This paper examines the comovement and

Transcription

1 INTERDEPENDENCE BETWEEN THE SLOVENIAN AND EUROPEAN STOCK MARKETS A DCC-GARCH ANALYSIS SILVO DAJČMAN 1 MEJRA FESTIĆ 2 SILVIO DAJČMAN, MEJRA FESTIĆ ARTICLE INFO JEL classificaion: G15, G11, F36 Keywords: - sock markes - DCC-GARCH - Slovenia - reurn comovemen - sock marke volailiy ABSTRACT This paper examines he comovemen and spillover dynamics beween he Slovenian and some European (he UK, German, French, Ausrian, Hungarian and he Czech) sock marke reurns. A dynamic condiional correlaion GARCH (DCC-GARCH) analysis is applied o reurns series of represenaive naional sock indices for he period from April 1997 o May 2010 o answer he following quesions: i) Is correlaion (comovemen) beween he Slovenian and European sock markes ime-varying; ii) Are here reurn and volailiy spillovers beween European and Slovenian sock markes; iii) Wha effec did financial crises in he period from April 1997 o May 2010 have on he comovemen beween he invesigaed sock markes? Resuls of he DCC-GARCH analysis show ha comovemen beween Slovenian and European sock markes is ime-varying and ha here were significan reurn spillovers beween he sock markes. Financial crises in he observed period increased comovemen beween Slovenian and European sock markes. Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis 1. Teaching assisan, Universiy of Maribor Universiy of Maribor, Faculy of Economics and Business, el.: , [email protected], Razlagova 14, 2000 Maribor, Slovenia (corresponding auhor). 2 Full Professor, Bank of Slovenia, Vice-governor, [email protected] 379

2 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) I. INTRODUCTION Inernaional sock marke linkages are of grea imporance for he financial decisions of inernaional invesors. Since he seminal works of Markowiz (1958) and he empirical evidence of Grubel (1968), i has been widely acceped ha inernaional diversificaion reduces he oal risk of a porfolio. This is due o non-perfec posiive comovemen beween he reurns of porfolio asses. Increased comovemen beween asse reurns can herefore diminish he advanage of inernaionally diversified invesmen porfolios (Ling and Dhesi, 2010). Modeling he comovemen of sock marke reurns is a challenging ask. The convenional measure of marke inerdependence, known as he Pearson correlaion coefficien, is a symmeric, linear dependence meric (Ling and Dhesi, 2010), suiable for measuring dependence in mulivariae normal disribuions (Embrechs e al., 1999). However, correlaions may be nonlinear and ime-varying (Xiao and Dhesi, 2010; Éger and Kočenda, 2010). Also, he dependence beween wo sock markes as he marke rises may be differen han he dependence as he marke falls (Necula, 2010). I only represens an average of deviaions from he mean wihou making any disincion beween large and small reurns, or beween negaive and posiive reurns (Poon e al., 2004). A beer undersanding of sock marke inerdependencies may be achieved by applying economeric mehods: Vecor Auoregressive (VAR) models (Malliaris and Urruia, 1992; Gilmore and McManus, 2002), coinegraion analysis (Gerris and Yuce, 1999; Paev e al., 2006), GARCH models (Tse and Tsui, 2002; Bae e al., 2003; Éger and Kočenda, 2010; Cho and Parhizgari, 2008) and regime swiching models (Garcia and Tsafack, 2009; Schwender, 2010). Among hem, he GARCH (Generalized Auoregressive Condiional Heeroskedasiciy) models gained a lo of populariy. The GARCH models are used o analyze he volailiy of individual asses (Bollerslev e al.; 1994; Palm, 1996; Shephard, 1996), while inernaional invesors are more ineresed in comovemen and spillovers beween he asses (or markes). A ime-varying comovemen beween asses (or markes) can be effecively analyzed by mulivariae GARCH (MGARCH Mulivariae Generalized Auoregressive Condiional Heeroskedasiciy) models (Tse and Tsui, 2002; Bae e al., 2003; Éger and Kočenda, 2010; Cho and Parhizgari, 2008; Xiao and Dhesi, 2010; Éger and Kočenda, 2010). There are several MGARCH models 3, of which he DCC-GARCH (Dynamic Condiional Correlaion GARCH) models have grealy increased in populariy. They offer boh he flexibiliy of univariae GARCH models and he simpliciy of parameric correlaion in he model (Swaray and Hamad, 2009). They are an exension of CCC-GARCH (Consan Condiional Correlaion GARCH) models (Silvennoinen e al., 2005). More DCC-GARCH models have been developed: he version by Engle (2002), he version by Engle and Sheppard (2001), he model by Tse and Tsu (2002), a model by Chrisodoulakis and Sachell (2002), a model by Lee e al. (2006). The paper aims o answer hese quesion i) Is correlaion (comovemen) beween he Slovenian and European sock markes ime-varying; ii) Are here reurn and volailiy spillovers beween European and Slovenian sock markes; iii) Wha effec did financial crises 3 An overview of he MGARCH models can be found in Bauwens e al. (2006), Silvennoinen and Teräsvira (2009) or Linon (2009). 380

3 in he period from April 1997 o May 2010 have on he comovemen beween he Slovenian and European sock markes? These quesions will be answered by applying a DCC-GARCH model of Engle and Sheppard (2001). II. THE DCC-GARCH MODEL SILVIO DAJČMAN, MEJRA FESTIĆ The DCC-GARCH model of Engle and Sheppard (2001) assumes ha reurns from k asses are condiionally mulivariae normal wih zero expeced value of reurn ( r ) 2 and covariance marix H. Reurns of he asse (socks, sock indices), given he informaion se available a ime 1 ( 1), have he following disribuion 4 : and where D is a r ~ N(0,H ) (1) 1 H D R D (2) k k diagonal marix of ime varying sandard deviaions from univariae GARCH models wih h i on he i-h diagonal, and R is he ime varying correlaion marix. The loglikelihood of his esimaor is wrien as: L 2 1 T 1 1 ' ( k log(2 ) 2log( D ) log( R ) R ), (3) where ~ N(0,R ) are he residuals sandardized by heir condiional sandard deviaion. Elemens of he marix D are given by a univariae GARCH model (Engle and Sheppard 2001) h i P i Q i 2 ipri p p 1 q 1 h (4) i iq i q for i = 1,2,..., k (variables, in our case sock indices), wih he usual GARCH resricions (for P i Q i non-negaiviy and saionariy ip iq 1). p 1 q 1 Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis Dynamic correlaion srucure is defined by he following equaions M N m m 1 n 1 n M N ' m( m -m) m 1 n 1 Q ( 1 ) Q Q n n (5) 4 The descripion of he DCC-GARCH models is from Engle and Sheppard (2001). The same noaions as by he auhors are used. 381

4 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ), R Q * 1 * 1 Q Q (6) where M is he lengh of he innovaion erm in he DCC esimaor, and N is he lengh of he lagged correlaion marices in he DCC esimaor ( 0, 0 m M N n, m m 1 n 1 1). Q is he uncondiional covariance of he sandardized residuals resuling from he firs sage esimaion and elemens of Q : * Q is a diagonal marix composed of he square roo of he diagonal n The elemens of he marix Q * = R are: q q q kk (7) qij ij (8) q q The DCC-GARCH model is esimaed in wo sages. In he firs sage univariae GARCH models are esimaed for each residual series, and in he second sage, residuals, ransformed by heir sandard deviaion esimaed during he firs sage, are used o esimae he parameers of he dynamic correlaion. More specific, he parameers of he DCC-GARCH model,, are wrien in wo groups:,,...,, ) (, ) ( 1 2 k ii jj, where he elemens of i correspond o he parameers of he univariae GARCH model for he i-h asse series, i i, 1i,..., Pi, i 1i,..., Q 1i. In empirical applicaions, normally a bivariae DCC(1,1)-GARCH(1,1) model is esimaed, wih wo financial asses, r 1, and r 2, (Engle, 2002; Lebo and Box-Seffensmeier, 2008; Éger and Kočenda, 2010). To esimae a DCC(1,1)-GARCH(1,1) model of sock indices reurn comovemens, we firs esimae a VAR (Vecor Auoregressive) model: p p 1, 1 a1, ir1, i b1r 2, i 1, i 1 i 1 r (9) 382

5 SILVIO DAJČMAN, MEJRA FESTIĆ p p 2, 2 a2, ir2, i b2, ir1, i 2, i 1 i 1 r (10) and hen, using residuals of he VAR model, esimae a DCC(1,1)-GARCH(1,1) model: III. EMPIRICAL RESULTS A. Daa h i Q 2 i i 1 ri 1 i1hi 1 ' ( 1 1 1) Q 1( 1-1) 1Q 1 (11) Sock indices reurns are calculaed as differences of logarihmic daily closing prices of indices ( ln( P ) ln( P 1) ), where P is an index price). The following indices are considered: LJSEX (for Slovenia), ATX (for Ausria), CAC40 (for France), DAX (for Germany), FTSE100 (for he UK), BUX (for he Hungary) and PX (for he Czech Republic). The period of observaion is April 1, 1997 May 12, Days of no rading on any of he observed sock marke were lef ou. Toal number of observaions amouns o 3,060 days. Daa sources of LJSEX, PX and BUX indices are heir respecive sock exchanges, daa source of ATX, CAC40, DAX and FTSE100 indices is Yahoo Finance. Table 1 presens some descripive saisics of he daa. This is due o non-perfec posiive comovemen beween he reurns of porfolio asses. Increased comovemen beween asse reurns can herefore diminish he advanage of inernaionally diversified invesmen porfolios (Ling and Dhesi, 2010). TABLE 1 Descripive saisics of indices reurn series Min Max Mean Sd. deviaion Skewness Kurosis ATX CAC DAX FTSE BUX PX LJSEX BUX SOURCE: Own calculaions. Noes: Skewness: The skewness of he normal disribuion (or any perfecly symmeric disribuion) is zero. If he saisic is negaive, hen he daa are spread ou more o he lef of he mean han o he righ. If skewness is posiive, he daa are spread ou more o he righ.. Kurosis: The kurosis of he normal disribuion is 3. Fa-ailed disribuions have kurosis greaer han 3; disribuions ha are less oulier-prone han normal disribuion have kurosis less han 3. Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis Jarque-Bera es (Table 2) rejecs he hypohesis of normally disribued observed ime series. Al indices reurns are asymmerically (lef) disribued around he sample mean, kurosis is greaer han wih normally disribued ime series. Ljung-Box Q-saisics rejec he null hypohesis of no serial correlaion in sock index squared reurns for all sock indices. 383

6 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) Since we use GARCH process o model he variance in he asse reurns, we also es for he presence of he ARCH effec. The null hypohesis of no ARCH effecs is rejeced a 1% significance level. This suggess ha GARCH parameerizaion migh be appropriae for he condiional variance processes. TABLE 2 Jarque-Bera, Ljung Box and ARCH effec es Min Max Mean ATX 18, *** 2,759.19*** *** CAC40 2, *** 1,495.14*** *** DAX 1, *** 1,450.47*** *** FTSE100 5, *** 1,939.78*** *** BUX 21,260.91*** *** *** PX 59, *** 1,773.01*** *** LJSEX 38, *** *** *** SOURCE: Own calculaions. Noes: Jarque-Bera saisics: *** indicae ha he null hypohesis (of normal disribuion) is rejeced a he 1% significance (** ha null hypohesis is rejeced a he 5% significance and * ha he null hypohesis is rejeced a 10% significance. Ljung-Box Q 2 saisics (Q 2 (10)) repors values of he saisics wih 10 lags: *** indicae ha he null hypohesis of no serial correlaion can be rejeced a 1% significance level. Engle (1988) ARCH es repors he value of LM es saisics a 5 lags included: *** indicae ha he null hypohesis can be a 1% significance level. To es saionariy of sock index reurn ime series Augmened Dickey-Fuller (ADF) es, Phillips-Perron (PP) and Kwiakowski-Phillips-Schmid-Shin (KPSS) es are applied. The null hypohesis of KPSS es (i.e. he ime series is saionary) for a model wih a consan plus rend can be rejeced a he 5% significance level for he reurn series of LJSEX and ATX. Since rend is no significanly differen from zero, we give advanage o KPSS model resuls wih no rend. For ha model we canno rejec he null hypohesis of saionary process for any sock index reurn series (expec for LJSEX) a he 1% significance level. The null hypohesis of PP and ADF ess is rejeced for all sock indices. On he basis of he saionariy ess we conclude ha ime series of indices reurns are saionary. Resuls of saionariy ess are presened in Table

7 SILVIO DAJČMAN, MEJRA FESTIĆ TABLE 3 Resuls of saionariy ess KPPS es (a consan + rend) KPSS es (a consan) PP es (a consan + rend) PP es (a consan) ADF es (a consan + rend) ADF es (a consan) 0.19** *** ** *** ATX *** (15) (12) (13) (15) (L=1) (L=1) *** *** *** *** CAC40 (15) (15) (14) (14) (L=2) (L=2) *** *** *** *** DAX (1) (1) (3) (3) (L=0)) (L=0) *** *** *** *** FTSE100 (9) (9) (7) (7) (L=3) (L=3) *** *** *** *** BUX (6) (6) (6) (6) (L=0) (L=0) 0.16* *** *** *** *** PX (10) (10) (10) (10) (L=8) (L=8) 0.25*** 0.59** *** *** *** *** LJSEX (11) (12) (0) (3) (L=1) (L=1) SOURCE: Own calculaions. Noes: KPSS and PP ess were performed for wo models: for a model wih a consan and for he model wih a consan plus rend. Barle Kernel esimaion mehod is used wih Newey-Wes auomaic bandwidh selecion. Opimal bandwidh is indicaed in parenhesis under he saisics. For ADF es, wo models are applied: a model wih a consan and he model wih a consan plus rend; number of lags o be included (L) for ADF es were seleced by SIC crieria (30 was a maximum lag). Exceeded criical values for rejecion of null hypohesis are marked by *** (1% significance level), ** (5% significance level) and * (10% significance level). B. DCC-GARCH condiional correlaion resuls Before esimaing a DCC(1,1)-GARCH(1,1) model, ime series have o be filered o assure zero expeced (mean) value of he ime series. A bivariae Vecor Auoregressive (VAR) model for he reurn series is used o iniially remove poenial linear srucure beween pairs of sock indices reurns. Then he residuals of he VAR model are used as inpus for he DCC- GARCH model. An imporan elemen of specifying a VAR model is o deermine he opimal lag of he explanaory variables. More crieria can be used. In he empirical lieraure mos frequenly used are: SIC (Schwarz Informaion Crierion), HQC (Hannan-Quinn Crierion), AIC (Akaike Informaion Crierion), LR es (Likelihood Raio es), FPE (Final predicion error) and BIC (Bayesian informaion crieria). Liew (2004), in a simulaion sudy, compares hese crieria and his findings show ha he performance of he selecion crieria depends on he size of he sample o which hey are applied. For he small sample sizes (30 o 60 observaions) bes resuls achieve AIC in FPE crieria, whereas for larger sample sizes (120 and more observaions) bes resuls are obained by HQC and SIC crieria. In a similar simulaion sudy, Ashgar and Abdi (2007) find evidence ha generally suppor findings of Liew (2004): HQC performs he bes for sample sizes of 120 observaions, whereas for larger sample sizes (more han 240 observaions) SIC ouperforms all he oher crieria. On his foundaion, we use SIC crieria o selec he opimal lag lengh of he VAR model. Resuls of he opimal lag selecion are presened in Table 4. Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis 385

8 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) TABLE 4 Opimal lag in he bi-variae VAR models KPPS es (a consan + rend) PX 1 BUX 1 ATX 1 CAC40 1 DAX 1 FTSE100 1 SOURCE: Own calculaions. Noes: Opimal lag is seleced by SIC crieria. The resuls (Table 5) show ha lagged reurns of PX, BUX, ATX, CAC40, DAX and FTSE100 are saisically significanly explaining LJSEX reurns. Also LJSEX lagged reurns saisically significan explain reurns of oher sock indices. This is evidence of a feedback mechanism -- reurn spillovers beween LJSEX and oher sock markes are bi-direcional. TABLE 5 Resuls of he VAR models for sock indices pairs PX BUX ATX CAC40 DAX FTSE100 A consan LJSEX (lag1) Oher index in pair (lag1) A consan LJSEX (lag1) (1.41) *** (10.84) *** (4.22) PX-LJSEX (0.95) *** (-2.85) (1.11) (1.33) *** (10.84) *** (6.42) BUX- LJSEX (1.37) ** (-2.44) (1.55) (1.40) *** (9.59) *** (8.61) ATX- LJSEX (0.91) (-1.07) * (1.93) (1.44) *** (10.85) *** (8.70) CAC40- LJSEX (0.53) ** (-2.73) (-1.23) (1.41) *** (10.92) *** (7.74) DAX- LJSEX (0.76) *** (-2.83) * (-1.73) (1.46) *** (10.73) *** (8.75) FTSE100- LJSEX (0.43) *** (-2.98) * (-1.66) Oher index in pair (lag1) SOURCE: Own calculaions. Noes: In parenheses under he parameer esimaion, -saisics are given. *** (**/*) denoe rejecion of he null hypohesis ha parameer is equal o zero a 1% (5%/10%) significance level. The firs index (for example LJSEX in PX pair) in he indices pairs represens dependen variable in a bivariae VAR model regression. Nex, a es of Engle and Sheppard (2001) for consan correlaion was applied in order o deermine wheher he correlaion beween every pair of sock indices is ime-varying or no. The hypoheses of he es are: H u 1 vech p p u u u ( R ) vech ( R ) 1vech ( R 1)... vech ( R ), H o 386 R R (12) u where vech is a modified vech which only selecs elemens above he diagonal. The esing procedure is as follows. Firs he univariae GARCH processes are esimaed, and hen residuals are sandardized. Then he correlaion of he sandardized residuals is esimaed, and he vecor of univariae sandardized residuals is joinly sandardized by he symmeric square roo decomposiion of he R. Under he null of consan correlaion,

9 hese residuals should be IID wih a variance covariance marix given by I k. The arificial regressions will be a regression of he ouer producs of he residuals on a consan and lagged ouer producs. The vecor auoregression is: Y SILVIO DAJČMAN, MEJRA FESTIĆ 1 Y 1... sy s (13) u ' 0.5 where Y vech ( R D )( R D ) I k and R D 1 joinly sandardized under he null hypohesis. is a k 1 vecor of residuals Under he null hypohesis he inercep and all of he lag parameers in he model should ˆ ˆ' X ' X 2 be zero. The es can hen be conduced as 2 ˆ, which is asympoically ( s 1), where ˆ are esimaed regression parameers and X is a marix consising of regressors. The null hypohesis of consan correlaion was rejeced for he nex sock indices pairs -- PX, BUX, DAX and FTSE100 (See Table 6). For ATX and CAC40 pairs we canno rejec he null hypohesis of consan correlaion. For he former pairs, a DCC(1,1)-GARCH(1,1) model is esimaed, for he laer a DCC(1,1)- GARCH(1,1) and a CCC-GARCH(1,1) model. TABLE 6 A es of consan correlaion for sock indices pairs Parameer PX BUX ATX CAC40 DAX FTSE p-value *** **** *** ** SOURCE: Own calculaions. 2 Noes: A consan correlaion model es of Engle and Sheppard (2001) wih 10 lags is esimaed. The es saisic is wih degress of freedom. *** denoe rejecion of he null hypohesis of consan correlaion a 1% significance (**a 5% significance, and * a 10% significance) level.. The resuls for he DCC(1,1)-GARCH(1,1) model are presened in Table 7 and for he CCC- GARCH(1,1) model in Table 8. All esimaed GARCH model parameers (ω LJSEX - oher index, ω oher index - LJSEX, α LJSEX - oher index, α oher index - LJSEX, β LJSEX - oher index and β oher index - LJSEX ) are saisically significan. Condiional variance of LJSEX reurns is influenced by pas reurn innovaions in he foreign index in he pair (α LJSEX - oher index and α oher index - LJSEX ) and by is lagged variances Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis (β LJSEX - oher index and β oher index LJSEX ). Saisically significan parameers β LJSEX - oher index and β oher indicae, ha volailiy ransmission is bi-direcional beween he indices in pairs index - LJSEX (so hey are ransmied o Slovenian sock marke and, vice versa, from he Slovenian sock marke o he oher markes). The DCC parameer β is saisically significan in all cases, while α is significan only for sock indices pairs PX, BUX and ATX. If we also consider ha for all indices pairs, we can argue, ha behavior of curren variances is more affeced by magniude of pas variances as by pas reurn innovaions. Having value β close o 1 indicaes high persisance in he ime series of correlaion, 387 R. The sum of he

10 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) DCC parameers ( ) is larger han zero (meaning ha condiional correlaion beween he pairs of indices reurns is no consan); acually, values close o 1 are observed, indicaing ha condiional variances are highly persisen and only slowly mean-revering (Lebo and Box-Seffensmeier, 2008). Resuls of he Ljung-Box saisics do no rejec he null hypohesis of no serial correlaion in squared residuals of esimaed DCC-GARCH model, suggesing a DCC(1,1)-GARCH(1,1) model is appropriaely specified. TABLE 7 Resuls of he DCC(1,1)-GARCH(1,1) model for sock marke indices ω oher index PX 4.37e-06 (3.45)*** α oher index *** (6.19) β LJSEX - oher index Ljung-Box Q 2 (10) saisics ω oher index - LJSEX *** (12.37) BUX 4.50e-06 (3.54)*** (5.90)*** *** (12.42) ATX 4.54e-6*** (3.18) *** (5.40) *** (10.83) CAC e-6*** (2.76) *** (4.44) *** (9.53) DAX 4.37e-6*** (3.26) *** (5.29) *** (11.37) FTSE e-6*** (2.85) *** (4.52) *** (9.88) * e-06*** (4.39) α oher index -LJSEX *** (8.60) β oher index -LJSEX Ljung-Box Q 2 (10) saisics α *** (57.42) 1.55e-05** (2.05) *** (2.66) *** (12.47) 3.49e-6*** (3.76) *** (5.72) *** (42.38) 2.39e-6*** (2.76) *** (7.01) *** (67.19) 3.32e-6*** (3.06) *** (6.83) *** (55.22) * *** (2.55) *** (2.45) ** (1.70) * (1.45) * (1.56) 1.32e-6*** (3.15) *** (8.09) *** (78.99) (0.67) *** *** *** *** *** *** β (25.58) (14.23) (172.83) (211.22) (25.73) (5.83) SOURCE: Own calculaions. Noes: Parameers ω oher index,α JSEX-oher index,β oher index are esimaed parameers of a univariae GARCH (1,1) model, wih residuals inpu from he esimaed bivariae Vecor Auoregressive (VAR) model wih LJSEX reurns as dependen variable and he oher index reurns as explanaory variable. ω oher index LJSEX, α, β are esimaed parameers of oher index LJSEX oher index LJSEX a univariae GARCH (1,1) model, wih residuals inpu from he esimaed bivariae Vecor Auoregressive (VAR) model wih LJSEX reurns as explanaory variable and he oher index reurns as dependen variable. In parenheses under he parameer esimaion, -saisics are given: *** (**/*) denoe rejecion of he null hypohesis ha parameer is equal zero a 1% (5%/10%) significance level. Ljung-Box Q 2 (10) saisics repors he value of he saisics a lag 10: ***(**/*) indicae ha he null hypohesis of no serial correlaion in squared residuals of esimaed DCC-GARCH model can be rejeced a 1% (5%/10%) significance level. 388

11 TABLE 8 Resuls of he DCC(1,1)-GARCH(1,1) model for sock marke indices Parameer ATX CAC40 SILVIO DAJČMAN, MEJRA FESTIĆ 4.56e-06*** 4.40e-06*** ω LJSEX - oher index (3.18) (2.76) *** *** α LJSE - oher index (5.40) (4.44) *** *** β LJSEX - oher index (10.83) (9.53) 3.49e-06*** 2.39e-06*** ω oher index - LJSEX (3.76) (2.76) *** *** α oher index - LJSEX (5.72) (7.02) *** *** β oher index - LJSEX (42.38) ( ) Consan correlaion esimaion Parameer ATX CAC40 SOURCE: Own calculaions. Noes: See noes for able 7. We can observe a highly volaile ime pah of condiional correlaion beween pairs of sock indices reurns (Figure 1). Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis 389

12 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) DCC-GARCH CONDITIONAL CORRELATION BETWEEN RETURN OF THE LJSEX AND OTHER EUROPEAN STOCK INDICES FIGURE 1 0,4 LJSEX_ATX RFC DCC WTC EU GFC 0,3 0,2 0,1 0 0,3 LJSEX_CAC40 RFC DCC WTC EU GFC 0,2 0,1 0 0,4 LJSEX_DAX RFC DCC WTC EU GFC 0,3 0,2 0,1 0-0,1 SOURCE: Auhor 390

13 SILVIO DAJČMAN, MEJRA FESTIĆ DCC-GARCH CONDITIONAL CORRELATION BETWEEN RETURN OF THE LJSEX AND OTHER EUROPEAN STOCK INDICES (CONTINUED) FIGURE 2 0,3 0,2 0,1 0 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0-0,1-0,2-0,3 0,6 0,5 0,4 0,3 0,2 0,1 0-0,1 LJSEX_FTSE100 RFC DCC WTC EU GFC LJSEX_BUX RFC DCC WTC EU GFC LJSEX_PX RFC DCC WTC EU GFC Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis SOURCE: Auhor Noes: On he ime axis he financial crises are denoed: RFC = Russian financial crisis (oubreak on Augus 13, 1998), DCC = Do-Com crisis (he dae, March 24, 2000, is aken, when he peak of S&P500 was reached, before he docom crisis began), WTC = aack on WTC in New York (Sepember 11, 2001), EU = he dae when he Slovenia joined European Union (May 1, 2004), GFC = Global financial crisis (Sepember 16, 2008). The verical doed lines indicae hese evens. 391

14 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) The main findings of figure 1 are he following. Firs of all, one can observe high volailiy of condiional correlaions beween LJSEX and European sock indices reurns, meaning correlaion (comovemen) beween Slovenian and European sock markes reurns is imevarying. The finding of ime varying comovemen beween sock markes is in accordance wih he empirical lieraure on measuring inernaional sock marke comovemens (Forbes and Rigobon, 2002; Phylakis and Ravazzolo, 2005; Syriopoulos, 2007; Gilmore e al., 2008; Kizys and Pierdzioch, 2009).Secondly, he rend of correlaion beween Slovenian and developed European sock markes (Ausrian, German, French, he UK) in observed period is rising, indicaing ha Slovenian sock marke has become more inerdependen wih hese sock markes. Furher, comovemen beween Slovenian and he Cenral and Easern European sock markes (PX and BUX) during he observed period was more volaile han wih developed European sock markes. Considering he whole observed period, no increasing rend of condiional correlaion can be confirmed beween Slovenian and Cenral and Easern European sock markes. Financial crises, especially he global financial crisis of , had a major impac on increased comovemen of Slovenian sock marke wih European sock markes. Our findings confirm mouning evidence ha correlaions among inernaional markes end o increase when sock reurns fall precipiously (Lin e al., 1994; Longin and Solnik, 1995; Karolyi and Sulz, 1996; Chesnay and Jondeau, 2001; Ang and Bekaer, 2002; Baele, 2005). IV. CONCLUSION In his paper he comovemen and spillover dynamics beween reurns of he Slovenian and six European sock markes (he Unied Kingdom, German, French, Ausrian, Hungarian and he Czech sock marke) were sudied. A DCC-GARCH model proved o be a saisically appropriae model o sudy reurn comovemen and spillovers beween hese markes, and he key resuls obained are: (1) Saisically significan bi-direcional volailiy spillovers were idenified beween Slovenian and European sock markes; (2) Volailiies of sock indices reurns were more affeced by magniude of pas variances as by pas reurn innovaions; (3) Condiional correlaions beween LJSEX and European sock indices reurns in he observed period were highly volaile; (4) Comovemen beween Slovenian and developed European sock markes in he observed ime period has generally increased (a rising rend of comovemen could be indenified), while comovemen wih Cenral and Easern European sock markes did no; (5) Financial crises, especially he global financial crisis of , had a major impac on increased comovemen of Slovenian sock marke wih European sock markes. 392

15 SILVIO DAJČMAN, MEJRA FESTIĆ REFERENCES Ang, A., Bekaer, G Inernaional asse allocaion wih regime shifs, Review of Financial Sudies 15(4): Ashgar, Z., Abid, I Performance of lag lengh selecion crieria in hree differen siuaions. Inersa aricle, april (Rerieved on March 5, 2011: hp://inersa.sajournals. ne/year/2007/aricles/ pdf). Bae, K.H., Karolyi, A.G., Sulz, R.M A new approach o measuring financial conagion. The Review of Financial Sudies 16(13): Baele, L Volailiy spillover effecs in European equiy markes. Journal of Financial and Quaniaive Analysis, 40(2): Bauwens, L., Lauren, S., Rombous, J.V.K Mulivariae GARCH models: A survey. Journal of Applied Economerics, 21(1): Cho, J.H., Parhizgari, A.M Eas Asian financial conagion under DCC-GARCH. Inernaional Journal of Banking and Finance, 6(1): Chesnay, F., Jondeau, E Does correlaion beween sock reurns really increase during urbulen periods?. Economic Noes 30(1): Chrisodoulakis, A.G., Sachell, S.E Correlaed ARCH: modeling he ime-varying correlaion beween financial asse reurns. European Journal of Operaions Research 139(2): Crespo-Cuaresma, J., Wojcik, C Measuring moneary independence: Evidence from a group of new EU member counries. Journal of Comparaive Economics 34(1): Éger, B., Kočenda, E Time-varying synchronizaion of European sock markes. Empirical Economics, 40(2): Embrechs, P., McNeil, A.J., Sraumann, D Correlaion and Dependence in Risk Managemen: Properies and Pifalls. In: M.A.H. Dempser (ed.), Risk Managemen: Value a Risk and Beyond, (Cambridge Universiy Press, Cambridge), pp Engle, F.R Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion. Economerica, 96(5): Engle, F.R Dynamic condiional correlaion: A simple class of mulivariae generalized auoregressive condiional heeroskedasiciy models. Journal of Business and Economic Saisics, 20(3): Engle, F.R., Sheppard, K Theoreical and Empirical properies of Dynamic Condiional Correlaion Mulivariae GARCH, NBER Working Paper No. 8554, (Rerieved on February 05, 2011: hp:// Forbes, K., Rigobon, R No conagion only inerdependence: measuring sock marke comovemens. Journal of Finance, 57(5): Gerris, R.J., Yuce, A Shor- and long-erm links among European and US sock markes. Applied Financial Economics, 9(1): 1-9. Gilmore, C.G., Lucey, B., McManus, G.M The dynamics of cenral European equiy marke comovemens. Quarerly Review of Economics and Finance, 48(3): Gilmore, G.C., McManus, G.M Inernaional porfolio diversificaion: US and Cenral European equiy markes. Emerging Markes Review, 3(1): Grubel, H. (1968). Inernaionaly diversified porfolios: welfare gains and capial flows. American Economic Review, 58(5): Karolyi, G.A., Sulz, R.M Why do markes move ogeher? An invesigaion of Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis 393

16 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) U.S.-Japan sock reurn comovemen. Journal of Finance, 51(3): Kizys, R., Pierdzioch, C Changes in he inernaional comovemen of sock reurns and asymmeric macroeconomic shocks. Journal of Inernaional Financial Markes, Insiuions and Money, 19(2): Lebo, J.M., Box-Seffensmeier, J.M Dynamic condiional correlaions in poliical science. American Journal of Poliical Science, 52(3): pp Lee, M.C., Chiou, J.S., Lin, C.M A sudy of value-a-risk on porfolio in sock reurn using DCC mulivariae GARCH. Applied Financial Economics Leer, 2(3): Liew, V.K.S., Which Lag Lengh Selecion Crieria Should We Employ?. Economics Bullein, 3(33): 1 9. Lin, W.L., Engle, R.F., Io, T Do bulls and bears move across borders? Inernaional ransmission of sock reurns and volailiy. Review of Financial Sudies, 7(3): Ling, X., Dhesi, G Volailiy spillover and ime-varying condiional correlaion beween he European and US sock markes. Global Economy and Finance Journal, 3(2): Linon, B.O., Semiparameric and Nonparameric ARCH Modelling. In: T. G. Andersen, R. A. Davis, J.-P. Kreiss and T. Mikosch (eds.), Handbook of Financial Time Series, (Springer: New York), pp Longin, F., Solnik, B Is he correlaion in inernaional equiy reurns consan: ?. Journal of Inernaional Money and Finance, 14(1): Malliaris, A.G., Urruia, J.L The inernaional crash of Ocober 1987: Causaliy ess. Journal of Financial and Quaniaive Analysis, 27(3): Markowiz, H Porfolio Selecion. Journal of Finance, 7(1): Necula, C Modeling he dependency srucure of sock index reurns using a copula funcion. Romanian Journal of Economic Forecasing, 13(3): Palm, C.F GARCH models of volailiy. In: G. S.Maddala, C. R. Rao (eds.), Handbook of Saisics, vol. 14, (Elsevier Sciences: Amserdam), pp Paev, P., Kanaryan, N., Lyroudi, K Sock marke crises and porfolio diversificaion in Cenral and Easern Europe. Managerial Finance, 32(5): Phylakis, K., Ravazzolo, F Sock marke linkages in emerging markes: implicaions for inernaional porfolio diversificaion. Journal of Inernaional Financial Markes, Insiuions and Money, 15(2): pp Poon, S.H., Rockinger, M., Tawn, J Exreme-value dependence in.nancial markes: diagnosics, models and financial implicaions. Review of Financial Sudies, 17(2): Schwender, A The esimaion of financial markesby means of regime-swiching model. Disseraion. Universiy of S. Gallen. Silvennoinen, A., Teräsvira, T Mulivariae GARCH models. In: T. G. Andersen, R. A. Davis, J.-P. Kreiss in T. Mikosch (Ed.), Handbook of Financial Time Series, (Springer: New York), pp Swaray, R., Hammad, R.S Non-inegraed companies in he oil supply chain and ime-varying correlaions of sock reurns. 14h annual conference on economeric modelling for Africa, 8-10 July, Abuja, Nigeria. (Rerieved on March 10, 2011 hp:// org/documens/conference09/papers/swaray_hammad.pdf). Tse, Y.K., Tsui, A.K A Mulivariae Generalized Auoregressive Condiional Heeroscedasiciy Model wih Time-Varying Correlaions. Journal of Business and Economic Saisics, 20(3):

17 Xiao, L., Dhesi, G Volailiy spillover and ime-varying condiional correlaion beween he European and US sock markes. Global Economy and Finance Journal, 3(2): ODVISNOST IZMEĐU SLOVENSKOG I EUROPSKIH DIONIČKIH TRGOVA DCC- GARCH ANALIZA SAŽETAK SILVIO DAJČMAN, MEJRA FESTIĆ U ovom radu se analizira dinamika kreanja donosa i prijenosa volailnosi između dioničkih rgova Slovenije i pojedinih europskih država (Velike Brianije, Njemačke, Ausrije, Madžarske i Češke republike). Uporijebljena je DCC-GARCH analiza na podacima dnevnih donosa dioničkih rgova za period između aprila 1997 i maja 2010 kako bi se odgovorilo na sledeča pianja: i) Da li je korelacija između donosima slovenskog i europskih dioničkih rgova dinamična; ii) Posoje li prijenos donosa i volailnosi između slovenskog i europskih dioničkih rgova; iii) Kako su financijske krize u Europi i svijeu u israživanom periodu ujecale na korelaciju donosa dioničkih rgova? Rezulai pokazuju, kako je korelacija između donosima slovenskog i europskih dioničkih rgova dinamična i da posoje prijenos donosa i volailnosi između slovenskog i europskih dioničkih rgova. Financijske krize su vodile u poras u međusobni odvisnosi slovenskog i europskih dioničkih rgova. KLJUČNE RIJEČI: DCC-GARCH, dionički rg, analiza kreanja donosa, prijenos volailnosi Inerdependence beween he Slovenian and European sock markes - A dcc-garch analysis 395

18 Economic Research - Ekonomska israživanja, Vol. 25 (2012) No. 2 ( ) 396