An Empirical Analysis of the Exchange Rate Volatility: Application of Brazilian and Australian Exchange Markets
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1 An Empirical Analysis of he Exchange Rae Volailiy: Applicaion of Brazilian and Ausralian Exchange Markes Wann-Jyi Horng Deparmen of Hospial and Healh Care Adminisraion, Chia Nan Universiy of Pharmacy & Science, Tainan, Taiwan. Ju-Lan Tsai Graduae Insiue of Managemen Sciences, Accouning Secion, Tamkang Universiy, Taipei, Taiwan. ABSTRACT This aricle uilizes he Suden- disribuion o consruc an appropriae model of Brazilian and Ausralian exchange raes, and furher analyzes he associaions beween hese wo exchange rae markes. The empirical resuls demonsrae bivariae asymmeric IGARCH (1, 1) wih a dynamic condiional correlaion (hereafer DCC) model can be applied o esimae he muual effecs of he Brazilian and Ausralian exchange rae markes. The resuls also indicae ha here exiss a posiive correlaion beween Brazilian and Ausralian exchange rae markes; more specifically, he wo volailiies of Brazilian and Ausralian exchange rae reurns are synchronic influence, in which he average esimaed value of he DCC coefficien of Brazilian and Ausralian exchange rae reurn volailiies is In his conex, he good and bad news of Ausralian exchange rae volailiy will affec he variaion risk of he Brazilian exchange rae. Somewha similarly, he good and bad news of Brazilian exchange rae volailiy affec he variaion risk of he Ausralian exchange rae. Moreover, Brazilian and Ausralian exchange rae markes do have he asymmerical effec in he selecing period. Keywords: Exchange rae marke, DCC, bivariae IGARCH model, Suden- disribuion, asymmerical effec. 1
2 I. INTRODUCTION Wih he rend of he financial liberalizaion and inernaionalizaion faciliaes he augmen in inernaional capial flows, he heighened aenion o reurn on invesmen, and he ascensive research of exchange rae marke across counries, i is worhwhile o explore he ineresing relaion beween Brazilian and Ausralian exchange marke. Brazil, he larges Lain American economy and one of he group of four emerging economies named BRIC naions ogeher wih Russia, India and China, has seen is economy soar in recen years, wih growh far oupacing he US and wesern Europe. The Cenre for Economics and Business Research reveals ha Brazil, an island economy, has jus passed he UK o become he sixh-larges economy in he world and he enh larges a marke exchange raes. However, Ausralia being famous for he subsanial social welfare sysem and social and poliical sabiliy is hough o arac foreign invesors. In addiion, Brazil and Ausralia boh are he wo powerhouses bu diverse counries in he Souhern Hemisphere, and hey are now working a leaders' level, hrough he G0, which has been considered o be he premier forum for inernaional discussing and coordinaing economic policies. Brazil is also he larges Ausralian rade parner in Lain America. From such exciing business relaionship being expanded, closer economic, rade and culural ies are developing beween Ausralia and Brazil, herefore, he relaion beween Brazil and Ausralia exchange rae markes is really worh furher discussing. There are many mehodologies being applied in he field of financial marke volailiy. For example, evolved from auoregressive moving average (ARMA) model demonsraed by Box-Jenkins, Engle (198) declared he auoregressive condiionally heeroskedasiciy (ARCH) model while Bollerslev (1986) proposed he generalized auoregressive condiionally heeroskedasiciy (GARCH) model. Alhough hese models menioned above migh capure he financial propery of he condiional variance no being a fixed parameer, Nelson (1990) hen discovered ha negaive impac of he markes will have differen influences on he fuure price volailiy. This phenomenon is resuled from he main assumpion of he GARCH model, i assumes he curren condiional variance depends on he condiional variance and squared error erm of preceding period; hence, he condiion variance varies wih only he size of error erm raher he sing of error erm. To modify his drawback, Nelson (1991) propounded an asymmerical model wha we call exponenial GARCH model, and Glosen, Jaganahan and Runkle (1993) adduced he hreshold GARCH model. Wih respec o he research of asymmeric problems, one may also refer o Poon and Fung (000), French, Schwer and Sambaugh (1987), Campell and Henschel (199), Koumos and Booh (1995), and Koumos (1996). Correspondingly, a growing body of research invesigaes he reurn volailiy mehod, mos noably he mulivariae GARCH model, such as Yang (005), Yang and Doong (004), Granger, Hung and Yang (00), and Bollerslev (1990) for he applicaion of bivariae GARCH model. This aricle uilizes RATS and EVIEWS programs o invesigae he impacs of he Ausralian exchange rae volailiy, o wha exen, and in wha ways, on he Brazilian exchange rae marke; also, he muual influences. Meanwhile, we deliberae Suden- disribuion and he maximum likelihood algorihm mehod of BHHH (Bernd e. al., 1974) o esimae he unknown parameers. This aricle has been srucured as follows: firs descibes he daa characerisics of Brazilian and Ausralian exchange rae and he volailiy of hese exchange raes. Then, inroduces he asymmeric es of bivariae DCC-GARCH model underlying his sudy are implemened. Nex, he proposed model
3 of bivariae DCC-GARCH and he empirical resuls are presened, and finally some concluding remarks are discussed. II. DATA CHARACTERISTICS A. Basic Saisics and Trend Chars The sample is comprised of Brazilian and Ausralian exchange rae prices, drawn from DaaSream, and sample period exends from January, 004 o December, 010. The Brazilian exchange rae price measures as he Brazilian Real dollar o US dollar in New York marke, while he Ausralian exchange rae price as he Ausralian dollar o US dollar in he New York marke. To capure he more exac iner-influence beween he Brazilian and Ausralian exchange rae markes, we excluded he daa ha are non-common rading day, holidays; herefore, he final sample of 1,86 observaions provide us o furher explore. The Brazilian exchange rae marke reurn ( ) for daily closing price akes naural logarihm difference and muliple by 100, his namely: = 100 (log( BER / BER 1 )) (1) where BER denoes he closing price of Brazilian exchange rae in year. Also, he Ausralian exchange rae marke reurn ( RAUER ) for daily closing price akes naural logarihm difference and muliple by 100, his namely: RAUER = 100 (log( AUER / AUER 1)) () where AUER denoes he closing price of Ausralian exchange rae in year. From Fig. 1, he volailiy of Brazilian and Ausralian exchange rae reurn skeched ou he clusering phenomenon, we hus may exrapolae ha he Brazilian exchange rae marke and Ausralian sock marke have cerain relevance, bu sill need more conscienious analysis. Besides, according o he basic saisics of hese sequences saed in Table 1, he Jarque-Bera es of he wo sequences boh rejec he null hypohesis of normal disribuion. Therefore, i is more appropriae o use he heavy ails disribuion o evaluae he proposed model. 3
4 RAUER Figure 1 Tend chars of Brazilian and Ausralian exchange rae volailiy raes Table 1 Basic saisics of he research daa Saisics BER AUER RAUER Mean S-D Skewed Kurosis J-B (p-value) (0.000) *** (0.000) (0.000) *** (0.000) Sample Noe: (1) J-B denoes he normal disribuion es of Jarque-Bera. ()S-D is denoed he sandard deviaion. (3) *** denoes significance a level α=1%. B. Uni Roo Tes and Co-Inegraion Tes This paper furher conducs he uni roo ess of ADF (Dickey and Fuller, 1979, 1981) and KSS (Kapeanios e al., 003) o deermine he sabiliy of he ime series daa. Table summarizes he ADF and KSS ess resuls, i shows ha he volailiies of he Brazilian and Ausralian exchange rae do no have he uni roo characerisic, i implies hese markes boh are saionary sequences a he significance level ofα = 1%. Table Uni roo es of ADF and KSS mehods ADF KSS Iem RAUER RAUER Saisic *** -.4 *** *** *** (α =1%); -.80(α =1%); Criical -3.41(α =5%); -.0(α =5%); value -3.18(α =10%) -1.90(α =10%) Noe: *** denoes significance a he 1% level. By he coinegraion es of Johansen (1991), as illusraed in Table 3, we find ha λ max is no significan under he level α =5%. This demonsraes ha he volailiies of 4
5 Brazilian and Ausralian exchange rae reurn do no have co-inegraion wih each oher. Therefore, we do no consider he model of error correcion. Table 3 Johansen co-inegraion es (var lag=1) Null H 0 λ max Criical value None A mos Noe: (1) The lag of VAR is seleced by he AIC rule (Akaike, 1973). () The criical value is given under he 5% level. C. ARCH Effec Tes Based on he equaion (3) and (4) as below, we uses he mehods of LM es (Engle, 198) and F es (Tsay, 004) o es wheher he volailiies of exchange rae reurn have he condiionally heeroskedasiciy phenomenon. In Table 4, he resuls of he ARCH effec es exhibi ha hese wo markes exis he condiionally heeroskedasiciy phenomenon. This resul suggess ha we can employ he GARCH model o mach and analyze i. The deail is omied here. Table 4 ARCH effec es Iem RAUER Saisics (p-value) Saisics (p-value) Engle LM es *** (0.0000) *** (0.0000) Tsay F es *** (0.0000) *** (0.0000) Noe: *** denoes significance a level α=1%. III. ASYMMETRIC TEST OF THE BIVARIATE DCC - GARCH MODEL Based on aforemenioned, his paper consrucs a bivariae asymmeric DCC- IGARCH (1, 1) model, he deails are omied. Wih respec o he mehods of asymmeric es (Engle and Ng, 1993), posiive size bias es and join es are implemened. Table 5 sysemaically displays he resul for he Brazilian exchange rae marke as: (1) he posiive size bias es reveals significan (α =1%); () he join es reveals significan (α =1%). In addiion, resuls for he Ausralian exchange rae marke show as: (1) he posiive size bias es does no reveal significan (α =10%); () he join es reveals significan (α =1%). In a nushell, he evidence in asymmeric es suggess ha he volailiies of exchange rae reurn in Brazilian and Ausralian exchange markes do have he asymmery effecs. Table 5 Asymmeric es of he bivariae IGARCH Asymmeric es Posiive size bias es Join es F saisic (p-value) (0.0087) (0.0000) RAUER F saisic (p-value) (0.39) (0.0049) Noes: p-value <α denoes significance. (α =5%) 5
6 IV. PROPOSED MODEL Based on he resuls of he asymmeric es, a bivariae asymmeric DCC- IGARCH (1, 1) is proposed in his secion, he model is formulaed as follows: = φ 10 + φ 1 + φ1 + φ13rauer 1 + φ14rauer + a (3) 1, = φ 10 + φ 1 + φ1 + φ13rauer 1 + φ14rauer + a (4) 1, ' a = a, a ) ~ T (0,( ν ) H / ν ) (5) ( 1,, v α + α a + β h ) + (1 w )( α + α a + β h ) (6) (, = w , 1, , 1, 1 h h q α + α a + β h ) + (1 u )( α + α a + β h ) (7) (, = u 1 0, 1, 1 1 0, 1, 1 = γ 0 + γ 1ρ 1 + γ a1, 1a, 1 / h, 1h, 1 ρ = exp( q ) /(exp( q ) + 1) (8) = h h (9) h 1, ρ,, u w 1 = 0 1 = 0 if, if if, if a a 1, 1, a a,, 0, (10) > 0 0, () > 0 where Tv ( 0,( v ) H / v) denoes he bivariae Suden- disribuion, is mean is equal o 0 and is covariance marix is equal o ( v ) H / v, and v is he degree of freedom. Here a1, > 0 and a, > 0 denoes good new, and a1, 0 and a, 0 denoes bad news. The bivariae DCC- IGARCH (1, 1) model can also refer o he papers of Engle (00) and Tse and Tsui (001). V. EMPIRICAL RESULTS The empirical resuls in Table 6 reveal ha he bivariae asymmeric DCC- IGARCH (1, 1) model is appropriae o depic he relaion beween he Brazilian and Ausralian exchange rae reurn volailiy. We observe he esimaed coefficien parameers o be significan or no wih a p-value. In sample period, he curren volailiy of Brazilian exchange rae depends on he exchange rae reurn volailiy in only preceding one year ( φ =0.0766), bu do no been affeced by Ausralian exchange rae reurn volailiy. However, he volailiy of Ausralian exchange rae no only depends on he Brazilian exchange rae reurn in preceding year ( ϕ =0.833), bu only one year; i also been influenced by he volailiy of he Ausralia s exchange rae in preceding wo years ( ϕ 13 = andϕ 14 =0.0464). Alernaively, he average esimaion value ( ρˆ =0.37) of he DCC coefficien of he Brazilian and Ausralian exchange rae reurn volailiy is significan, his evidence also indicaes ha he volailiy of he Brazilian exchange rae reurn posiively influence Ausralian exchange rae reurn volailiy. The muual synchronizaion can be observed from he resuls in Table 6, when variaion risk of he Brazilian exchange rae volailiy increases, he invesmen risk of he Ausralian exchange rae volailiy accompanying 6
7 increase; likewise, when variaion risk of he Brazilian exchange rae volailiy naurally decline, he invesmen risk of he Ausralian exchange rae volailiy reduce as well. In addiion, esimaed value of he degree of freedom for he Suden- disribuion is , and i is significan under he significance level of α = 1%. I is well known ha his research daa has he heavy ail disribuion. Table 6 Parameer Esimaion of The DCC and he Bivariae Asymmeric IGARCH(1, 1) Model Parameer φ 10 φ φ φ 1 13 φ 14 Coefficien (p-value) (0.0000) ( ) (0.50) (0.5698) (0.3916) Parameer ϕ 10 ϕ ϕ ϕ 1 13 ϕ 14 Coefficien (p-value) (0.00) (0.0000) (0.447) (0.0044) (0.0616) Parameer ν α 10 α β α 10 Coefficien (p-value) (0.0000) (0.490) (0.0000) (0.0000) (0.0098) Parameer α β α 0 α β Coefficien (p-value) (0.0000) (0.0000) (0.917) (0.0000) (0.0000) Parameer α 0 α β γ 0 γ 1 Coefficien (p-value) (0.3361) (0.0000) (0.0000) (0.0764) (0.545) Parameer γ ρ min ρ max ρ Coefficien (p-value) (0.35) ( ) Noe: (1) p-value<αdenoes significance. () α = 1 %, α = 5%, α = 10%, α is he significance level. (3) minρ denoes he minimum value of ρ and max ρ denoes he maximum value of ρ. Moreover, he condiional variances of Brazilian and Ausralian exchange rae volailiy boh affec he reurn volailiies of Brazilian and Ausralian exchange rae, respecively. In aspecs of he condiional variance equaion, he resuls of α + β = 1, α + β = 1, α + β = 1 and α + β = 1 conform he condiion supposiion of he IGARCH model. And, he volailiy of Brazilian exchange rae volailiy will also affec he variaion risk of Ausralian exchange rae marke; conrariwise, he volailiy of Ausralian exchange rae volailiy will also affec he variaion risk of Brazilian exchange rae marke. The good and bad news of Ausralian exchange rae volailiy will affec he variaion risk of he Brazilian exchange rae. Somewha similarly, he good and bad news of Brazilian exchange rae volailiy affec he variaion risk of he Ausralian exchange rae. Addiionally, he empirical resul shows ha he likelihood raio es again confirms ha he bivariae asymmeric IGARCH (1, 1) model is qualified o characerize he relaionship beween Brazilian and Ausralian exchange rae volailiies. 7
8 To es he inappropriaeness of he bivariae DCC- IGARCH (1, 1), we conduced he Ljung- Box (1978) o examine auocorrelaion of he sandard residual error. This model does no provide any auocorrelaion evidence of he sandard residual error, he deails are omied. Therefore, he DCC and he bivariae asymmeric- IGARCH (1, 1) model are appropriae. VI. CONCLUSIONS The empirical diagnosis of our principal research quesion is o examine he associaion beween Brazilian and Ausralian exchange rae volailiies. The reciprociy beween Brazilian and Ausralian exchange rae marke can be consruced in he Suden- disribuion and he bivariae asymmeric DCC-IGARCH (1, 1) model. To ensure he appropriaeness, his model also overcomes a series ess such as sandard residual error and ARCH effec es, showing bivariae DCC- IGARCH (1, 1) model is appropriae o evaluae Brazilian and Ausralian exchange marke reurn volailiies. From he empirical resul, he dynamic condiional correlaion coefficien average esimaion value ( ρˆ =0.37) of he Brazilian and Ausralian exchange rae markes is posiive. This finding poins ha he volailiies of hese wo exchange raes affec each oher. Specifically, here exiss synchronizaion beween Brazilian and Ausralian exchange marke. The empirical resul also shows ha he volailiy of Brazilian exchange rae marke is affeced by he volailiy of Ausralian exchange rae, and he volailiy of Ausralian exchange rae marke is affeced by he volailiy of Brazilian exchange rae, implying ha he volailiies do have asymmerical in he Brazilian and Ausralian exchange rae markes. The empirical resuls also show ha he good and bad news of he Ausralian exchange rae volailiy will also affec he variaion risk of he Ausralian exchange rae marke, and he good and bad news of he Brazilian exchange rae volailiy will also affec he variaion risk of he Brazilian exchange rae marke. However, he proposed model is differen from he model of he bivariae GARCH wih a consan condiional correlaion (hereafer CCC). Based on he paper of Engle (00), he bivariae DCC GARCH model has a beer explanaory abiliy compared o he radiional bivariae CCC-GARCH model. REFERENCES Akaike H. Informaion heory and an exension of he maximum likelihood principle, In nd. Inernaional Symposium on Informaion Theory, edied by B. N. Perov and F. C. Budapes: Akademiai Kiado, 1973: Bernd E.K., Hall B.H., Hall R.E., and Hausman J.A. Esimaion and inference in nonlinear srucural models, Annals of Economic and Social Measuremen 4, 1974: Bollerslev T. generalized auoregressive condiional heroscedasiciy, Journal of Economerics 31, 1986: Bollerslev T. Modeling he coherence in shor-run nominal exchange raes: a mulivariae generalized ARCH model, Review of Economics and Saisics 7, 1990: Campell J.Y., and Henschel L., No news is good news: An asymmeric model of changing volailiy in sock reurns Journal of Financial Economic 31, 199:
9 Dickey D.A. and Fuller W.A. Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica 49, 1981: Dickey D.A., and Fuller W.A., Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion 74, 1979: Engle R.F. Auoregressive condiional heeroskedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica 50, 198: Engle R.F., Dynamic condiional correlaion- a simple class of mulivariae GARCH models, Journal of Business and Economic Saisics 0, 00: Engle R.F., and Ng V.K. Measuring and esing he impac of news on volailiy, Journal of Finance, vol. 48(5), 1993: French K.R., Schwer G.W., and Sambaugh R.E. Expeced Sock Reurns and Volailiy, Journal of Financial Economics 19, 1987:3-9. Glosen L.R., Jagannahan R., and Runkle D.E. On he Relaion beween he Expeced Value and he Volailiy on he Nominal Excess Reurns on Socks, Journal of Finance 48, 1993: Granger C.W., Hung J.B., and Yang C.W. A bivariae causaliy beween sock prices and exchange raes: Evidence from recen Asian Flu, The Quarerly Review of Economics and Finance 40, 000: Johansen S. Esimaion and hypohesis esing of coinegraion vecor in Gaussian vecor auoregressive models, Economerica 59, 1991: Kapeanios G., Shin Y., and Snell A. Tesing for a uni roo in he nonlinear STAR framework, Journal of Economerics, no., 003: Kearney C. The causes of volailiy in a small, inernaionally inegraed sock marke: Ireland, July June 1994, Journal of Financial Research, 1998: Koumos G. Modeling he Dynamic Inerdependence of Major European Sock Markes, Journal of Business Finance and Accouning 3, 1996: Koumos G. and Booh G.G. Asymmeric volailiy ransmission in inernaional sock markes, Journal of Inernaional Money and Finance 14, 1995: Ljung G.M., and Box G.E.P. On a measure of lack of fi in ime series models, Biomerika 65, 1978: Nelson D.B. Saionariy and persisence in he GARCH (1,1) model, Economeric Theory 6, 1990: Nelson D.B. Condiional heeroscedasiciy in asse reurns: A new Approach, Economerica 59, 1991: Nelson D.B. Saionariy and persisence in he GARCH (1,1) model, Economeric Theory 6, 1990: Nieh C.C., and Lee C.F. Dynamic relaionship beween sock prices and exchange raes for G-7 counries, The Quarerly of Economics and Finance 41, 001: Poon W.P.H., and Fung H.G. Red chip or H shares: Which China-backed securiies process informaion he fases? Journal of Mulinaional Financial Managemen 10, 000:
10 Tsay, R.S. Analysis of Financial Time Series. New York: John Wiley & Sons, Inc., 004. Tse Y.K., and Alber K.C. Tsui, A mulivariae GARCH model wih ime-varying correlaions, Journal of Business and Economic Saisics 0, no. 3, 00: Yang S.Y. A DCC analysis of inernaional sock marke correlaions: The role of Japan on he Asian Four Tigers. Applied Financial Economics Leers 1, no., 005: Yang S.Y., and Doong S.C., Price and volailiy spillovers beween sock prices and exchange raes: empirical evidence from he G-7 counries, Inernaional Journal of Business and Economics 3, no., 004:
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