuller (Fuller, 1976;Dickey and Fuller, 1979).Consider the simple model;

y , =q-,+E ,Where E, is a stationary error term with zero mean, constantvariance and non-autocorrelated. Recall integrated processes anddifferencing from Section 5.2.2, E, is I(0). Thus, can bedenoted I(l), since A T =E, . The above model can be expressed inmore general formas the first-order autoregressive process,AR(1)

Y, =ax-,+E ,Table 5.2.4.1Stationary orNon-stationary Unitroot decision rule

I c I I & INon-stationary Stationary

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Table 5.2.4.1carries out that if la(

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However, the DF t-test statistics do not follow the usualtdistribution under the null hypothesis, since the null is one ofnon-stationary. The statistics follow a non-standard distribution,and critical values have been tabulated by Dickey and Fuller onthe basisof Monte Carlo simulations (1979).TheDF test decisionrules are described in Table 5.2.4.2.b.

Table5.2.4.2.bStationary or Non-stationary TheDF test decision rule

DF >critical value DFcritical value, then y =0, hence containingaunit root can be identified. This implies that after taking a first

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difference procedure, the series Y, appears to be a stationaryprocess. Hence, we can arrive at the conclusion that Y, expressesnon-stationary time series.

Conversely, if DF < critical value, the null hypothesis ofnon-stationary time-series will be rejected.

5.2.4.3 TheAugmented Dickey-Fuller TestTheDF tests are valid only if E, iswhite noise. However, if E, isserial correlation, theADF test will be employed. TheADF test isproposed to accommodate error autocorrelation by adding laggeddifferences of Y, .

Recall the case (iii) model in Table 5.2.4.2.a, the DF unit roottesting procedure,

Which can be rewritten by adding lagged changes in U, on theright-hand side of the equationas follows,

The lags of A& cancel out the serial correlation, to ensure that E,42

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,,.,le 5.2.4.3.bStationaryorNon-stationary TheADF test decision rule

ADF >critical value

1 I

1 + fI I I1 Non-stationary 1 I Stationary 1The above table shows theADF test decision rule is that ifADF Identifying the values of p, d and q for each stock market from

October 1992 through J une 2003.

> ModelingARIm (p,d,q) equations for the above sample period.9 Forecasting three month stock monthly returns based on the

estimated ARIMA model from J uly 2003 to September 2003.

9 Plotting the forecasted and actual series for the monthlyreturns in the four Chinese stock markets.

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largest one month fall in the four Chinese stock markets is aboutdouble compared to the Nikkei 225.

From the above evidence, we understand that the Chinese stockreturns seem to exhibit much higher volatility than thewell-developed Nikkei 225 during the test period. The certainlyhigh volatility implies that the risk is absolutely great in theChinese stock markets than in the Japanese stock market.Referring to the relationship between risk and returns, the highrisk may reflect that there are considerably great returns in theChinese stock markets than in Japan. Nevertheless, the risks arealso obviously high.

Consequently, it can reasonably be concluded that normality isrejected for any of the four Chinese stock returns. Conversely, theNikkei 225 reflectsanormal distribution in the test period.

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coefficients may reflect that there is no correlation between thetwo Shanghai shares and the Nikkei 225.

These correlation coefficients may provide information on howinvestors can deal with risk. It has been widely argued in financeliterature that the standard deviation of returns on an individualasset isnot itself an appropriate measure of risk since the investor,by holding a portfolio, can diversify some risk away. The ability todo this will largely depend on the correlation between returns ondifferent shares. This suggests that investors could form adiversified portfolio to improve their risk-return trade-off.

By recalling from Chapter 2, A shares are subscribed by andtraded among Chinese citizens and/or entities. While, B sharescan only be subscribed by and traded among foreign legal andnatural persons and other entities, legal and natural persons fromHong Kong, Macau and Taiwan, and Chinese citizens who areresident abroad.

Hence, an individual investor could only form a diversifiedportfolio from eitherA shares or B shares. A lthoughacombinationof an A share and a B share can diversify some risk away, thiswould notbe applicable in the Chinese stock market. However, forthe international investors, the combination of the Chinese andthe Japanese shares would be a good case to avoid risk.

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After considering the generalitiesof the empirical distribution andcorrelation in the Chinese and the Japanese stock markets, weturn to concentrate on testing the stationary in the four Chinesestock markets. We first investigate whether their share priceindices exhibit stationary processes, and then consider their firstdifferences of share price indices stochastic processes, namelyreturns.

Figure 6.3plots their share price indices and returns during theperiod considered. By visual inspection of the graphs, we caneasily arrive at the conclusion that the share price indicesstochastic properties cannot be assumed to be invariant withrespect to time, since none of them having the tendency to returnto its mean and fluctuate around it. Therefore, we consider thatthe four stock price indices stochastic processes are clearlynon-stationary.

However, the graphs of their returns in Figure 6.3 illustrateconversely that their characteristics of the stochastic processesseem to be approximately constant and fluctuating around theirmeans. In other words, all of the returns seem to be stationarytime-series.

Nevertheless, it is important to note that there are some highervolatilities which cannot be considered to be constant, especially

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for SZA. The variation in the series appears to be fluctuating withseveral clusters of large movements. Although the variancebecomes unusually high, we still consider that returns seem to bestationary time-series in the stock returns.

Recall our discussion of the integrated processes and differencingin Section5.2.2, we can summarize that the four stock share priceindices imply I O), since taking the first difference produces astationary process. While, their returns appear to be I(O, namelystationary time-series.

6.4The Correlogram for Share Price Indicesg, Returns

Another method to test the stationary is the correlogram, whichwe analysed in Section5.2.3.1. The correlograms for the four shareprice indices and for their returns are shown in Figure 6.4.a. Thecomplete version of the results is included in Appendix.

A t a glance, we observe that the share price indices decreaseslowly toward zero as the number of lags increase. While, thecorrelograms for the returns illustrate that the coefficients fallquickly to near zero at lag 1 and fluctuate around it. Thesephenomena perhaps suggest that the series of the four stockreturns plot white noise processes. Conversely, their original share

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I t isworth noting that the phenomena of the nearly zero SACF atthe early lags, indicates that there is no strong evidence ofautocorrelation in the stock returns, and the successive pricereturns exists independently.

The above finding illustrates that all of the SACF are notstatistically different from zero for the four stock returns. Thisconfirms the suggestion observed from the correlogram, thatreturns plot white noise processes. Inother words, they appear tobe stationary processes.

Consequently, the empirical results of the correlograms consistwith the outcome observed from integrated processes anddifferencing, that original share price indices indicatenon-stationary time-series, but their returns show stationarytime-series.

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lower than the critical value at the 5% level. These results suggestthat none of the four stock returns is significantly autocorrelatedfor the sample autocorrelation series. This supports the outcomefromSACF.

Hence, we can conclude that the null hypothesis ofnon-autocorrelation in E, is not rejected. I n other words, the fourstock returns appear to be stationary time-series.

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A s we can see from Table6.6, the two B shares show that there iscertainly no serial correlation of residuals. Even at the lower lags,they still reflect significantly higher probability of falsely rejectingthe null hypothesis. This result is consistent with our priorfindings of stationary time-series from integrated processes anddifferencing, the correlogram and the Q & Q' tests.

In contrast, both the LM and the F tests provide a serialcorrelation of residuals at the lower lags for the two A shares.However, the remaining statistics do not appear to be serialcorrelated, apart from 9th lag for SHA. Hence, it is difficult toconclude whether the returns of the SHA and the SZA exhibitstationary time-series, even major theLM andF statistics< x i . Wewill employ the unit root test to illustrate this matter in thefollowing section.

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We have detected from Figure 6.4.a, that a certain serialcorrelation exists of up to 12 ags in the four share price indices forthe samples. While, Figure 6.3 reveals the patterns of all of theindices which are random walk with clearly drifting andno strongtrend. Hence, we conduct the ADF unit root test to demonstratethe stationary for the share price indices by using case(id,namelyrandom walk with drift, referringtoTable 5.2.4.3.a.

Table 6.7.1 reports the ADF test up to 12 lags for all of the log oforiginal share price indices. Itprovides all the computed ADF teststatistics that are greater than the critical value of -2.8857 at 5%significant level. Thus, we cannot reject the null hypothesis. Thismeansall of the four share price indices series haveaunit root andare non-stationary time-series.

This finding consists with the outcomes observed from integratedprocesses & differencing method and the correlogram method.

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6.7.2 Unit Root Test for Returns

In previous Section 6.6, we have detected there isserial correlationof residuals in the SHA and the SZA at lower lags. Therefore, weemploy the ADF test for theA shares. On the other hand, the DFtest will be selected for the B shares, since their residuals appearto be independent.

Moreover, reviewing the Figure6.3again, the patterns of the fourstock returns show white noise process visibly has no trendingbehaviour. Hence, the random walk with drift model can bespecified for the four stock returns.

SHA&SZABefore carrying out the unit root test, the order of the ADFregression needs to be selected. Looking at the Figure 6.4.b again,it exhibits that the autocorrelation coefficients of SHAand SZA at9thlag appear to be the highest one in the samples. Furthermore,theLM & theF test statistics in Table6.6 illustrate that there areserial correlationsat lag 1, 2 and 9 in theSHA,and at up to lag3in SZA, respectively.

Thus, we posit the appropriate lag length for the augmentedregression is 9. However, we choose 12 lags, just in case the laglength of 9cannot minimize the value of an information criterion.

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Table 6.7.2.c gives the computed D F test statistics they areconsiderably smaller than the critical value of -2.8838 at 5%significant level. Thus, we can conclude to reject the nullhypothesis. This means that the SHB & the SZB returns appear tobe stationary time-series.

Furthermore, we can conclude that both of the SHB and SZBexpress AR(1) process in the same sample period.

Consequently, the above findings are consistent with ourprevious results of non-stationary share price indices andstationary returns, examined from Section 6.3 and 6.4, which arethe integrated processes & differencing and the correlogrammethods.

Conclusion

In conclusion, the characteristics of the four Chinese stock shareprice indices can be assumed to change over time, in other words,they appear to be random walk in the sample period.

In contrast, the Chinese stock returns illustrate invariant withrespect to the same period. This suggests that we can model thereturn process via an ARIMA(p,d,q) model with fixed coefficientsestimated from past data, to forecast future return process.

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Note that since all the sample stock returns appear t obe I(O), thuswe employ the ARIM A(p,O,q) or simply the ARM A(p,q)specification to forecast returns.

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In the previous section, we have identified all of the four stockreturns appear to be AR(1) process. Thus, the ARMA(p,q) modelswill simply be the ARMA(1,q) specifications for our samples. Table6.8.1 gives the details of estimating the ARMA(1,q) models.forq=0,1,2,3,respectively. Comparing the values of the AIC andlor theSBC, we select the model specification with the highest value.Thus, we observe that the two A share returns show an ARMA(1,l)model, while the SHB returns appears to be simply an AR(1)model.

Note that there isaproblem of the specification of the MA(q) in theSZB, in which when we using the AIC, we have ARMA(1,2) isselected, on the other hand, ARMA(1,O) ischosen by the SBC. Todeal with this task, we adopt the Box-Jenkins approach using thecorrelogram provided in Figure 6.4.a. Reviewing the correlogramagain, it can be seen that the SZB returns does not seem to beMA(2) process. Therefore, we conclude that anARMA(1,O) model isselected for the SZB, namely an AR(1) specification.

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almost capture the trends, and the predicted values are veryclose to the actual values in the tested three months, especiallyfor the first two month forecasts.

P SZB This is the only one forecasted values fluctuating theactual values. TheAR(1) model appears to capture the trend inJuly, but fails to predict the turn occurred from August toSeptember.

On the whole, the regression models seem to be efficient for thefirst one month stock return prediction in a l of the Chinese stockmarkets during the sampling period. Moreover, the ARMA(1,l)model shows apowerful tool in forecasting monthly returns in theSZA. In addition, the AR(1) model predicted successfully in thefirst and the third month returns in theSHB.

Conclusion

Wecan arrive at the conclusion that the historical returns can beused to forecast stock returns in short horizon in all of the Chinesestock markets, especially in the SZA. This evidence of thestatistical studies reveals that share prices appear not to berandom walks and exist significantly potential predictability inthe Chinese stock markets. This implies that the weak form of theEMH seems to be unsatisfied over the testing period from October

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1992 to J une 2003. The inefficient Chinese stock markets indicatethat investors are able to identify share price movements usingpast sequence of share prices, and may can statistically oreconomically beat the markets.

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CHAPTER 7M odellingVolatility

7.1 IntroductionIn Section 5.2.1,we introduced variance is assumed to be constantover time in a stationary time series, known as homoscedasticity.Then, in the following chapter, we determined that all the Chinesestock returns series appeared t o be stationary in the sample period.Thus, we may consider that the variance of the error terms, (r 2(second moment), isconstant over that time.

However, &om the Figure 6.3, it can be easily seen that there areevidences of some clumps of large and small errors, known asvolatility clustering originally described by Mandelbort (1963),whostated that large changes (of either sign) to follow large changes andsmall changes (of either sign) t o follow small changes. This kind ofvolatility clustering implies that volatility at time t tends t o bepositively correlated with its level during the immediately precedingperiods, such as at time t -1 . Hence, we could consider that volatility isautocorrelated. Furthermore, the Figure 6.3 also expresses thatperiodsof high volatility follow by periods of low volatility.

These phenomena would suggest that the classical assumption of

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errors having a constant variance, both unconditionally andconditionally, is not valid. Conversely, o2 appears to change fromperiod to period. I n other words, o2 s heteroscedastic in al theChinese stocks returns and, this implies that o2 depends on thevolatility of the errors in the recent past.

Under such heteroscedasticity, we are able to model volatility byusing autoregressive conditional heteroscedastic (ARCH) modelsintroduced by Robert Engle(1982) and generalised ARCH (GARCH)models developed by Tim Bollerslev (1986).

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7.2 ARCH ModelsARCH models spec& how to model and forecast conditionalvariances of the error terms, o, ? a isexplained as follows,

The above equation describes that a, ! is equal t o the conditionalexpected value of E,? . In other words, a depends on how large theerrors were in the past.AnARCH(q) model isgiven as

v2 2a, =a,+Ea,,-,,=

In the ARCH(q) model, a,?dependson q lags of squared errors. E,is normally distributed with zero mean and variance a, ? .n short,a has two components:

c, !=a constant+theARCH termWhere a constant is a, and the ARCH term means the last period'ssquared errors, namely, lastperiod's news about volatility. The ARCHeffect decision rulesaregiven in Table7.2.

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Table 7.2 ARCH effectdecisionrdesH , : a,#O,a,#O;..,a, f 0

NoAFK!H,effect ARCH effect

Table 7.2 suggests that if there is no autocorrelation in the errorvariance, we have the null hypothesis of no ARCH effect, otherwise,wehave the alternative hypothesis of ARCH effect presented.

Referring to our samples, we have already demonstrated in lastchapter that all the Chinese stock returns appear to beautoregressive processes of order 1.Thus, ARCH(q) models would beARCH(1) models in this thesis. TheARCH(1) test involves runningaregression of squared OLS errors estimated from the AR(1) model.The key point is to examine whether a,=0, we will employ the LMtest andF test to ensurethismatter. Recall from Section5.2.3.3,wehave introduced the LM & theF tests. The decision rules forARCHeffects are if LM > x2 and F >F ,,(I ,n-2) , we reject the nullhypothesis of no ARCH effect and vice versa.

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basedon stationary time series do seem to be valid.

I t is importantto note that although we reject the null hypothesis ofno ARCH effect in the SHA and the SZA returns, this does notcertainly imply that the conditional varianceof the error terms isnotconstant. The reason for this is that the serially correlated error termat the lower lags, reported in Table 6.6, may cause t.he conditionalvariance to be variable. Consequently, the ARCH effectsmay be lesssignificant inthis case.

However, we still consider the ARCH effects are present in the Ashares returns series. By recalling the volatility literature review, theARCH effects suggest that the two A share returns series appear tobe stationary process. This fmding is consistent with our previousresults from last chapter.

The further discussion would be that whether or not there aregeneralized GARCH effects presented in the SHA & the SZA returnsover the same sample period.

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7.4 GARCHModelsTim Bollerslev (1986) extended Rober Engle (1982)'s work fromARCH(q) models toGARCH(p,q) models. GARCH(p,q) models areshown asfollows,

In the GARCH(p,q) model, the conditional variance dependson q lagsof squared errors and p lags of the conditional variance. In otherwords, the conditional variance of the error terms has threecomponents:

0; =a constant+ the ARCH term + the GARCH term 30: =a constant+last periods volatility +last period's variance

The above expression means the variance today depends on all pastvolatilities and all pastvariance and a constant term.

Table7.4 GARCHeffectdecisionrulesH , :PI 0,P2+O,...,ppf 0

No GARCH effect GARCH effect

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Table 7.4 shows the decision rules of GARCH effects. It can be easilyseen that if the coefficients of the conditional variances are equal tozero, namely no autocorrelation, we cannot reject thenul l hypothesisof no GARCH effect. Conversely, we reject the no GARCH effecthypothesis.

Tests for determining whether GARCH affects are present in theerrors inour samples, we conduct using the following steps;

.

F Todetect the order of p in GARCH(p,q) models for theSHA & theSZA returns, we refer toourprevious result of order 1gained fromMACS) progress approach in Section 6.8.1. The reason why,depending on the moving average of order q, is that GARCH(p,q)models are effectively ARMA(p,q) models for the conditionalvariance. Since, the equation of GARCH(p,q) models look verymuch like an ARMA(p,q) process [Walter Enders (1995)pp 1461.Therefore, we consider that the order of q in an ARMA(p,q) modelisequal to the orderof p in aGARCH(p,q) model.

Recall from Section 7.3, we have already examined the order of qis1 or ARCH. Hence, GARCH(p,q) models would be GARCH(1,l)models for the SHA & SZA returns fromOctober 1992 t o J une2003. Therefore, we have the following GARCH(1,l) model for thetwoA share returns.

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D To estimate the coefficients of p, ,with the aid of Microfit we usethe maximum likelihood (ML) estimation.

D To find out if p, =0, we use t-tests shownas follows,

coefficiertStd.Error=

The t-test of significance decision rules is that if the computed tstatisticisgreater than 1.645 at the5% level, then the coefficientof the conditional variances is significant. Hence, we reject thenull hypothesis of no GARCH effect. On the other hand, if tO and a,+p,(1, then we have a positiveunconditional variance, this means the, GARCH(1,l) model is astable process.

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0 If ai+pi>1, Vur(&,) becomes negative, the unconditionalvariance of E, is not defined, and this would be termednon-stationary in variance. Moreover, as the forecasting horizonincreases, the conditional variance of the error terms will tendtowards infinity.

0 If a,+PI=1, it is known as a unit root in variance, calledintegrated GARCH(1GARCH). IGARCH models are not stationaryGARCH models, they become less and less useful as the predictionhorizon increases.

In addition, GARCH estimations can be carried out by using either anormal or at-distribution for the conditional distribution of the errors.Wewill firstly estimate the coefficients of a,, a, and pi under thetwo assuming distributions respectively; then compare whichdistribution is more suitable in our samples, basedon the AIC & theSBC model selection criteria. The selection procedure involveschoosing the appropriate distribution with the highest value of theAIC and/or the SBC.

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* Red c ol o r f i g ur e d e no t e s s i g ni f i c a nc e at the 5% l e ve l i n t - r a t i o c ol umn .* Red col or f i gur e d eno t e s t h e h i gh es t c r i t e r i o n i n t he A l C and SBC co l umns.Under the assumptions of a tdistribution and a normal distributionfor conditional errors, we have estimated the above results ofcoefficients of GARCH(1,l) models for theSHA and the SZA returnsin the sample period from October 1992 to J une2003.

The values reported in Table 7.5 based on the A IC & the SBCselectioncriteria,suggest that the conditional distribution of theSHAreturn errors appeartobenormal. Thus, the results in Table 7.5.b aretaken into account. The table b shows all of the t-statistics aresignificantly higher than the critical value of 1.645. This seems toreflect GARCH effect presented in the SHAreturns.

Nevertheless, since at+PI = 1.0015 > 1, then we have theunconditional variance of the errors, Vur ( ~, ) given bya,/l-(al+PI) is negative. This means that Vu r ( ~ , )cannot bedefined and is non-stationary. It will lead to conditional variance ofthe error terms tendto infinity, as the forecasting horizon increases.

Moreover, a,+3, = 1.0015 is very close to unity. This implies thatshocks to the conditional variance will be highly persistent. In fact,we have observed an IGARCH(1,l) model for theSHA returns. As weintroduced early, an IGARCH model is not a stable GARCH model

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and becomes weaker and weaker when the prediction horizonincreases. Therefore, the evidence of GARCH effect observed fromtstatistics would be less important.

Consequently, we consider that there is a GARCH effect in a veryshort forecasting horizon. Under this consideration, we will forecastthe volatility month by month for July, August, and September in2003 respectively in the next section. The IGARCH(1,l) model isestimated as follows.

SZAA s we can see from Table 7.5, the AIC & the SBC selection criteriachoose the t-distribution for the conditional distribution of the SZAreturns errors.

In Table 7.5.a, the calculated tstatistics of p,, the coefficient of theGARCH term, isat 1.410, which isslightly lessthan the critical valueof 1.645 at the 5% signifcant level. Thus, we have p,=O. Thismeansno GARCH effect presented. However, if we consider the significanceat the 10%level, we have p, is greater than the relevant criticalvalue of 1.282, then we have PI z 0. Thiswould suggest the GARCHeffect presented.

Todetermine whether or not the GARCH effect is present, we refer to95

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the assumption of a normal distribution, ignoring theAIC & the SBCselection. The result isthat GARCH effectisstrongly presented, sincet-statisticof p, is absolutely higher than the critical value of 1.645at the 5%significant level, and also greater than the critical value of2.326at even1% ignificant level. Furthermore, since the restrictionsof IP,1O and a,+/3,

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7.6Forecasting Volatility with GARCH(1,l) ModelsVolatility (risk) isoneof the most important concepts in the whole offinance. GARCH models are the most popular non-liner financialmodels for modeling and forecasting volatility, which allows thebehaviour of a series to follow different processes at different pointsin time. In this thesis, we forecast volatility using the GARCH(1,l)models estimatedfrom last section for the twoA shares returns.

SHARecall the results of GARCH(1,l) effects observed &om Section 7.5,we have found the presence of IGARCH effect in the SHA returns,namely an IGARCH(1,l) model. Thus, we forecast its volatility inonly one-months time. To do this we follow three steps;

1. Using IGARCH(1,l) model estimated, from October 1992 to June2003 in Section 7.5, t o forecast volatility for J uly 2003.

2. %-estimate a new GARCH(1,l) model using the period fromOctober 1992 to July 2003, by adding the actual volatility in July,to forecast volatility for August 2003.

3. Repeat the procedure again for 6; in September 2003.

The reason for forecasting only on one month each time isthat, in thetheory, an IGARCH model isnot a stableGARCH model and becomes

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*Red color fi gur e denotes the small est absolute er ror i n thesamemonth.

It is interesting to note that the forecasts observed basedonrepeatingthe IGARCH'(1,l) models do not show better performances than theIGARCH(1,l) method as expected. Conversely, using theIGARCH(1,l) model givesus some slightly smaller forecasting errors,comparedto using the IGARCH' (1,l)model. This result may be duet o the different testing horizons, between the one month period andthe three month period, cannot be seen horizon increases significantly.Therefore, to discover whether or not the IGARCH(1,l) modelsbecome less and less useful as horizon increases, asthe theory stated,will remain forour further work.

More interestingly, from the inspection of the forecasting basedontheARMA(1,l) model, we can see that the ARMA model predicted aslightly better result than the most popular GARCH model inashorthorizon. However, the GARCH model does show that itspredictabilities are stronger than the ARMA model as horizonincreases, in the case of theSHA.

SZAUnder the assumption of normal distribution for conditional errors,we forecast volatility based on the GARCH(1,l) model estimated fromTable 7.5.b for the SZA returns, and summarised in Table 7.6.ctogether with the forecasts observed from the ARMA(1,l) model inSection 6.8.3.

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Conversely, the ARMA(1,l) models show more accurate forecastingvolatility for theSHA,rather than for theSZA.

However, when we measure the forecast performances based on thetwo models in either the SHA or the SZA, we can conclude that theGARCH(1,l) models express their forecasts having a smaller degreeof errors than the ARCH(1,l) models inour samples.

I n addition, it is important to note that all of the values reported inTable 7.7 are considerably small. This means that the GARCH(1,l)models and the ARMA(1,l) models determine that they areappropriate for predicting future return volatility in the twoA sharestock markets. I nother words, return volatility can be forecasted wellby A R M and GARCH models. This implies that theSHA & the SZAappeartobe inefficient markets in thetestperiod.

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CHAPTER 8Summary and Conclusion

In general, the EMH is concerned with whether stock prices fullyreflect all the information available at that point in time. Weak formtests of the EMH model focuson the information subset of historicalpriceor return consequences. This thesis examines the behaviour ofthe CSMs, with a view to determine whether or not they areconsistent with the weak form of the EMH.

In this thesis, we have examined the CSMs do not appear to beconsistent with EMH, by using some econometrics time-seriesmethodologies.

We firstly carried out by analysing the empirical distribution ofreturns, and found out that the CSMs' returns diverge from thenormal distribution, compared to the Nikkei 225, and identified thatthere were certainly high volatility occurring in the CSMs.

In the following section, we estimated the correlation between theCSMs themselves and the Nikkei 225, and discovered that thecombination of the emerging CSMs and the well developed Nikkei225 would beagood strategic play to avoid risk.

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After considering the above issues, we turned to concentrate ontestingthe stationary time-series n the CSMs share price indices andtheir returns by testing their error serial correlations. To do so,several approaches were employed, including the integratedprocesses & differencing, the SACF, the Q & Q' tests, the LM test,theF test, the Unit Roottest (theDF test & the ADF test) with aid ofthe A IC & the SBC selection criteria. Through these tests, weidentified that the characteristics of the CSMs share price indicesappeared to be random walk, conversely their returns illustratedinvariant with respect to thetestperiod.

According to the stationary returns time-series, we could carry outforecasting returns with ARIMA(p,d,q) modelsusingfixed coefficientsestimated from the in-sample returns, to forecast the out-of-samplereturns, and showed the forecasted versus the actual returns forthree month period. We arrivedat the conclusion that the historicalreturns can be used to forecast stock returns in short horizon in all ofthe CSMs, especially intheSZA.

Furthermore, we examined volatility using models of the GARCHfamily and more specifically the GARCH(1,l) models together withcomparisonto theARMA(1,l) models. Wefound that the GARCH(1,l)models are appropriate for predicting future return volatility in thetwo A share stock markets. Meanwhile, the GARCH(1,l) modelsexpress their forecasts having a smaller degree of errors than theARCH(1,l) modelsby using the RMSE models.

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Consequently, we can arrive at the conclusion that the historicalreturns can be used to forecaststock returns in theCSMs, especiallyin the SZA. This reveals that share prices appear not to be randomwalks and exist significantly potential predictability. This impliesthat the weak form of theEMH seemstobe unsatisfied over the testperiod. The inefficient CSMs indicate that investors are able toidentlfy share price movements using past sequence of share prices,and may canstatisticallyor economically beat the markets.

Finally, concerningour extension of studies, we intend to apply andtest whether the Neural Network Regression (NNR) and RecurrentNeural Network (RNN) models can produce a substantialimprovement in the out-of-sample performance of our volatilityforecasts.

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