Time Varying Model of Test of Stock Exchage

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A Time-Varying Parameter Model to Test for Predictability and Integration in the Stock

Markets of Transition EconomiesAuthor(s): Michael Rockinger and Giovanni UrgaReviewed work(s):Source: Journal of Business & Economic Statistics, Vol. 19, No. 1 (Jan., 2001), pp. 73-84Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/1392543 .

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A Time-Varyingarameter M o d e l t o T e s t f o rPredictabilityn d Integrationn t h e S t o c kMarke t s o f Transition EconomiesMichael ROCKINGERHEC-Schoolof Management, epartmentf Finance, 8351Jouy-en-Josas, rance [email protected])Giovanni URGACityUniversityusinessSchool,Departmentf Investment, iskManagementndInsurance,Frobisher rescent,BarbicanCentre,LondonEC2Y HB,[email protected])

This article introducesa model, based on the Kalman-filter ramework, hat allows for time-varyingparameters,latent factors, and a general generalized autoregressiveconditional heteroscedasticity(GARCH)structure or the residuals.With this extension of the Bekaert andHarveymodel, it is possi-ble to test if an emergingstock marketbecomes more efficient overtime and moreintegratedwith otheralreadyestablished markets n situations n which no macroeconomicconditioningvariablesare avail-able. We applythis model to the Czech, Polish, Hungarian,andRussian stock markets.We use data atdaily frequencyrunning rom April 7, 1994, to July 10, 1997. A latent factorcapturesmacroeconomicexpectations. Concerningpredictability,measuredwith time-varyingautocorrelations,Hungaryreachedefficiency before 1994. Russia shows signs of ongoing convergencetowardefficiency.For Poland andthe Czech Republic, we find no improvements.With regardto market ntegration, here is evidencethat the importanceof Germanyhas changedover time for all markets.Shocks in the United Kingdomare positively related to the Czech and Polish markets but not to the Russian or the Hungarianmar-kets. Shocks in the United States have no impact on these marketswith the exception of Russia. Astrong negativecorrelationbetween Russia and the UnitedStates and Germany ends to disappearoverthe time span studied.We also show that these marketsexhibitsignificant asymmetricGARCH effectswherebad news generatesgreatervolatility.In Hungary,good news, instead,generatesgreatervolatility,which leads us to formulatea liquidityhypothesis.KEY WORDS: Central and Eastern Europe; Kalman filter; Market integration;Stock indexes;Volatilitytransmission.

There is a set of interestingnew stock markets that haveemerged out of the former communist bloc and that havebeen little investigatedin the literature.Because these mar-kets are even newer than other emerging Asian or SouthAmerican markets (already studied extensively by Bekaert1995; Claessens, Dasgupta, and Glen 1995; Bekaert andHarvey 1997; among others), and also because of their eco-nomic and culturaldifferencesfrom the other newermarkets,it appears nteresting o gain insightinto the workingand evo-lution of these countries' financial markets.In our study wefocus on a sampleof Centraland EasternEuropeanFinancialMarkets (CEEFM)--namely, the Czech, Hungarian,Polish,and Russian markets.The methodologicalcontributionof this articleis the intro-duction of a model that allows for latentfactors,time-varyingparameters,and a general generalized autoregressivecondi-tional heteroscedasticityGARCH)structure or the residuals,extending the Bekaert and Harvey (1997) model. The basicframeworkused in this article is the Kalman filter.The use of a model with latent factorsis motivatedby theobservationthat, unlike in the main related works such asthose of Harvey (1995) and Bekaert andHarvey(1995, 1997),for the countriesin our panel, very little informationbeyondthe level of stock indexes is available.Typically,data are avail-able only for a few years for these countries. It is thereforeunreasonable o use data at a monthly frequencyas is done inother studies of this type because the sampleis just too small.

Furthermore,he macroeconomicdata is of doubtfulquality.We would like to emphasizethe fact that,even if longertimeseries of macroeconomicvariables were available,our modelwould allow the captureof unobservablevariables.The fact that our model allows for time-varyingparametersfurther allows us to address two importanteconomic ques-tions: (1) Have the CEEFMbecome more efficient over time,and (2) did they become more integratedwith other alreadyestablished markets?

First, the marketsunder investigationare very young andhave emerged out of centrally planned economies. One canexpect that these markets, o attract oreign capital,have triedto adapttheirstandards o international tandardsby improv-ing disclosurepracticesof firms,orderexecution,and owner-ship rights and by bringingdown limitations to internationalcapital flows. As a consequenceof these improvements, iq-uidity should improve.Moreover,apparentarbitrageopportu-nities due to autocorrelationsn returnsshoulddisappear.Wetest if suchchangestakeplace by investigatingf predictability(measured throughtime-varyingautocorrelations)has indeedevolved over time. This corresponds o a test of a weak formof marketefficiency.

? 2001 AmericanStatistical AssociationJournalof Business &Economic StatisticsJanuary2001, Vol. 19, No. 173

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74 Journalof Business & EconomicStatistics,January2001Second, for the investor interested n internationaldiversi-fication,the knowledgeof a country'scorrelationwith world-wide risk is of prime mportance.Certainmodels have assumedperfect ntegration,while othershave assumedsegmentationorpartialsegmentation.Bekaert and Harvey (1995, 1997) com-bined both extremes in a model allowing for time-varyingintegration,which they applied to a large set of emergingmarkets.Their work thereforeencompassesmodels in which

marketsare assumedto be perfectly integrated Solnik 1983;Harvey 1991; Fersonand Harvey 1993, 1994), perfectly seg-mented(Sharpe1964;Lintner1965), or constantly n between(Errunzaand Losq 1985). We obtaintime-varying ntegrationby assumingthatwe have time-changingparameters.Further,we allow forgeographic ntegrationby investigatingheimpactof a few selected establishedstock markets ESM) rather hanby using a single world index. The set of ESM consists ofthe U.S. market(the largest capitalizationof the world), theU.K. market (the largest Europeancapitalization),and theGermanmarket (geographicalvicinity and importanceas atradepartner).Ourmodel is also able to deal with very complex GARCHeffects.The incorporation f such effects leads to an improvedefficiency of estimates. This model is, therefore, of use inany situationin which there are time-varyingparametersandparametricheteroscedasticity n the residuals. Beyond this,for the study of market ntegration,country-specificGARCHeffects are necessary to gauge the relative component indomesticvolatilityof foreign shocks. The GARCH effect thatwe consider allows for asymmetries.It is well documented(Campbelland Hentschel 1992) that for establishedmarketsbad news leads to subsequent ncreasedvolatility.This is theso-calledBlack (1972) leveragehypothesis.The asymmetry nthe GARCHprocessallows us to test if the CEEFMalso obeythe leverage hypothesis. On the other hand, for those coun-tries sufferingfrom low liquidity,one can imagine scenariosin which good news can lead to increased iquidity,which inturncan lead to increasedvolatilityas investorsrebalance heirportfolios.We call this phenomenon he liquidityhypothesis.Thearticle s organizedas follows. In Section 1 we describethe general model allowing for latent factors, time-varyingparameters,and GARCH in the residuals. In Section 2 weprovidedescriptivestatistics.We then reportand discuss theresultsof the estimationof our model and test for integration,predictability, nd the leverage-liquidityhypothesis.Section 3presentsour conclusions.

1. A GENERALMODELWITHTIME-EVOLVINGPREDICTABILITYND INTEGRATION

In a recentarticle on emergingmarkets,BekaertandHarvey(1997)-BH henceforth-presented a very interestingframe-work within which it is possible to study whether marketsevolve toward greater integration.In this article we extendtheirmodelby using the Kalman-filter pproach,which allowsus to deal explicitlywith time-varyingcoefficientsand a gen-eral GARCH structure or the residuals.1.1 Theoretical Framework

In testing for time variation of market integration, wefocus on geographicalsegmentationrather hanon worldwide

integrationas in BH; ratherthan having one world index,we allow fora countrythatmay geographicallydominate.Letthis countrybe indexed by D. Its continuously compoundedstock returnat time t is denoted by ro,,. All returns n thisarticle are definedby the formular, = 100.- n(S,/St_1), whereSt stands for the closing value of the index at time t. It isassumedthatthe marketD hasreturns hatevolve according oro,D= aD, tXD, t + E,t, (1)

aD,t = aD, t-l + lo,,, (2)ED,t = "D,tD, t, (3)

and2 0? P?E2,ILD,t = DDDt--1I D,t-l>0}+ , l +ot O} , t1 2 1, (4)

where aD, t and D, represent, espectively,a time-varyingvec-tor of parameters nda parametermatrixallowingforpossiblyautoregressivebehavior n the parameters. D, and roD,,repre-sent randomnoises, assumedto be distributednormallywithmean 0, and respectivevariances1 and QD,. QD,trepresentsa squarematrixwith dimension the numberof rows of aD ,.The vector x, t corresponds o variablesthat are assumedtodescribethe conditionalmean. Such variablesmay be laggedreturns,seasonal dummies,or otherpredictingvariables-forexample, see Taylor (1986) for possible seasonalities n stockreturns.Since aD,t representsa vector,by setting an elementin x, t equalto 1 we obtaina model with a latent factor.Morecomplicated atent structures uch as autoregressiventegratedmovingaverage ARIMA)processescan also be implemented.The term aD,,tx,, in (1) is called the conditionalmean.Theresidual ED, is the unexplainedpart of the returnof coun-try D. For volatilitywe have chosen in Equation 4) a widelyused GARCH(1,1) that allows for asymmetries.In the liter-ature,variousspecificationsallowing for asymmetriescan befound-for example,CampbellandHentschel(1992), Glosten,Jagganathan,and Runkle (1993), and Zakoian (1994). Theparameters3o, 13, 3o, 3o represent,respectively,a constant,the importanceof positive shocks, the importanceof nega-tive shocks, and the importanceof persistence."{condition}s adummyvariable akingthe value 1 wheneverconditionis trueand 0 otherwise. In Appendix A we show how the Kalmanfilter and the smoother can be adaptedto deal with GARCHeffects. Weemphasizethat this method can be appliedto othermodels,estimatedby the Kalman ilter,whereresiduals ollowGARCHdynamics.We next consider a given countryi, for which we wish totest predictabilityand time-varying ntegrationwith the dom-inant country D. We assume that returns'dynamics can bemodeled as in the following, where the exponent betweenparenthesesrepresentsan index, not a power:

S= a(2) + e1, (6)Ei, r =-- i D, t i, t ,()

ei,t, -=

i,tZi,t, (7)



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Rockingerand Urga:A Time-VaryingarameterModel o Test forPredictabilitynd Integration 752 = 3/+,2P+2 >o, t ,t- {et l? i e, t ,_o


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76 Journalof Business & EconomicStatistics,January20012.1 DataDescription

For the CEEFMwe consider stock indexes for the CzechRepublic (CZ), Poland(PO),Hungary HU), andRussia(RU).Other stock indexes are available such as those of Bulgaria,Slovenia, Romania, Croatia,and Estonia. However, we didnot analyze these because they are available for too shorta period of time. Most importantly,these countries stillhave very high barriers o internationalcapital flows, whichmakes the issue of integration irrelevant. The establishedstock markets(ESM) consideredin this study consist of theAmerican(US), German(GE), and British(UK) markets.Allserieswill be taken at a daily frequency.For furtherdetailsonthe originof this data,see AppendixB.Since we take the standpointof an international nvestorwith a dollarreferential,ndexes were converted nto U.S. dol-lars,when necessary.This implies thatany effect measured ndollarreturnscan come from movementsof the exchangerateor from a variationof returnsmeasured n local currency.Asin most of the literature,ncludingBH, we do not separate hevariouseffects.

To illustrate he evolution of the CEEFM ndexesdescribedpreviously, we present in Figure 1 a graph of the indexesfor the longest possible time span. All indexes have a com-mon periodfrom April 7, 1994, to July 10, 1997. They wererescaledto takethe value 100 on April7, 1994. Forcompara-tive purposes,we also present n Figure2 the evolutionof theU.S., German,and U.K. stock markets.These graphs ndicatethat 100 U.S.$ investedon April 7, 1994, in a portfolio repli-cating the indexes would have yielded by July 1997 signifi-cantly differentamounts of wealth takingthe values $46 forthe CzechRepublic,$77 for Poland,$397 forRussia,$221 forHungary,$158 for the United Kingdom, $169 for Germany,and$202 forthe United States.Suchbig differences ustify themodelingof the variousindex to gain a furtherunderstandingof how they interact.The series for Russia shows a strong peak located in themiddle of 1994, which also appears n other Russianindexesnot used in this study.The peakcoincideswith the creationofa CentralDepositoryClearingHouse in July and the creation520500480460 ji440420 F400 I380 Czech I340 Hungory320 ............ Polond i I300 . Russio I280 I260 ,l ,.240 I | i220 II200 I AI ,140

100 )%j,,

Figure 1. Plot of VariousCentralEasternEuropeanFinancialMarketIndexes.

240

200

USA160 - Germany iUK

120

80

Figure2. Plot of VariousEstablishedStock-Marketndexes.

of the Russian FederationCommissionon Securities and theCapitalMarket.The end of this spurtwas caused by the col-lapse of the banking system. This peak was also documentedby RockingerandUrga (1997).2.2 Descriptivetatistics

Toensure that the statisticalpropertiesmeasured n the timeseries for the various ndexesarecomparable,we focus on thedataover the commontime span (April7, 1994, throughJuly10, 1997), which corresponds o 867 observations.Followingtherecent iterature Richardsonand Smith 1993;Bekaertand Harvey 1995, 1997), we obtain heteroscedastic-robustestimates of the mean, variance,skewness, and excesskurtosiswithin the generalizedmethod of moments (GMM)framework.This frameworkalso provides t tests for signifi-cance of the moments.A test for normalitycan be constructedwith the Wald principleby imposing zero skewness and noexcess kurtosis in the GMM estimationsince undernormal-ity both statisticsshould be 0. The associatedoveridentifica-tion statistic W is then distributedas a X2 under the null. Wealso reportthe Jarque-Beratest for normalitydistributedasa 2Inspectionof Table1reveals thatthe various ndexes behavein a very complex manner. For the mean of the returnsthe range is between -.09 for the Czech index and +.20for the Russian index. The annualized volatility, definedas N2 times daily volatility, ranges from 9.4% for theUnited Kingdom up to 51.4% for Russia. The mean andvolatilityfor ESM are of a similarmagnitudeandrather mall.Claessenset al. (1995, p. 138) reported or the emergingmar-kets of Asia andSouthAmericafor datarunningbetween1975and 1992, coefficientssimilar to those for our set of emergingmarkets.However,they find a higher volatilityfor establishedmarkets. This is because in our sample these markets wererathercalm and without crashes.For all series (except for Hungary)we notice a significantnegative skewness. This means that for these markets thereare occasional drops that cannot be capturedwith a normaldensity.Furthermore,or all series we notice excess kurtosis



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Rockingerand Urga:A Time-VaryingarameterModel o TestforPredictabilitynd Integration 77Table1. DescriptiveStatisticsat DailyFrequency

CountriesStatistics CZ HU PO RU US GE UKSample size 850 868 868 868 868 868 868Mean -.0910 .0838 -.0760 .2000 .0766 .0539 .0573Median .0000 .0340 .0000 .0000 .0968 .0681 0.1013Annual.volatility 17.21 22.62 39.19 51.46 11.46 11.53 9.40Skewness -.64 .17 -.36 -0.21 -.53 -.73 -.20sk* -6.16 2.11 -7.04 -4.69 -3.47 -2.79 -1.51Kurtosis 6.72 3.48 4.29 38.70 2.92 2.63 .99ku* 11.78 15.86 50.21 151.54 3.80 3.65 1.30W 141.68 231.45 2,539.30 22,967.52 18.22 15.75 3.10Jarque-Bera 1,660.10 430.30 673.14 57,518.61 366.23 281.36 44.08Engle(1) 64.99 28.09 48.00 .02 0.74 2.10 1.19Engle(2) 72.94 28.02 89.38 60.05 3.01 9.27 5.55AutocorrelationsRho(1) .231 .119 .187 .135 -.047 -.018 .026Rho(2) .219 .012 .057 -.020 .032 .027 .080Rho(3) .080 .006 .005 .064 -.048 .000 -.063Rho(4) -.007 -.013 .076 .077 -.001 -.012 .001Rho(5) -.003 -.011 -.078 .182 -.079 .026 -.070Rho(6) -.052 .004 -.044 .097 .028 -.108 -.057Rho(7) -.012 .083 -.031 .065 -.027 -.008 -.048Rho(8) -.049 .063 .010 .076 .032 -.005 -.039Rho(9) .001 .009 .020 .104 .057 -.026 .029Rho(10) .031 .030 .008 .139 -.056 -.002 -.056Rho(15) -.043 .091 -.050 .036 -.035 .007 .010Rho(20) .054 .048 -.096 .062 -.045 -.083 -.031BL(10) 107.73 46.14 61.93 114.03 32.43 31.03 35.98NOTE:Wereport eteroscedastic-robuststimatesof the mean,variance, kewness andexcess kurtosis btainedwithin GMMramework.his rameworklso provides tests forsignificanceof skewnessand kurtosis sk*and ku*respectively).We also reportW,a statistic orrespondingo a test fornormality.hedistributionf thisvariable s a X2under he nullof normality.hetraditionalarque-Beraest fornormalitys distributed s a X2with2 df.Topre-test orheteroscedasticity, e reportEngle(L)-that is, the LagrangemultipliertatisticT R2 correspondingto a test of significance f the parameters , j = 1,..., L, inthe regressionr2= ao+ L ajr_ + ui, wherewe choose L to take the values1 and2. These statisticsare distributeds a X2with1, respectively, df BL 10) respresentsa Box-Ljungype portmanteauest constructedwith10 lags. When he Engle ests suggest heteroscedasticity,he Box-Ljungest is adjusted orheteroscedasticity.hisstatistic s distributed s a X20.The 95%critical evel or a X2(X2,X20) s 3.84 (5.99, 18.3).The critical evel orsignificance f autocorrelationss .067 (.056) or he 5%(10%)evel.

implying fat tails of the returns distribution.Finally, the Wand the Jarque-Berastatistics indicate that all series are non-normallydistributed.Possible explanationsfor nonnormalityare that the underlyingreturnsare heteroscedasticand/or thatthere arejumps in the indexes.We now focus on autocorrelations.Marketswith low auto-correlations are considered to satisfy one criterion for weakinformationalefficiency. General equilibriummodels allowfor autocorrelationsn the long run (e.g. Campbell,Lo, andMacKinlay 1997). Because of transactionscosts and becauseof possible thin trading in stocks (a particularly mportantissue for emergingfinancialmarkets),a significantautocorre-lation cannot be ruled out. We test for autocorrelationusinga Box-Ljung-typetest adjusted or possible heteroscedasticityfollowing CumbyandHuizinga (1992). Inspectionof the auto-correlationsreveals for most CEEFMseries a strong positivefirst-orderautocorrelation.For the ESM, on the other hand,we observe a very small autocorrelation.We test for parametricheteroscedasticitywith the Engle(1982) test. For all CEEFM, we find series-significanthet-eroscedasticity up to the second order. There is no sign ofARCH-typeheteroscedasticity or the ESM, the only excep-tion being Germany,which exhibits some second-orderhet-eroscedasticity.Weverifiedthese results with a directGARCHestimation.These observations eadus to stipulate he following restric-tion for the ESM describedby Equations(1) to (4): ro,, =

aD EDt, where ED,t is a homoscedasticresidual.We will usethese residuals as the dominant-countryhock that may havean impacton the four CEEFM.2.3 Estimationf the GeneralModel orEmergingCountries

Havingobtaineda specification or the dominantcountries'stock-indexreturnsdynamics, we turn to test the integrationof transitioneconomies,the predictability f asset returns,andthe leverage-liquidityhypothesisby estimatingEquations 11)through(14) for the transitioneconomies.It is worthnotingthat we experimentedwith selected mod-els allowing for seasonalities in the mean specificationandwe verified that omission of such features does not substan-tially changethe resultsto be reported.Moreover, ntroducing,for instance, a day-of-the-weekeffect in the GARCH equa-tion does not change the generalpatternsreportedbut highlyincreases the time required o reachconvergence.The results arereportedn Table 2. We know (Harvey1989,p. 236) that a formaltest of qj = 0 involvesnonstandardtatis-tics and, hence, that the associatedstandarderrors are mean-ingless. Forthis reason we do not report hemin the article. Ifthe estimatedqj = 0, thenclearlythe associatedparameters aconstant.It is thenpossibleto formallytest at the conventionallevel if the correspondingao()= 0 or not. If the estimatedqjis nonzero,then the associated j) variesand it is possible to



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78 Journalof Business &EconomicStatistics,January2001

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Rockingerand Urga:A Time-VaryingarameterModel o TestforPredictabilitynd Integration 79test if duringsome period of time the aj) = 0. This can beconvenientlyachievedin a graphwhere one reportssmoothedestimates of atj) and 95% confidenceintervals.2.3.1 Testing or Integration. Inthis section we discuss ifthe geographicallydominantcountries'shocks have an impacton the CEEFM.We measurethe impactof a dominantcountrythrough the time-varying parametera', whose dynamic isgiven by at2) 1+ ,2) where rl2) N(0, qYCzechRepublic:Forthis countrywe notice thatq2 equals0for the United States and the United Kingdom. Moreover,since for the United States also a(2) is not significantlydiffer-ent from 0, we conclude that there is no integrationbetweenthe U.S. and the Czech market.Moreoverthe estimate of a02)for the UnitedKingdom (.1077) is marginally ignificant.Thissuggeststhat shocksin the UnitedKingdomhave an impactonthe Czech marketand, moreover, hat the relationbetween thetwo markets did not change. When we turnto Germany,wefind a nonzeroq2of .0099 and, thus, we find that the relationhas changed through ime. Turning o the plot of the evolutionof the parametera(2) displayed in Figure 3, we notice thatbetween the beginning of our sample and the end of spring1995 shocks in Germanybecame more and more importantfor the Czech Republic, with the coefficient ac2) increasingto .25. Since then,both countrieshave become less integratedwith a coefficientof at2) equal to .1 by the end of June 1997.Hungary: For Hungary we notice that q2 is 0 for boththe United States and the United Kingdom. Moreover,eventhough the point estimates of a2) are positive, they are notstatisticallysignificant.This means that shocks in the UnitedStates and in the United Kingdom had no impact on theHungarianmarket.When we turn to Germany,we obtain apositive q2. As Figure 4 shows, the point estimate of ac2)increased to .18 by February1995, but it decreased subse-quently to less than -.2. Moreover,the confidence intervalsaround the a (2) trajectoryget larger toward the end of thesample. This leads us to conclude that Hungary has beeninfluenced very little, over the period under considerationin this study, by any of the potentiallydominantcountries.Anecdotalevidence confirmed he fact thatduringthis period

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-0.4

-0.6C4 - -

Figure 4. Smoothed Estimatesof a2,t Indicatingthe Impact ofGermanShocks on the HungarianMarket.of time theHungarianmarketwas little influencedby foreignforces. The only countrythatmattered ignificantly or a shortperiodwas Germany.Poland: The pattern or Poland is somewhatsimilar to thatof the Czech Republic.We observeagain thatq2equals 0 forboth the United States and the United Kingdom.Once morea(2) is significantlydifferent from 0 for the United Kingdombut not for the United States. We do find that the importanceof Germanyhas changedthroughtime (see Fig. 5). After aninitialperiodwhen Germany'sshocks mattereda lot, politicalevents matteredmuch less.Russia: As could be expected given the importanceof theRussianmarket, he pattern or this countryis somewhat dif-ferent from the previous patterns.We notice that q2 equals 0for the United Kingdom only. For the United Kingdom theestimate of a(2)has a negative sign but is nonsignificant.Boththe United States and Germanyare found to have positive q2-In Figure6 we presentthe graphof a(2) for the UnitedStates;the graphfor Germany s very similar.Initiallywe notice thatthis coefficient is strongly negative (-1.19), but it increases

1.8at 1.96/Ptrr

1.4 . - %-1.96 V, r

1.0 -

-0.2 /

Figure 5. Smoothed Estimates of a2,t Indicating the Impact ofGermanShocks on the Polish Market.



9/13

80 Journalof Business & Economic Statistics,January20010.8

- - ot+i.96 PT

-0.0

-0.84

o 00o o0o oooo-,- - 0ooo?) it o

Figure6. SmoothedEstimatesof a2,t Indicating he Impactof U.S.Shocks on the RussianMarket.

through ime, ending up close to 0. This finding ndicatesthat,since 1994 when the Russian marketappeared o live a life ofits own, it startedto evolve towarda situationof no correla-tion rather hannegativecorrelation.2.3.2 Testing for Predictability. In this section weaddressthe issue of whether the CEEFMunder considerationhave become less autocorrelated,which we would interpretasa condition of increasing(weak) marketefficiency.We mea-sureautocorrelationhrough he possible time-varyingparam-(1) (1) (1) (i)eter a( = at1 I+ t , where q ,- N(0, q ). We continue topresentthe results of our global model includingthe variousforeign shocks. For cases in which the foreign shock has notbeen found to be statistically significant,one could estimatethe model without t. To save space,we continue to present heoverallresultsreferring o the estimatesobtained n a restrictedmodel when necessary.CzechRepublic:When consideringthe regressionsinclud-ing German and U.K. shocks, we find a q, of .0167 and of.0140, respectively,and as a consequence we conclude that0.6 / - - ,Ot"+1.96 /Pr0.5 - -196 Pt

0.4

-0.1

-0.2

Figure 7. Smoothed Estimates of ac1t RepresentingTime-VaryingPredictabilityfor the Czech Market (parameters from the GEregression).

predictabilityhas changedthrough ime. We also find that theequation involving the U.S. market leads to no variation inthat parameter.We notice that all the estimates of a0 aresimilar-.2614 for the U.S. regression, .2881 for Germany,and .2548 for the United Kingdom.The graphsobtained fora ') for Germanyandthe United Kingdomarevirtually ndis-tinguishable.For this reason we present only the graph forGermany(see Fig. 7). We notice that ac1) always oscillatesaround.26, the value found in the U.S. regression.In a firststage, lasting until November 1994, we found thatthe marketbecame more predictable.Anecdotal evidence suggests thatduringthis periodhundredsof companiesof the first wave ofmass privatizationwerebeingtradedandthat a second wave ofprivatizationswas underway. Foreignersseemed to be reluc-tantto investin this marketbecause of its apparentnefficientfunctioning.As domestic funds bought second-wavecompa-nies, the marketbecame moreilliquidand moreautocorrelatedfrom then until mid-June1996, but as liquidity subsequentlyincreased,autocorrelation iminished.This is theperiodwhenthe Ministryof Finance took action against a dozen fraudu-lent investmentbanks showingdetermination o deal with thebanking-sectorproblems,as a consequenceof which the mar-ket rose and becameagainless liquid.This culminated owardthe end of 1996 when a Senate election saw the reform-eagergovernmentcoalition confirmed. For the Czech market,wetherefore find two periodsof increasing predictability.Hungaryand Poland: All the estimates of q, are found tobe equal to 0 for the two countries.There is no time variabil-ity in predictability.When we turn to the point estimate ofao , we notice that for Hungary he parameters arybetween.0265 (for the U.K. regression)and .0348 (for the U.S. regres-sion). In no case do we findsignificantcoefficients. For Polandwe find that the estimates of a4l) vary between .1639 (forthe Germanregression)and .2439 (for the U.K. regression).Unlike in Hungary, n Poland the parameters highly signifi-cant. These resultssuggest thatthe Hungarianmarketappearsto have reached a ratherhigh level of weak efficiency alreadyby April 1994 when our sample starts. A possible explana-tion is that this market was characterizedby its ratherspe-cial stature within the former Soviet bloc. When the StockExchange was officially founded in 1990, it alreadyhad 10years of experience in securities trading.Moreover,thanksto an automated radingsystem that was introduced n 1994,transparencyn the orders was assured. For the Polish mar-ket the coefficient of predictabilitys constantand ratherhigh.Anecdotal evidence suggests that trades were due mostly todomestic activities. It should be recognized that this marketis also rathernew since restrictions o foreign participationnthe marketwere eased only in July 1994.Russia: Inspection of q, indicates that predictabilityhasevolved throughtime. We also notice very similarpoint esti-matesof auoj or the variousregressions.Figure8 displaysthetrajectoryof al) using the parameters f the Germanregres-sion (the figuresfor the otherparameters revery similar).Wenotice that at the beginningof the sample days with returnshigherthanexpectedwere followedby days with returns owerthan expected. This picturehad changedby mid-1995 whenwe observe a decreasingreverse relation.However,the stan-dard errorsare found to be largerso that the null of no pre-



10/13

Rockingerand Urga:A Time-VaryingarameterModel o Test forPredictabilitynd Integration 810.30 1 1 1Off 9%Ptr0.25 -- a1.6

0.20 --0.15 '0.10 -

0.05 --0.00 - --.----0.05 o-0.10-0.15 ,

-0.20 ,

Figure8. Smoothed Estimates of a ,t Representing Time-VaryingPredictability or the Russian Market (parameters from the GEregression).

dictabilitycannotbe rejected.Our results suggest that,after aperiodof some overreaction,marketsbecamemore liquid.2.3.3 TheGARCHStructureor the CEEFM. We wouldlike to emphasize that to the best of our knowledge this isthe firstarticlein which the Kalman-filtermodel incorporatesasymmetricGARCH features n the residuals.We will discussthe normalityof the residuals,the asymmetryof the GARCHeffect, and possible correlationsbetween residuals.We test for normalityby using a Waldtest, W, as outlinedin Section 2.2. Inspection of Table 2 and comparisonwithTable 1 revealthat these statisticshave stronglydecreased forall markets.However,for all countries we continue to rejectnormality.This justifies the fact that in Table 2 we reportmaximum ikelihood standard rrorsadjusted ornonnormalityfollowing BollerslevandWooldridge 1992).We notice that for the Czech Republicthereis no asymme-try in the GARCHprocess.For Poland (except for the regression with the UnitedKingdom)and for all regressions nvolvingRussia,we observetraditional asymmetries: Negative news creates volatility.This finding seems to confirm the leverage hypothesis ofBlack (1972). When a negative shock hits the market, thevalue of equity decreases, leading to a shifted debt-equitystructure.The increasedrisk in the companiestranslates ntohighersubsequentvolatility.ForPoland,once we have the UnitedKingdom n the equa-tion, asymmetries disappear.This indicates that bad news inPoland is related to bad news from the United Kingdom.Possibly,when investors n the UnitedKingdomsuffer a draw-back, they withdraw funds from Poland, which in turn leadsto a fall in the Polish market.For Hungarywe find that positive news increases volatil-ity. A similar feature was discoveredby Bekaert and Harvey(1997) for 3 out of 10 emergingcountries,but it has not beencommented on. Possible explanationsfor this findingare thefollowing: It is possible that the markets under considerationaregenerallyvery illiquid.Once a piece of good news hits themarket,foreign capital may be attracted.This could lead toincreased liquidity.In typical market-microstructure odels,

greater liquidity also leads to smaller volatility.In emergingeconomies, greatervolatility can arise subsequentto greaterliquidity if investorsare initially deterred from selling in anilliquid market and take advantageto dump their positionsonce greater iquidityhas been achieved, a featurewe calledthe liquidityhypothesis n the Introduction.Alternatively,t ispossible that given the short time series no relevantnegativenews has hit the market,or it is possible that markets havebeen anticipatingonly negativenews.The parametermeasuringthe persistenceof volatility, 1',takes for all countries,except Hungary,values around 7. ForHungarywe find a value of about .28 implyingthatvolatilitydies off very quickly.2.3.4 Evolutionof the LatentFactor We now turn to thediscussion of a0?).Again the dynamicsof this parameteraregiven by a =(oa )1+ ,where N(0, qo0). hisparam-eter representsa latent factor and is expected to capturetheevolution throughtime of the expectationof macroeconomicvariablessuch as interestrates and other fundamentals.CzechRepublic:For all regressions,we find that q0is pos-itive and between .0146 for the U.S. regressionand .0190 forthe U.K. regression.The values of q0are thereforevery sim-ilar. Furthermore,or all regressionswe find extremely sim-ilar values for aoo).Figure 9 displays the evolution throughtime of this coefficient for the Germanregression.As could beexpectedfromthe fact that thepointestimate of a(0) takesthevalue -.4469 and its varianceq0 is very small, we find thatfor most of the time the latent factoris negative.This obser-vation indicates that for this marketexpectationswere rathergloomy. This observation s in line with what we may inferfrom Figure 1, which shows a ratherpoor performanceof theCzech market.

Hungary: Again we find that q0 is positive and that for allthe regressions he coefficientis very similar,rangingbetween.0096 and .0098, suggestingthat at capturesa time-varyinglatent factor. Figure 10 plots the dynamics for the Germanregression.We notice that,after an initialpessimisticfinancialmarket, romJune 1995 on, this marketwas ratheroptimistic.0.4

a 1.96 VPr0.2

-0.4 " 0 00

-0.6 i i I ii0 i i

Figure9. Smoothed Estimates of a, RepresentingEvolutionofthe Latent Factor for the Czech Market(parameters rom the GEregression).



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82 Journalof Business & EconomicStatistics,January20010.6 aI I

a- - P++1.96 /PU0.5 0- T -- - -. am-1.96 %/Ptl0.4

0.3

0.20.1//

-0.2

Figure10. Smoothed Estimatesof aot RepresentingEvolution fthe LatentFactorfor the HungarianMarket parameters rom the GEregression).Poland:Inspectionof q0reveals thatwhen we considertheregression ncorporatinghe shocks of Germanyor the UnitedStates, then no time variability s found for the latent factors.On the otherhand,when we consider as foreignshocks thoseinnovationsdrivenby the U.K. market, hen q0is positiveandthe latentfactorappears o be time varying.This suggeststhatPoland has not only a time-varying ntegrationwith Germanybut that those foreign shocks are able to act as a substitutefor Polish macroeconomicexpectations.These observationsunderscore he regionalimportanceof the Germanmarketnotonly on the financial sectorbut on the economy as a whole.Russia: Here q0 has an order of magnitude of .10-.12,which is similarto the Czech case. The estimates for the start-

ing value are very similar, ranging between 2.4831 for theU.S. regressionand 3.2419 for the U.K. one. Parameter sti-mates, when allowing for differentforeign shocks, are com-parable.Figure 11 displaysthe variation hrough ime of a! ).We observe large fluctuationsin this coefficient, indicatinggreatreversals n the expectations concerningRussian funda-

- -1 o\n+1.96VPmat"1 \ " -/-

" \ r /\/I

o /I \ I' I

\ I-2 .

-3

Figure11. Smoothed Estimatesofao,t RepresentingEvolution fthe LatentFactorfor the RussianMarket parameters romthe U.S.regression).

mentals.Again, these variationsgo hand in hand with thosethat can be deduced fromFigure 1.3. CONCLUSION

This article introducesa model, based on the Kalman-filterframework,hat allows fortime-varyingparameters,atentfac-tors,and a generalGARCHstructureor theresiduals,extend-ing the Bekaert andHarvey (1997) model. With this extensionit is possibleto test if anemergingstock marketbecomes moreefficient over time and more integratedwith other alreadyestablished markets.We apply this model to the main Central and EasternEuropean Financial Markets-namely, the Czech, Polish,Hungarian,and Russianstock markets.First,concerningmar-ket integration,we find very similar results for the CzechRepublic, Hungary, and Poland. For these countries, theUnited Kingdom always played an importantrole. Germanyplayed an importantrole until spring 1995 but not afterthen. Given its geographicaldistance,these marketswere notaffectedby the U.S. market.For the Russianmarket, he pic-ture is different. Before 1995, access to the Russian marketwould have allowed U.S. or German nvestors o hedge againstlocal risks. The negativecorrelationbetween Russia and theUnited States and Germanydecreased after that.Concerningpredictability,we findthat the Hungarian tockmarket has a rather low level of predictability.One possi-ble reason is high liquidity and the fact that among all thetransition conomies considered he Hungarianmarketalreadyexisted for 10 yearsbeforeit opened officiallyin 1994. Polandand the Czech markethave high predictabilitywith peaks forthe Czech market in November 1994 and April 1997. ThePolish market remainedconstantly high. The Russian markethas a verydifferentpattern. t evolved from a marketwith neg-ative autocorrelationpossibly due to overreactionof marketparticipants)o a marketwith no predictabilityby June 1997.Furthermore,within the general model developedwe findthat for all countries investigated there exist significantGARCH effects compatible with Black's (1972) leveragehypothesis.The exceptionis Hungary,where it is found thatgood news generatesmore volatilitythanbad news. We pro-vide severalexplanations or this phenomenon.

ACKNOWLEDGMENTSWe acknowledge valuable comments from R. Chirinko,B. Dumas, S. Hall, and E. Jondeau.We also thank the editorandan associateeditorforhelpful suggestions.We thankJordiRiera for research assistance. The data used in this studywere extracted romDatastream,Reuters,Bloomberg,and the

Intemrnet.inancialsupport romPHARE-ACEProjectN. T97-8118-R is gratefullyacknowledged.The first authoracknowl-edges financialhelp from the HEC Foundation.APPENDIXA: IMPLEMENTATIONF THE KALMANFILTERAND THE SMOOTHERWITHGARCHEFFECTS IN THE RESIDUALSIn this appendixwe describe how to implement he Kalmanfilter and smoother with GARCH effects in the residuals.



12/13

Rockingerand Urga:A Time-VaryingarameterModel o Test forPredictabilitynd Integration 83Following the notationsof Harvey (1989, pp. 100-105), weassume a generalstate-spacemodel writtenas

Yt= zat + E,, E[E,]= 0, V[E,]= Ht (A.1)and

at,= T,a,_, + R,r,, E[r,] = 0, V[r,] = Q,. (A.2)Equations(A.1) and (A.2) are referred o as the measurementandtransitionequations,respectively.The disturbances,E,andrq,,which can be vectors, are assumedto be distributednor-mally and to be uncorrelatedwith each other and across alltime periods.y, is an observation.z, correspond o explanatoryvariables.The a, are latent variablesthat we try to estimate.Time runs from t = 1 to T.Let Is be the set of all informationavailableat time s. Then,by defining a1ls= E[a,lIs],Ptls= E[(a, - a/is)(a, - atls)'lls],the traditionalKalman-filterquations hat allow estimationofequations (A.1)-(A.2) are

artlt- =- tat_l,Plt-,_= T,P,_T/+ RtQtRt,

Ylt-1 = ztatlt-1,vt = Yt- Ytit-l

F, = ztP, ltz Ht,a, = atlt_1+ Ptlt_IZF,-'v,,

andP, (I - Ptlt_,z'Ft' z,)P,I,_I.

We notice, as did Emerson,Hall, and Zalewska-Mitura1996),thatvt representsan estimateof the residualEt.Clearly, giventhe way the filter is conceived, at time t, v, v2, ... , vt areknown. It is therefore possible to incorporateany GARCHeffect by adjusting Ht. For instance, a GARCH(1,1), withasymmetriesmodeled as by Zakodian1994) can be imple-mentedwith

H, = bo+ bvt_1,_ o}+b -vt_lR, + bH,_,.Ht.OtherGARCH models (see CrouhyandRockinger 1997), canbe similarly implemented.Various initializations are possible for the GARCHcomponent. One possibility is to set H0 = [b_+ (b +?b-) 1/2ir]/(1 -b,). The log-likelihoodfor observation forthe Kalman filter is given by

1 1 1I, = I-- ln(2ir)- - ln(F,)- -vFt'vt.2 2 2tErrors hat are dueto a poor initializationcan be mitigatedbydropping he first few likelihood observations.The conventionalsmoothingequationsare given by

Pt* = PtT+,' P+'l,ItaLtT= ar + Pt(a+?1lT - at+Ilr)PtIT= Pt+ Pt (Pt+,r - Pt+IT)P?*.

Since these equations do not depend on v,, once parame-ters have been estimated,it is possible to use the traditionalsmoothingequationsdirectly.

APPENDIX : INFORMATIONONTENTOFTHESTOCK NDEXESUSEDIN THISSTUDYIn this appendix we provide informationon the indexesused. It shouldbe noticedthatall CEEFMcountrieshave con-tinuousauctions. Both the Russian and the Czech marketsdonot have any price controls,while the Polish and the Hungar-ian markets imit pricechanges from session to session.

1. CzechRepublic-PX50:AvailablebetweenApril7, 1994,and July 10, 1997, the PX50 (with PXL and PX-Glob) is theleading representative f a family of indexes that includes22indexes. The PX50 is the most attractiveCzech stock index(tradedon the PragueStock Exchange) in terms of turnoverand market capitalization.The composition of the index isrevisedquarterlyas of the firstsession in January,April, July,and October.2. Hungary-BUX:Available between December 12, 1991,andJuly 10, 1997, the BudapestStock Index (BUX) replacedthe unofficialBudapestStock ExchangeIndex that was usedduring the initial phases of the country's economic transi-tion. Currently, he BUX contains 17 stocks. To qualify forthe index, a stock has to comply with several requirements,includinga certainminimumface value, a defined minimumprice, a minimum number of transactions,and a cumulatedminimumturnoverof 10% of the registeredcapital duringthesix monthsprecedingthe revisions of the index.3. Poland-WIG:Availablebetween December6, 1991, andJuly 10, 1997, the Warsaw Stock Exchange index was thefirst index to be introducedafter the reopeningof the WarsawStock Exchange. The index is calculated after each tradingsession, and since January1997 it has contained 66 stocks,comparedwith 39 stocks in April 1995. It is calculated asa weighted index for the main market,once per trading day,after each tradingsession. The weight of an individualstockto its marketcapitalizationis limited to 10% of the indexsample.Furthermore, single sectormaynot accountformorethan 30% of the index. The index is regularlyrevised everythree months,mainly to account for the introductionof newstocks.4. Russia-ROS:AvailablebetweenDecember1, 1993, andJuly 10, 1997, this index is provided by the CS First Bostoninvestment bank. The index is capitalizationweighted andincludes the 30 most liquidstocks. This index is ruble denom-inated and availableon a daily basis since August 1, 1994.5. USA-S&P500: The S&P 500 Index consists of 500stocks chosen for market size, liquidity,and industrygrouprepresentation. t is a market-valueweighted index. For allESM, we use datacoveringthe periodfor which we also havedata for the CEEFM.

6. Germany-FAZ:The most quoted index for Germanyis the FAZ (FrankfurterAllgemeine Zeitung) index. It is aweighted index (100 stocks), the composition of which hasnot changedfor almost 10 years.



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84 Journalof Business &EconomicStatistics,January20017. UK-FTSE100: The FTSE ActuariesShare Index is a

weighted index of 100 stocks in which the weights are themarketcapitalizationof each company.[Received October 1998. RevisedApril 2000.]

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