Sudies in Nonlinear Dynamics & Economerics Volume 9, Issue 3 5 Aricle 5 An Empirical Analysis of Isanbul Soc Exchange Sub-Indexes Haan Berumen Yilmaz Adi Cemal Aaan Bilen Universiy, berumen@bilen.edu.r Anara Universiy, adi@science.anara.edu.r Anara Universiy, aaan@science.anara.edu.r Sudies in Nonlinear Dynamics & Economerics is produced by he Bereley Elecronic Press (bepress). hp://www.bepress.com/snde Copyrigh c 5 by he auhors. All righs reserved. No par of his publicaion may be reproduced, sored in a rerieval sysem, or ransmied, in any form or by any means, elecronic, mechanical, phoocopying, recording, or oherwise, wihou he prior wrien permission of he publisher, bepress, which has been given cerain exclusive righs by he auhor.
An Empirical Analysis of Isanbul Soc Exchange Sub-Indexes Haan Berumen, Yilmaz Adi, and Cemal Aaan Absrac his paper analyzes possible coinegraion relaions among he sub-indexes of he Isanbul Soc Exchange series - services secor, indusry secor and financial secor - for he period from February, 997 o Sepember 4, 3. he daa is analyzed by using various mehods iniiaed by Engle and Granger (987), Johansen (988) and Adi (995). he basic finding of his sudy is ha none of hese mehods sugges he presence of coinegraing relaionships among hese indexes.
Berumen e al.: Empirical Analysis of Isanbul Soc Exchange Sub-Indexes. Inroducion he purpose of his paper is o examine he relaionships among reurns of various sub-indexes in he Isanbul Soc Exchange by using various mehods. In paricular, we loo a he exen o which various sub-indexes are coinegraed or no by using hree differen mehods. For he firs wo, Engle and Granger s (987) single equaion models and Johansen s (988) mulivariae coinegraion mehods are he among he mos commonly used mehods for assessing long-run relaionships. Kamsra, Kramer and Levi (3) sugges ha seasonaliy does exis in he soc mare, and addressing he seasonaliy in he daa could aler he basic inference gahered from he daa (see, Cheung and Wesermann, 3; Maravall, 995; Hecq, 998 and Cubadda, 999). In order o accoun for his, a hird mehod is adoped: he periodiogram based coinegraion procedure developed by Adi (995) and Adi and Dicey (998). his es has he advanage of being seasonaliy robus, and model free from he selecion of he lag lengh. Periodogram based uniroo/coinegraion ess are immune o hese criicisms (see Adi, 995 and Adi and Dicey, 998). he non-exisence of coinegraion among hese sub-indexes enables he benefis of porfolio diversificaion among hese indexed asses o be realized. However, if here is a coinegraion among hese indexes, hen diversificaion will probably no lead o any benefi (see, for example, Besser and Yang; 3 and Francis and Leachman; 998). Mos of he sudies ha examine he coinegraion among indexes use differen indexes across counries (see, Yang, Khan and Poiner; 3 and references cied in). However, soc mare indexes of differen counries are subjec o differen moneary and fiscal policy shocs from heir respecive governmens, as well as he specific srucural problems each counry may face. hus, using daa from a single counry, urey, allows us o eliminae he effecs of differen policy and srucural shocs on soc mare indexes. Such an analysis will provide a differen angle for he co-movemens of he soc mare indexes. he use of daa on differen secors (or sub-secors) allows us o observe idiosyncraic elemens of differen secors of he economy. In his way, we can compare differen views on he source of secoral growh. Burns and Michell (946) argue ha he broad-based swings in differen secors are driven by an unobservable aggregae cyclical componen. In conras, by using real business cycle specificaions, Long and Plosser (983) and Engle and Issler (995) argue he convenional ess () require esimaion of oo many AR parameers o address he dynamics/seasonaliy of he series; and () es resuls change wih he sample sizes. However, he periodgram based mehod requires no parameer esimaion excep for variance (any consisen esimaor of he variance can be used in he es saisics); and (3) he criical values of he es saisics are free of sample size. herefore, especially in small samples, hese migh bring considerable advanages. Produced by he Bereley Elecronic Press, 5
Sudies in Nonlinear Dynamics & Economerics Vol. 9 [5], No. 3, Aricle 5 ha he presence of secoral componens hinges on he componens of secor specific shocs. herefore, if he shocs are no common across secors, comovemens among secors are no liely. In paricular, Durlauf (989) argues ha if aggregae uni roos are generaed by echnology, i is unliely ha growh innovaions will be common across secors. For example, improved echnology in service qualiy in ourism may no be helpful in he home equipmen secor. Socman (988), on he oher hand, claims ha boh common and secor specific shocs are imporan for sudying economic dynamics. Daa from he soc mare allows us o observe he co-movemens in differen secors. he soc mare sub-indexes are claims on fuure oupu. hese indexes could be aen as predicors of general business cycle condiions (see: Fama, 99; Chen, 99; and Ferson and Harvey, 99). hus, one may analyze he co-movemens of soc mare indexes o assess he role of fundamenals in various secors. his paper assesses he relaionships among sub-indexes by using daa from urey. Using he urish daa has is own advanages. urey is an aracive emerging mare for fund managers. According o he Word Federaion of Exchanges, for he value of share raded, he ISE is he 9 h larges soc mare in Europe, surpassing Ireland, Copenhagen, Oslo and Vienna. I is also he second larges emerging mare afer Kosdaq (Korea). Moreover, urey has a volaile soc mare and macroeconomic performance. his high volailiy allows us o minimize he ype error an error made when an incorrec null hypohesis is no rejeced. he basic evidence gahered from his sudy suggess ha hese sub-indexes are no coinegraed for any of he mehods ha were used. he following secion discusses he mehods, secion 3 presens he empirical evidence and he las secion concludes he paper.. Mehods Mos of he saisical inference of ime series is based on he saionariy assumpion. he mos pracical way o achieve saionariy for a non-saionary series is o compue heir differences. However, if a mulivariae ime series, is nonsaionary, someimes i is possible o find a vecor (or marix) such ha saionary. Such a sysem is called coinegraed and he vecor is called ' he coinegraing vecor. o assess coinegraion, hree mehods are considered in Neer, Wasserman and Kuner (985, p7) specify ha given he sample size and variance of he errors, he variance of he esimaed parameers are affeced by he spacing (increasing he variabiliy of he righ hand side variables) of he observed daa. hus, given he esimaed parameers, increasing he spacing decreases he sandard errors and increases he -saisics. hp://www.bepress.com/snde/vol9/iss3/ar5
Berumen e al.: Empirical Analysis of Isanbul Soc Exchange Sub-Indexes 3 his paper. he firs mehod is he sandard ordinary leas squares mehod proposed by Engle and Granger (987). Each componen of a bivariae nonsaionary ime series can be wrien as a linear combinaion of wo saionary and nonsaionary series as, = au + as (.), = au + as where, and, are he componens of a bivariae series. Here U and S represen uni roo and saionary series, respecively. Since each componen of he bivariae series includes he nonsaionary componen U, boh componens are non-saionary. However, if he a coefficiens in Equaion are nown, Z ( a / a ) = a ( a a ) a S = cs ( ) =,, / becomes a saionary ime series when he sysem is coinegraed. herefore, o find any coinegraing relaionship, i is enough o esimae he raio a / a. he series Z loos lie he residuals from he regression of, on, and hence if he residual series is saionary, hen he bivariae series is coinegraed. Secondly, we will use Johansen s race mehod in order o deermine if he ISE series are coinegraed or no. Consider a q h order vecor auoregressive model = A + A +... + Ap q + e, =,,3,..., hen, subracing from boh sides, we will have = + B + B +... + Bq q + + e where = I A A... A ), B = A + A + +... + A ) and ( q i ( i i q =. If he marix A i, i =,,..., q is nown, hen i is easy o deermine he exisence of any saionary linear combinaions by looing a he eigenvalues of (if all eigenvalues are less han one in absolue value, hen he process is saionary). However, he coefficien marices are unnown. Le ran ( ) = r. Johansen (988) elaboraes on a procedure o es wheher here is any saionary linear combinaion, based on he squared canonical correlaions. Le i be he squared canonical correlaions of he coefficien marix such ha... p where p is he dimension of. he es saisic p r = n ln( i ) (.) i= r + will rejec he null hypohesis H : r = r agains he alernaive of H a : r r + for large values of r. Criical values of he disribuion are given by Johansen Produced by he Bereley Elecronic Press, 5
4 Sudies in Nonlinear Dynamics & Economerics Vol. 9 [5], No. 3, Aricle 5 (988). ha is, he null hypohesis simply says ha a leas r linearly independen saionary linear combinaions exis. If we rejec he null hypohesis of H : r = hen a leas one coinegraing relaionship exiss. Oherwise, here is no coinegraion. Finally, we will consider he esimaion and esing mehod of coinegraion based on he periodogram ordinaes proposed by Adi (995) and Adi and Dicey (998). Given a ime series, he periodogram ordinae is ( a b ) n I n ( w ) = + (.3) where w = /, =,,3,..., / and a, b are he Fourier coefficiens defined as a = ( µ ) cos( w), b = ( µ ) sin( w). (.4) n n Since = = cos( w ) = = = sin( w ) =, he Fourier coefficiens are invarian o he mean. Given a firs order auoregressive ime series as ( Y µ ) = ( Y µ ) + e, =,,3,..., (.5) he following es saisic ( cos( w )) = I ( ) n w (.6) ˆ is used o es for a uni roo where ˆ is he esimaed residual variance. 3 Under he null hypohesis of a uni roo ( H : = ), he es saisic is disribued as a mixure of chi-squares for every fixed. ha is, ( cos( w )) = I ( w ) ~ Z n + 3Z (.7) ˆ where Z and Z are independen sandard normal random variables. Noe ha he disribuion is invarian o he mean. ha is, he periodograms are calculaed based on he original series wihou any model specificaion. Moreover, he criical values of he disribuion do no depend on he sample size (see Adi and Dicey, 998). Since he mehod is based on some rigonomeric ransformaions, he seasonaliy is addressed. Adi and Dicey (999) show ha he same es saisics can be used o es for seasonal uni roo. he null hypohesis of a uni roo will be rejeced for small values of. Some of he criical values of his disribuion are given below (see, Adi and Dicey, 998): 3 One may use a proxy of he daa generaing process as an any ARMA process for y o calculae ˆ due o Slusy s heorem (see Adi, 995: pp 33). hp://www.bepress.com/snde/vol9/iss3/ar5
Berumen e al.: Empirical Analysis of Isanbul Soc Exchange Sub-Indexes 5..5.5. ().348.88.78.368 he periodogram analysis can also be used o esimae he coinegraion vecor for a mulivariae ime series (Adi, 995). Suppose ha he componens of a bivariae nonsaionary series saisfy equaion. As menioned above, Z =, ( a / a), is a saionary ime series. ha is, he problem is o esimae he raio a / a. Le C denoe he real par of he cross periodogram ordinae of a bivariae nonsaionary ime series and V be he periodogram ordinae of one of he componen of a bivariae series (say he firs componen). hen consider a regression of C on V. In oher words, he model is C = + V +, =,,3,...,[ / ] (.8) where [ / ] denoes he ineger par of /. According o model (.8), he ordinary leas squares esimaor of is a consisen esimaor for he raio. ha is, as ˆ = [ / ] ( C = [ / ] = C )( V ( V V ) V ) P a a where C and V are he means for coinegraing vecor would be ˆ,). ( C and (.9) V respecively. herefore, he 3. Empirical Evidence (a) Idenificaion Figure plos he daily ISE series in he logarihmic form for he sample from February, 997 o Sepember 4, 3. 4 he componens of he ISE series, S = log(services), F = log( finance), I = log(indusry), are modeled as a q h order auoregressive ime series. Visual inspecion suggess ha 4 he daa was obained from he Cenral Ban of he Republic of urey s daa delivery sysem. Produced by he Bereley Elecronic Press, 5
6 Sudies in Nonlinear Dynamics & Economerics Vol. 9 [5], No. 3, Aricle 5 he ISE series may have drifs. herefore, he models considered for hese series are: i, = + rend + i, + i, +... + q i, q + ei, =,,3,...,, i = S, F, I (b) Uni Roo Analysis All hree series are analyzed in order o see wheher hey include a uni roo or no by using he Augmened Dicey-Fuller (wih a consan erm and ime rend, and a consan erm wihou ime rend) periodogram based uni roo ess. In order o apply he Augmened Dicey-Fuller mehod, we regress i,, i = S, F, and I on a consan, ime rend (when applicable), i, and i, + j, j =,3,..., q where q is deermined by he longes significan lag rule for each variable as suggesed by Ng and Perron (995). Laer we esed wheher he regression coefficien of i, is zero or no. ha is, we considered he model q i, = + + i, + j i, + j + ei, (Enders, 995, pp. 33) J = ˆ and he value of he ˆ saisic is calculaed for each series where ˆ =. If s( ˆ ) he value of his saisic is less han 5% criical value (-3.45), hen we rejec he null hypohesis of uni roo. In order o apply he periodogram based uni es procedure, we calculae he value of for each series and if he value is less han 5% criical value (. 78), hen we canno rejec he null hypohesis of a uni roo. he es saisic is consisen for each and i is suggesed ha he low frequencies be used. herefore, in he uni roo analysis was used insead of. he resuls are given in he following able. Panel A: Level able : Uni Roo ess Panel B: Firs Differences Series Consan rend Periodogram Consan rend Periodogram S (3) -.568 -.37 3.67 -.9* -.3*.3* F (5) -.78 -.58 6.86-8.867* -8.89*.4* I (7) -. -.8 8.6783-8.59* -8.59*.3* * indicaes he rejecion of null a % level hp://www.bepress.com/snde/vol9/iss3/ar5
Berumen e al.: Empirical Analysis of Isanbul Soc Exchange Sub-Indexes 7 able repors he uni roo ess for he series. he firs column repors he name of he series and he lag lengh in parenheses (as suggesed by Ng and Perron, 995) for he ADF ess. he second column repors he ADF ess wih consan erm. We clearly canno rejec he uni roo for eiher of he series. Column 3 includes ime rend and he consan erm for he ADF series, column 4 repors he uni roos by using he periodogram based ess. Neiher of hese ess could rejec he uni roo in eiher of he series. We also repea he analysis for he firs difference of hese series in Panel B. his ime, we rejec he null of uni roo. hus, we claim ha all 3 series are I(). (c) Coinegraion Analysis In he previous sub-secion, i was deermined ha all hree series are firs order inegraed ime series. herefore, we searched for a possible coinegraing relaionship among hese componens. We will use hree differen approaches, Engle and Granger (987), Johansen (988) and he periodogram based on analysis in order o find such a coinegraing relaionship. C) Engle and Granger (987) s wo-sep mehod: In his par, he componens of he ISE series are invesigaed o deermine he exisence of any bivariae coinegraion. he possible linear combinaions are: S vs F, S vs I and F vs I. Regress F on S. ha is, we consider he regression model as F, =, +, S, + e,, =,,3,..., (3.) ˆ F, =.54 +. 86 S,. Now, consider he residual he esimaed model is ^ series e, = F, ˆ F, and if his residual series is saionary, hen hese wo series are coinegraed. Now, regress e on e, ^ ^ e, =, e, +, (3.) If we rejec he null hypohesis H :, =, he series S vs F are coinegraed. he resuls for his relaionship and ohers are given in able (a). he firs column repors he name of he bivariae variables. he second column is for he esimaed parameer for he independen variable in equaion (3.). he hird column repors he -saisics for he, esimaion in equaion (3.). Produced by he Bereley Elecronic Press, 5
8 Sudies in Nonlinear Dynamics & Economerics Vol. 9 [5], No. 3, Aricle 5 Relaion able (a): Engle and Granger Mehod for Coinegraion ˆ ˆ ( E G) 5% Criical Decision i Value F vs S.86 -.66 -.94 Fails o rejec he null hypohesis of no coinegraion I vs S.8 -.59 -.94 Fails o rejec he null hypohesis of no coinegraion I vs F.879 -.7 -.94 Fails o rejec he null hypohesis of no coinegraion Following able (a), we fail o rejec he null of no-bivariae coinegraion for any of he bivariae relaionships. C) Johansen s Mehod: In order o perform his analysis, we consider a 3-variae ' series such as = ( S,, F,, I, ) and he corresponding squared canonical correlaions based on 663 observaions are =.64, =.3944, 3 =.86 Now, consider esing he null hypohesis of no coinegraion agains he alernaive of a leas one coinegraing relaionship. ha is, we consider he following hypohesis esing problem H : r = vs H a : r. he value of Johansen s race saisic is = 3 ln( r i i= ) = 7.49 which is smaller han he 5% criical value (wih m = p r = 3, able of Johansen, 988) 3.6 and herefore, we fail o rejec he null hypohesis of no coinegraion. C3 he Periodogram Mehod: here are 3 possible bivariae relaionships. (i) Firs, we will loo a he relaionship beween F and S. We calculae he real par of he cross periodogram ordinae of F and S (say C ) and he periodogram ordinae of S (say V ) and regress C on V. ha is, we consider he model, C =, + V +,, =,,...,[ / ] he OLS esimaor of, say P ˆ, is a consisen esimaor for he raio given P above (see Adi, 995). herefore, if he series Z = F ˆ S is saionary, hen hese wo series are coinegraed. he resuls for his relaionship and ohers are given in able (b). hp://www.bepress.com/snde/vol9/iss3/ar5
Berumen e al.: Empirical Analysis of Isanbul Soc Exchange Sub-Indexes 9 Relaion able (b): Resuls for Periodogram Based Coinegraion ˆ ˆ ( a) 5% Decision i Criical Value F vs S.43 -.8-3.43564 Fails o rejec he null hypohesis of no coinegraion I vs S.583 -.6-3.43564 Fails o rejec he null hypohesis of no coinegraion I vs F.868 -.567-3.43564 Fails o rejec he null hypohesis of no coinegraion According o able (b), we fail o rejec he null of no-bivariae coinegraion for any of he bivariae relaionships. 5 Overall, we could no find any coinegraion or long-run relaionship among hose indexes. However, his does no mean ha here is no relaionship among hose indexes in any ime frame. hus, we also explore he possibiliies of he shor-run relaionship among hose indexes by calculaing he correlaion coefficiens among he growh raes of each index. able 3 suggess he presence of posiive srong correlaions among hose indexes. Since here is no benefi of diversificaion under a correlaion coefficien of, we es if he correlaion coefficien is one. If one approximaes he sandard errors of he correlaion coefficien wih /, we canno rejec hese coefficiens differen from for any bivariae relaionship. here are (alhough limied) benefis of porfolio diversificaion. herefore, we conclude ha here is a benefi in he long run as well as he shor run of diversificaions of porfolios. able 3: Correlaion Coefficiens among Series Service Finance Indusry Service..838365.88866 Finance.838365..9473 Indusry.88866.9473. 5 he criical values are abulaed for differen sample sizes and differen significance levels wih replicaes Criical Values for a N % %5 % %9 %95 %99-4.85-3.43564-3.867 -.6775 -.6979.887 6-3.986-3.46-3.6 -.745 -.6483.8799 Produced by he Bereley Elecronic Press, 5
Sudies in Nonlinear Dynamics & Economerics Vol. 9 [5], No. 3, Aricle 5 4. Conclusion his paper assesses wheher here is any long-run relaionship among subindexes of he ISE by using hree differen coinegraion mehods. he empirical evidence gahered here could no find any long-run relaionships among hese indexes. In paricular, here exiss no bivariae coinegraion relaionship among he componens of he ISE series when we use a Engle-Granger regression mehod and he periodogram based es. Moreover, we were unable o find any coinegraing relaionships among hese hree indexes when he Johansen s race mehod was used. Figure : Graphs of he Series =log(services) =log(finance) S F I =log(indusry) 8. 8.5 9. 9.5 8. 8.5 9. 9.5. 7.5 8. 8.5 9. 9.5 4 6 8 4 4 6 8 4 4 6 8 4 hp://www.bepress.com/snde/vol9/iss3/ar5
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