Modeling Volatility in the Stock Markets using GARCH Models: European Emerging Economies and Turkey

Transcription

1 Inernaional Journal in Economics and Business Adminisraion Volume II, Issue 3, 14 pp Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey Erginbay Ugurlu 1, Elefherios Thalassinos, Yusuf Muraoglu 3 Absrac: This paper examines he use of GARCH-ype models for modeling volailiy of sock markes reurns for four European emerging counries and Turkey. We use daily daa from Bulgaria (SOFIX), Czech Republic (PX), Poland (WIG), Hungary (BUX) and Turkey (XU1) which are considered as emerging markes in finance. We find ha GARCH, GJR-GARCH and EGARCH effecs are apparen for reurns of PX and BUX, WIG and XU whereas for SOFIX here is no significan GARCH effec. For boh markes, we conclude ha volailiy shocks are quie persisen and he impac of old news on volailiy is significan. Fuure research should examine he performance of mulivariae ime series models while using daily reurns of inernaional emerging markes. 1 Insrucor Ph.D., Hii Universiy, FEAS, Deparmen of Economics Professor, Deparmen of Mariime Sudies,Universiy of Piraeus, Chair Jean Monne, halassic@unipi.gr 3 Research Assisan, Gazi Universiy, FEAS, Deparmen of Economics

2 E. Ugurlu, E. Thalassinos, Y. Muraoglu Inroducion The European emerging counries are mosly ineresed in macroeconomic and finance area. The counries presen differen research area because of he specific feaures deermined by he ransiion process o he marke-oriened economy which can be valued more han 5 billion EUR ha has grea opporuniy for he companies of he developed counries (Triandafil and Brezeanu, 8). Afer a 5-year break, he firs session of he sock exchanges of Warsaw, Budapes, Prague was held on April 16 h, 1991, June 1 s 199 and April 6 h,1993 respecively. As being he firs esablishing marke, Poland is emerged o be a symbol of developed capialis economies among he leading Cenral and Easern European counries (CEECs) (Nive, 1997). Among all Cenral European markes; Czech Republic, Hungary, Poland and Slovakia have an advanced capial markes, greaer poliical sabiliy and rapid economic growh (Harouounian and Price, 1; Svejnar ). Financial markes, mainly sock exchanges, play an imporan role in he process of economic growh and developmen. Modeling volailiy is imporan issue in financial markes and i has drew he ineres of academics and praciioners over he las hree decades. There are many sudies and various models abou volailiy in financial daa. Financial daa have shown ha he condiional disribuion of highfrequency reurns includes several feaures including excess of kurosis, negaive skewness, and emporal persisence in condiional movemens. To accommodae hem, economericians have developed ools a modeling and forecasing volailiy. Our paper examines he volailiy of five emerging sock markes in Europe ha is Bulgaria, Czech Republic, Poland, Hungary and Turkey 4 using GARCH, GJR- GARCH and EGARCH Models wih daily daa referring o he period beween As i is noed in Hajek (7); sudies (Filer and Hanousek,1996; Dockery and Vergari, 1997; Worhingon and Higgs, 3; Žikeš, ) of he Cenral European marke begun o emerge in he second half of he 199s. Main researches abou European emerging markes volailiy are Emerson e al. (1997), Shields (1997), and Scheicher (1999). While Emerson e al. (1996) provides a model for Bulgarian sock marke and Scheicher (1999) sudies Polish sock reurns, Shields (1997) deals wih modeling reurns for he Warsaw and Budapes sock exchanges reurns. On he oher hand, Harvey (1995), Bekaer and Harvey (1995), Bekaer and Harvey (1997) and Choudhry (1996) analyse emerging markes in he Medierranean, Asia, Souh America or Africa. Scheicher () analyses he movemens of he shor raes of 4 In our and many papers Bulgaria, Czech Republic, Poland, Hungary are named as a Eas European Emerging counries, Bulgaria, Czech Republic, Poland, Hungary and Turkey are named as he European Emerging counries. However, some papers such as Samias e al. (7) and Syriopoulos and Roumpis (9) also called Turkey and/or Bulgaria as a Balkan sock markes.

3 74 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey emerging markes in Cenral and Easern Europe and finds ha he shor raes in Prague, Warsaw and Budapes do no inerac wih he benchmark insananeous rae in Germany. Moreover, Scheicher () discusses inegraion of sock markes in Hungary, Poland and he Czech which are named as principal emerging sock markes in Europe in he paper. The auhor esimaes a VEC model and modeling is volailiy wih a Mulivariae GARCH (M-GARCH) model. The findings show ha counries which are invesigaed have limied ineracion and heir volailiy reveals a regional characer. Vošvrda and Žıkeš (4) use GARCH- model o deermine he volailiy of reurns of he Czech, Hungarian and Polish sock markes by using weekly daa gahered from he period of They use index series insead of heir reurns and afer ARCH es excep for he Hungarian BUX index, boh ess clearly indicae he presence of a condiional heeroskedasiciy in he esimaed residuals. Alhough he null hypohesis ha he shocks o reurns have symmeric impac on volailiy canno be rejeced for WIG and PX-5, he null hypohesis of risk-neuraliy is rejeced for BUX, PX-5. Hajek (7) ess he Efficien Marke Hypohesis on he PX-5 and PX-D index 5 and closing values and sock closing prices on he Prague Sock Exchange are analysed for period for monhly, weekly and daily daa 6. I is concluded ha he ime-variable variance is ypical for ime series of he Czech index and sock price changes. Therefore, Cenral European marke esing such as Czech marke heeroskedasiciy-consisen mehodology mus be applied o avoid significan biases. Syriopoulos (7) invesigaes he relaionships beween Czech Republic, Hungary, Poland, Slovakia as he examples of Cenral and Easern Europe (CEE) sock markes and Germany, US as developed sock markes over he period While, in he long run, he resuls show a relaionship beween he CEE and he developed sock markes, in he shor run, he US sock marke exers a sronger impac han he German marke on he CEE sock markes. Anoher paper which examines he volailiy in Cenral European markes is he sudy of Harouounian and Price (1). They analyse he Czech Republic, Hungary, Poland and Slovakia by using boh univariae and mulivariae GARCH models ha are GARCH, NGARCH, EGARCH, GJR-GARCH, AGARCH, NAGARCH and VGARCH. The findings do no reveal any asymmeric effecs in he markes. Alhough hey mainly conclude ha srong GARCH effecs are apparen for all four markes, i is found ha hree ou of seven specificaions of condiional volailiy are no for he marke of he Czech Republic. 5 PX-5 and PX-D indices are merged ino he PX index in 6. 6 Time series of monhly reurns would be insufficienly long and herefore i has been excluded from he analysis.

4 E. Ugurlu, E. Thalassinos, Y. Muraoglu Rockinger and Urga (1) employ a model by Kalman Filer and sudy he model residual by GARCH for Czech, Polish, Hungarian, and Russian sock markes as examples of ransiion economies and American, German and Briish sock markes as examples of esablished economies. Alhough hey focus on a sample of Cenral and Easern European Financial Markes (CEEFM) 7, hey prefer o use only hese four counries. I is saed ha oher CEEFM counries are available for a quie limied period of ime and hey have very high barriers for inernaional capial flows. The model resuls are very similar for he Czech Republic, Hungary, and Poland. The resuls show ha for hese counries, whereas Germany unil spring 1995 and U.S. has no effec, he Unied Kingdom always played an imporan role in hese markes. The res of his paper is organized as follows: The nex secion gives some deails abou he daa and summarizing he saisical properies of reurns. The hird secion gives brief informaion abou ARCH/GARCH models and he esimaion resuls are presened in he fourh secion. The fifh and he final secion summarizes and concludes he paper. Daa This paper is formed by daily observaions in sock exchanges of seleced European emerging markes which are Bulgaria, Czech Republic, Hungary, Poland and Turkey covering he period by he daa colleced from Reuers. These sock exchanges are Bulgarian Sock Exchange (SOFIX) 8, Prague Sock Exchange Index (PX), Budapes Sock Index (BUX), Warsaw Sock Exchange (WIG) 9 and Isanbul Sock Exchange Naional 1 Index (XU1) respecively. We use reurns o denoe proporionae price change over a sock exchange indices inerval. In parallel wih Yu (), reurn (r) is defined as naural logarihm of prize relaives as follows: where is capial index. Thus, reurn variables are defined as RSOFIX, RPX, RBUX, RWIG, and RXU. The daily reurns for boh indices (presened in Figure 1 and Figure, Fıgure 3, Figure 4 and Figure 5) are shown in he graphs of hose sock exchange indices and heir reurns. (1) 75 7 Czech Republic, Poland, Hungary, Russia, Bulgaria, Slovenia, Romania, Croaia and Esonia. 8 Sofia Sock Indexes 9 Warszawski Indeks Gieldowy

5 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey,.3 1,6 1, SOFIX RSOFIX Figure 1: Bulgaria, SOFIX daily prices and reurns, 1,6 1, PX RPX Figure : Czech Republic, PX daily prices and reurns 35, 3, 5,, 15, , -.1 5, -.15 BUX RBUX Figure 3: Hungary, BUX daily prices and reurns

6 E. Ugurlu, E. Thalassinos, Y. Muraoglu 77 7, 6, 5, 4, 3,, 1, WIG RWIG Figure 4: Poland, WIG daily prices and reurns 8, 7, 6, 5, 4, 3,, 1, XU RXU Figure 5: Turkey, XU1 (XU) daily prices and reurns Table 1 shows descripive saisics of he reurn series. Mos imporan values which are presened in he able are skewness, kurosis and Jarque Bera saisics. Linear srucural (and ime series) models are unable o explain a number of imporan feaures which are lepokurosis, volailiy clusering or volailiy pooling and leverage effecs mosly exis in financial daa. Lepokurosis, volailiy clusering or volailiy pooling and leverage effecs are endency for financial asse reurns. Posiive skewness means ha he disribuion has a long righ ail and negaive skewness implies ha he disribuion has a long lef ail. The kurosis of he normal disribuion is 3. If he kurosis exceeds 3, he disribuion is peaked (lepokuric) relaive o he normal; if he kurosis is less han 3, he disribuion is fla (playkuric) relaive o he normal. Tesing normaliy, Jarque Bera es is used which has null hypohesis of a normal disribuion and i is disribued as wih degrees of freedom. Table 1. Descripive Saisics

7 78 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey RSOFIX RPX RBUX RWIG RXU Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy..... Sum Sum Sq. Dev Observaions All series have negaive skewness and high posiive kurosis. These values signify he siuaion ha he disribuions of he series have a long lef ail and lepokuric. Jarque-Bera (JB) saisics rejec he null hypohesis of normal disribuion a he 1% level of significance for all five variables. In addiion o invesigaions abou he daa saionariy, he level of series are also defined. Augmened Dickey-Fuller (ADF) saisics clearly rejec he hypohesis of a Uni Roo a he 1% level of significance for all five counries sock markes indices reurns. Table summarizes he ADF es resuls. Table. ADF Tes Resuls 3. Mehodology Wihou Trend Wih Trend Variable ADF sa p ADF sa P RSOFIX *** ***. RPX *** ***. RBUX *** ***. RWIG *** ***. RXU *** ***. Noe: *** denoes significan a he 1% level Volailiy is an imporan concep for finance mosly in porfolio opimizaion, risk managemen and asse pricing. Since financial daa include lepokurosis, volailiy clusering, long memory, volailiy smile and leverage effecs, hey are insufficien

8 E. Ugurlu, E. Thalassinos, Y. Muraoglu o explain a number of imporan feaures common o much financial daa by linear models. Tha is, because he assumpion of homoscedasiciy is no appropriae when using financial daa (Floros 8:35) In order o model volailiy, Engle (198) developed Auoregressive Condiional Heeroscedasic (ARCH) model which is furher exended by Bollerslev (1986) o Generalized Auoregressive Condiional Heeroscedasic (GARCH) model. ARCH Model ARCH models are based on he variance of he error erm a ime depends on he realized values of he squared error erms in previous ime periods. The model is specified as: y () u u ~ N, q ju i (3) 1 This model is referred o as ARCH(q), where q refers o he order of he lagged squared reurns included in he model. If we use ARCH(1) model i becomes (4) 1u 1 Since is a condiional variance, is value mus always be sricly posiive; a negaive variance a any poin in ime would be meaningless. To ensure ha he condiional variance is sricly posiive coefficien in he equaion mus be and. If ha requiremen were no saisfied, realizaions of some of could be negaive. GARCH Model Bollerslev (1986) and Taylor (1986) proposed he GARCH(p,q) random process. The process allows he condiional variance of variable o be dependen upon previous lags; firs lag of he squared residual from he mean equaion and presen news abou he volailiy from he previous period which is as follows: q i1 p i i i i1 iu (5) All parameers in variance equaion mus be posiive and is expeced o be less han one bu i is close o 1. If he sum of he coefficiens equals o 1 i is called an Inegraed GARCH (IGARCH) process. GJR-GARCH 79

9 8 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey Glosen, Jagananhan and Runkle (1993) developed he GARCH model which allows he condiional variance has a differen response o pas negaive and posiive innovaions. where d 1 q i1 i 1 1 p u u d (6) i i i1 is a dummy variable ha is: 1 if u if u 1 1,, bad news good news In he model, effec of good news shows heir impac by, while bad news show heir impac by. In addiion if he coefficiens and he news impac is asymmeric and leverage effec exis respecively. The meaning of leverage effec is bad news increase volailiy. In order o saisfy non-negaiviy condiion, coefficiens would be >,, and. Since i, provided ha i i j i j, he model is accepable (Brooks, 8:45). Exponenial GARCH Exponenial GARCH (EGARCH) proposed by Nelson (1991) includes a form of leverage effecs in is equaion. In he EGARCH model, he specificaion for he condiional covariance is given by he following form: q p r u i u k log j log j i k (7) j1 i1 In he equaion, k represens leverage effecs which accouns for he asymmery of he model. While he basic GARCH model requires he resricions, he EGARCH model allows unresriced esimaion of he variance (Thomas and Michell 5:16). If k, i indicaes presence of leverage effecs and if k, he impac is asymmeric. The meaning of leverage effecs bad news increase volailiy. Table 3 summarizes parameers which mus be saisically significan for he analysis which is menioned above. i k1 Table 3 : Significance Condiions of Parameers in Models ARCH k 1u 1 1 1u 1 1h 1 1u 1 1u 1d 1 1h 1 GARCH 1 GJR- GARCH 1 i i

10 E. Ugurlu, E. Thalassinos, Y. Muraoglu 81 E- GARCH log log 4. Empirical Resuls The dependen variables are reurns in all series. We have ploed he colerogram of he series and found ou ha ha here is no ACF or PACF value ou of he band. Therefore all variables are regressed on consan erm. Before ARCH/GARCH model is used, we need o es wheher models includes ARCH effecs. This es is very imporan in ime series analysis o assure ha he model ARCH is appropriae for daa ha will be he case in he analysis. The es is one of a join null hypohesis ha all q lags of he squared residuals have coefficien values ha are no significanly differen from zero. Firs sep is esimaing he residual from he model hen ake a square of esimaed residuals and regress hem on q own lags o es ARCH of order:.. u u (8) where is an error erm. From he regression, is obained o calculae es saisics. The es saisics is defined as N (number of observaion) x. If he value of he es saisic is greaer han he criical value derived from he disribuion, he null hypohesis is rejeced. We es all models for he ARCH effec by ARCH-LM Tes. Table shows ARCH-LM es resuls. Table 4. ARCH Tes Resuls Dependen Variable of Model ARCH(1)LM Sa P RSOFIX ***. RPX 49,797***. RBUX ***. RWIG 8.658***. RXU ***. Noe: *** denoes significan a he 5% level

11 8 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey Table 4 shows ha all models have ARCH effec on heir residuals. Therefore, we can model residual erms by GARCH models. Alhough ARCH ( and GARCH( and coefficiens are saisically significan in all four GARCH models for reurns of SOFIX leverage effec and are no saisically significan (Table 1 in Appendix). For GARCH(1,1), GJR-GARCH(1,1), EGARCH(1,1) models, all coefficiens are posiive. However, is no less han one ha means he GARCH and GJR-GARCH models do no hold for he reurns of SOFIX. Taking in o consideraion res of he counries (Appendix: Table, Table and Table 4 and Table 5), all coefficiens are saisically significan and posiive in GARCH and GJR-GARCH models bu we do no need for EGARCH model his consrains. We conclude ha srong GARCH and GJR-GARCH effecs are apparen for reurns of PX and BUX, WIG and XU and EGARCH effecs he reurns of five sock markes. Inerpreing he resuls of models, he sum of coefficien of and less han one and volailiy shocks are quie persisen. The magniude of he coefficien is especially high for RWIG index among all oher indices indicaing a long memory in he variance. Moreover, lagged condiional variance is significanly posiive and less han one indicaing ha he impac of old news on volailiy is significan. Furhermore, he esimae of is smaller han he esimae of in boh cases ha is o show negaive shocks do no have a larger effec on condiional volailiy han posiive shocks of he same magniude. In GJR-GARCH model, he news impac is asymmeric on he oher words bad news increase volailiy. In he E- GARCH models, negaive and significan leverage effec parameer shows he exisence of he leverage effec in reurns. I shows ha he sock reurns are negaively correlaed wih changes in volailiy signify ha volailiy ends o rise following bad news and fall following good news. 5. Conclusion The emerging economies are very imporan for growh of world economies. Sock markes are favorable indicaor for economies. Alhough financial daa such as sock markes are invesigaed in researches by economeric models, hey have some feaures such as lepokurosis, leverage effecs, volailiy clusering (or pooling), volailiy smile and long memory which canno be modeled by linear approaches. The sudy presened in his paper invesigaes he five emerging economies four of which are members of he European Union and he remaining one is Turkey. We have employed hree GARCH ype model; GARCH, GJR-GARCH and E-GARCH o specify volailiy processes in reurns of heir sock markes namely SOFIX

12 E. Ugurlu, E. Thalassinos, Y. Muraoglu (Bulgaria), BUX (Czech Republic), PX (Hungary), WIG (Poland) and XU1 (Turkey) for period. The resuls have shown ha srong GARCH effecs are exis all markes excep Bulgarian marke SOFIX, herefore i is offered o subsequen researches o invesigae differen ordered GARCH models for Bulgaria. For oher four markes, we have concluded ha volailiy shocks are quie persisen and he impac of old news on volailiy is significan. Among all oher markes which are examined, Polish sock marke has he longes memory on variance. Addiionally, he resuls have indicaed ha bad news increase volailiy and leverage effec in reurns exis in he markes. Fuure researches should examine he performance of mulivariae ime series models when using daily reurns of inernaional emerging markes. References Bekaer G, Harvey C. R. (1997) Emerging Equiy Marke Volailiy, Journal of Financial Economics 43: Bekaer G. and Harvey C. R.(1995) Time-Varying World Marke Inegraion. Journal of Finance 5: Bollerslev, T., (1986) Generalized Auoregressive Condiional Heeroskedasiciy. Journal of Economerics, 1986, vol. 31, Issue 3, pages Brooks C.,(8) Inroducory Economerics for Finance: Second Ediion Cambridge Universiy Press Dockery, E. and Vergari, F. (1997), Tesing he Random Walk Hypohesis: Evidence for he Budapes Sock Exchange. Applied Economics Leers, 4, Emerson, R., Hall, S. G. and Zelweska-Miura, A. (1997) Evolving Marke Efficiency wih an Applicaion o Some Bulgarian Shares, Economics of Planning, Volume 3, 75-9 Engle, R.F. (198) Auoregressive Condiional Heeroskedasiciy wih Esimaes of The Variance of UK Inflaion, Economerica 5, Filer, R.K. and Hanousek, J. (1996) The Exen of Efficiency in Cenral European Equiy Markes. CERGE-EI Working Paper Series, No. 14, Prague, November Floros C. (8) Modelling Volailiy Using Garch Models: Evidence from Egyp and Israel Middle Easern Finance and Economics, (), Glosen, L.R., Jagannahan, R. And Runkle, D. (1993) On The Relaion Beween he Expeced Values and he Volailiy of The Nominal Excess Reurn on Socks., Journal of Finance 48, Harouounıan M. K. and Price S. (1) Volailiy in he Transiion Markes of Cenral Europe, Applied Financial Economics, 11, Hájek J. (7), Czech Capial Marke Weak-Form Efficiency, Seleced Issues, Prague Economic Papers, 4,

13 84 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey Harvey C. R. (1995) Predicable Risk and Reurns in Emerging Markes,". Review of Financial Sudies, Oxford Universiy Press For Sociey For Financial Sudies, Vol. 8(3), Thomas S. and Michell H. (5) GARCH Modeling of High-Frequency Volailiy in Ausralia s Naional Elecriciy Marke, Discussion Paper. Melbourne Cenre for Financial Sudies, Minik S., Paolella M.S. Rachev S.T () Saionariy of Sable Power-GARCH Processes, Journal of Economerics, 16, Nelson, D. B. (1991) Condiional Heeroscedasiciy in Asse Reurns: A New Approach Economerica, 59(), Nive J. F. (1997) Sock Markes in Transiion: The Warsaw Experimen Economics of Transiion, Volume 5 (I), Rockinger, M., Urga, G., (1999) Time Varying Parameers Model o Tes for Predicabiliy and Inegraion in Sock Markes of Transiion Economies. Cahier De Recherche Du Groupe Hec 635/1998. Samias, A., Kenourgios D. and Palalidis N. (7) Inegraion and Behavioural Paern in Emerging Sock Markes Annual Meeing of he European Financial Managemen Associaion 7, Vienna. Scheicher, M., (1). The Comovemens of Sock Markes in Hungary, Poland and The Czech Republıc Inernaional Journal of Finance And Economics In. J. Fin. Econ. 6: 7 39 Shields K. (1997) Sock Reurn Volailiy on Emerging Easern European Markes, The Mancheser School Supplemen: Svejnar J. () Transiion Economies: Performance and Challenges, Journal of Economic Perspecives Volume 16(1), Winer, 3 8 Syriopoulos, T., (7) Dynamic Linkages Beween Emerging European and Developed Sock Markes: Has The Emu Any Impac?, Inernaional Review of Financial Analysis 16, Syriopoulos T. and Roumpis, E. (9) Dynamic Correlaions and Volailiy Effecs in The Balkan Equiy Markes Journal of Inernaional Financial Markes, Insiuions and Money, 19(4), Taylor, S. J. (1986), Modelling Financial Time Series, John Wiley & Sons, Chicheser. Triandafil M. C. and Brezeanu P. (8) Corporae Finance Mechanisms Wihin Eas European Emerging Counries: An Analyical Approach on IT Commercial Companies, 4h Inernaional Conference of ASECU, Developmen Cooperaion and Compeiiveness, The Buchares Academy of Economic Sudies, -4 May 8, Buchares, Romania Worhingon, A.C. and Higgs, H. (3), Weak-form Marke Efficiency in European Emerging and Developed Sock Markes. Queensland Universiy of Technology Discussion Paper, No. 159, Sepember Yu, J., (). Forecasing Volailiy in he New Zealand Sock Marke, Applied Financial Economics,, 1, 193-

14 E. Ugurlu, E. Thalassinos, Y. Muraoglu Zikeš, F. (3), The Predicabiliy of Asse Reurns: An Empirical Analysis of Cenral-European Sock Markes (Maser Thesis). Charles Universiy of Prague (IES). 85 APPENDIX Table 1: Esimaed Coefficiens of GARCH Models for RSOFIX GARCH(1,1) GJR-GARCH E GARCH Coefficien p Coefficien p Coefficien p Mean Equaion Variaion Equaion AIC SIC DW-sa ARCH *** *** *** LM es Obs. 836 Table : Esimaed Coefficiens of GARCH Models for RPX GARCH(1,1) GJR-GARCH E GARCH Value p Value p Value p Mean Equaion Variaion Equaion AIC SIC

15 86 Modeling Volailiy in he Sock Markes using GARCH Models: European Emerging Economies and Turkey DW-sa ARCH-LM es.3666 Obs. 899 Table 3: Esimaed Coefficiens of GARCH Models for RBUX GARCH(1,1) GJR-GARCH E GARCH Value p Value p Value p Mean Equaion Variaion Equaion AIC SIC DW-sa ARCH-LM es Obs. 89 Table 4: Esimaed Coefficiens of GARCH Models for RWIG GARCH(1,1) GJR-GARCH E GARCH Value p Value p Value p Mean Equaion Variaion Equaion

16 E. Ugurlu, E. Thalassinos, Y. Muraoglu 87 AIC SIC DW-sa ARCH-LM **.3454 es Obs. 898 Table 5: Esimaed Coefficiens of GARCH Models for RXU GARCH(1,1) GJR-GARCH E GARCH Value p Value p Value p Mean Equaion Variaion Equaion AIC SIC DW-sa ARCH-LM es Obs. 896