Interdependence and volatility spillover among the euro, pound sterling and Swiss franc. Yoshihiro Kitamura Working Paper No.

Transcription

1 Inerdependence and volailiy spillover among he euro, pound serling and Swiss franc Yoshihiro Kiamura Working Paper No.226 Ocober, 2007

2 Inerdependence and volailiy spillover among he euro, pound serling and Swiss franc Yoshihiro Kiamura Faculy of Economics, Toyama Universiy, 3190 Gofuku, Toyama , JAPAN Absrac To examine inerdependence and volailiy spillover among he euro, pound serling and Swiss franc, we employ he dynamic condiional correlaion model of mulivariae generalized auoregressive condiional heeroskedasiciy. Our main findings are: 1) a shock in he reurn volailiy of he euro spills over ino pound serling and he Swiss franc; and 2) hese markes are highly inegraed wih he euro, he degree of inerdependence being sae dependen. Euro news has a simulaneous impac on pound serling and he Swiss franc, co-movemens of hese currencies and he euro becoming much higher in proporion o news arrival of he euro. JEL classificaion: F31; F33; G15 Keywords: DCC MV-GARCH; High frequency daa; Informaion; Inerdependence; Volailiy spillover o: kiamu@gmail.com

3 1. Inroducion This sudy examines he causaliy in reurn variances and he inerdependence of he euro, pound serling and Swiss franc foreign exchange spo (FX) markes. The erm inerdependence corresponds o any coninued marke correlaion a high levels (see, for example, Chiang e al., 2007). While he dynamics of hese hree currencies, such as he inerdependence and he causaliy among hem, is well observed and known by no only raders bu also academic researchers, here is sill room for research quesions on heir inraday dynamics: Is he degree of inerdependence among hem sae dependen or no? Wha inraday reacion do pound serling and Swiss franc volailiies show afer a shock in he reurn volailiy of he euro? Of course, here are a number of sudies which focus on hourly and daily dynamics of hese currencies (e.g., Malik, 2005; Nikkinen e al., 2005; Inagaki, 2007). The aim of his sudy is o reinforce he exan lieraure o examine hose dynamics in more deail using a 10-minue high frequency daa se. To undersand he deails of he dynamics of he euro, pound serling and Swiss franc is crucial for implemening hedging sraegies and allocaion decisions among asses evaluaed by hose currencies. This sudy employs he dynamic condiional correlaion (DCC) model of mulivariae generalized auoregressive condiional heeroskedasiciy (MV-GARCH) developed by Engle (2002), and Tse and Tsui (2002) o capure he inraday dynamics of he euro, pound serling and he Swiss franc. The virues of his model are: 1) o esimae fewer parameers han he oher models (e.g., BEKK, inroduced by Engle and Kroner, 1995); and 2) o overcome he issue of posiive definiion of he variance-covariance marix, which frequenly causes problems in he exan models in execuing heir esimaion. Moreover, he DCC MV-GARCH model poses a general assumpion on he correlaion coefficien ha is ime varian. This enables us o examine wha is he underlying driving facor of movemen of a correlaion coefficien: if a correlaion coefficien is ime varian, a which iming does i reach is peak and which facors explain such high level correlaions beween currency reurns? The res of his paper is organized as follows. The nex secion provides 2

4 informaion on our daa se. Secion 3 inroduces he DCC MV-GARCH model ha considers he causaliy in reurns and variances of he euro/pound serling and euro/swiss franc currency pairs, respecively. Secion 4 shows he esimaion resuls of he DCC MV-GARCH model and examines he deails of he dynamics of hose pairs. The las secion concludes our research. 2. The daa The daa se was purchased from elecronic broking sysem (EBS) corporaion. The sample period runs from April 2 o Augus 31, Throughou h is period, America and Europe adoped dayligh saving ime (DST). Therefore, we need no consider a change of inraday seasonaliy in he FX marke, caused by he iming of he adopion of DST by each counry (Io and Hashimoo, 2006). We exclude all daa colleced from Friday 23:30 Greenwich Mean Time (GMT) o Sunday 23:30 GMT from our sample since rading aciviy during hese hours is minimal. The daa se is creaed in periods of one-second ime slices comprising a Price Record and a Deal Record. The Price Record liss he EBS bes bid/ask prices a he end of a ime slice. The Deal Record liss he highes paid and lowes given deal prices during he period of he ime slice. No informaion abou rading volume or order ype (marke or limi order) is available. Wih a Deal Record, we consruc a rade indicaor ha akes 1 (-1) when a paid (given) rae shows up in he Deal Record. If here is no deal in h e EBS sysem, ha indicaor akes zero. In our sample, neiher he paid nor given raes are recorded a he same second for any of he currencies. We conver he original daa se ino 10-minue inervals. We employ as a price S, he midpoin quoe of he bes bid and ask raes observed lasly in each inerval. A reurn of each currency is defined as R = 100 ln( S/ S 1). By summing up rade indicaors in each inerval, we calculae order flow (buyer iniiaed rades minus seller iniiaed rades). Recen sudies (e.g., Evans and Lyons, 2002) sress he role of order flow which conveys a signal of privae informaion and fundamenals. We calculae he order flow of each currency in each 10-minue inerval for he empirical approach in he nex secion. Table 1. 3

5 Table 1 repors he summary saisics of he firs and he second momens of reurns and order flows of he hree currencies. For he second momen of he reurns, he Ljung-Box es saisics shows srong evidence of non-linear dependency for all he currencies, leading us o selec he GARCH framework o capure he dynamics of reurn volailiy. I is well documened ha a volailiy of an FX rae reurn shows inraday seasonaliy (e.g., Ballie and Bollerslev, 1990; Io and Hashimoo, 2006). This migh induce us o selec a longer GARCH lag erm because longer lags capure he spikes due o seasonaliy. However, o save he number of esimaed parameers, we remove he seasonaliy of volailiy. Figure 1. Figure 1 shows averaged squared reurns of each currency in each inerval. We observe he inraday U-shape paern of averaged squared reurns, he peaks corresponding o he iming of he opening and closing of he major markes, namely, he London and New York markes. 2 To remove such seasonaliy, we divide he sample reurns by he roo of five inerval moving average of averaged squared reurns. The bold line in Figure 1 is he moving average and ploed circles are averaged squared reurns in each inerval. Since we also observe seasonaliy in he squared order flows, which is quie similar o ha of he squared reurns, we remove he seasonaliy of he order flows using he same mehod adoped for squared reurns. 3. The model 1 This secion uilizes he DCC MV-GARCH model o examine deails of he inraday dynamics in he euro, pound serling and Swiss franc. In he DCC MV-GARCH model, we consider he causaliy in he firs and second momens of he 1 2 The Ljung-Box es saisics for variable y is TT ( + 2) r /( T K), where T is a sample size and T T 2 k = k+ 1 k = 1 y ). r = ( y y)( y y)/ ( y 6 k k = 1 2 When boh Europe and America adop DST, Melvin and Melvin (2003) idenify 5:30-15:30 and 11:30-20:00 GMT as he business hours of Europe and America, respecively. 4

6 reurns of he hree currencies. For his, we adop he Granger causaliy es for he firs and he second momens of he reurns of he euro and currency i (i = Table 2. gbp [pound serling] and chf [he Swiss franc]) prior o esimaion of he DCC MV-GARCH model. The Granger χ 2 es saisics is calculaed wih he Newey and Wes variance-covariance marix. 3 The lag selecion rule of he Granger es is based o n he Akaike (AIC), Schwarz (SC) and Hannan-Quinn (HQ) crieria. Table 2 shows he Granger causaliy from he euro o boh pound serling and he Swiss franc in he firs and he second momens, respecively. Moreover, we also observe he causaliy from pound serling o he euro in he second momen even hough he value of he summed coefficiens of pound serling is relaively small. Firs, he resuls from Table 2 lead us o se he following reurn equaions: R euro, a b R euro euro, 1 0 euro, 1 deuro Xeuro, eeuro, = + R i a b i euro 2 b i2 R i 1 dix i e,,,,, i, e e Φ =, euro, 1 N(0 ) e i, where Φ 1 is an available informaion se a pas im e 1, and i = + + (1),Ω (2) gbp (pound serling), chf (Swiss franc). R i, is currency i s reurn (100 ln( S / S 1), where S is he Unied Saes dollar spo rae quoed agains each currency). X i, is he order flow of currency i. As explained in he previous secion, R and X are seasonally adjused. In he above reurn equaions we consider he one-way causaliy from he euro o currency i, which is consisen wih he resu l in Table 2. Nex, we model he condiional volailiies depiced as follows: h ω α e β β h = + +, (3) euro euro 2, euro euro 1 euro i 1 euro,, 1,, 1 h 2 i ω i αie β i euro2 β,, i, 2 h, i, 1 where hi, is a condiional variance of currency i in period. Table 2 indicaes ha he pas volailiy of he euro has an impac on hose of pound serling and he Swiss franc. Moreover, even if is effec migh be small, here could also be causaliy from 3 14 The lag of he Newey and Wes variance-covariance marix is T /, where T is he sample size. 5

7 pound serling o he euro in he second momens. Therefore, we resric β i, 1 = 0 when i = chf in Eq. (3). Engle (2002), and Tse and Tsui (2002) model he variance-covariance marix Ω as follows: Ω = DΓ D 12 / 12 / h 0 1 ρ euro, i, heuro, 0 =, 12 / 12 / 0 h ρi 1 i,, 0 hi, whe re ρ i, is he correlaion coefficien beween e eu ro, and e i,. Since ρ i, < 1 and heuro,, hi, > 0 hold generally, all he principal minors of marix Ω are above zero. This is a necessary and sufficien condiion for a posiive definie marix of Theorem 1.E.11 in Takayama [ 1985]). follows: Following Tse and Tsui (2002), ime varian ρ i, in Eq. (4) is specified as whereψ i, i, Ω (see ρ = (1 θ θ ) ρ + θ ρ + θψ, (5) 2 ε ε = = /. k = 1 euro, k i, k 1 wih ε i, ei, hi, 2 ( ε )( ε ) k= 1 euro, k k= 1 i, k Wih an assumpion of normaliy in Eq. (2) and from Eq. ( 4), we specify he log likelihood funcion ln L and obain he se of parameers ˆΘ ha maximizes ln L( Θ ) as follows: T 1 1 ln L( Θ ) = ln 2π ln Ω ( Θ ) ( Θ) Ω ( Θ) The adoped rouine o maximize Eq. (6) is he Bernd, Hall, Hall (BHHH) algorihm. A variance-covariance marix of esimaed parameer evaluaed wih he sandwich esimaor (Whie, 1982), which is valid even if he probabiliy densiy in Eq. (2) is misspecified. Therefore, obained esimaors are T T 1 e = 1 = 1 (4) e ( Θ ). (6) and Hausman quasi-maximum likelihood ones which are valid even if he residuals from he model in Eq. (2) are no normally disribued. This enables us o draw he usual saisical inferences from he esimaed parameers. ˆΘ is 6

8 4. The resuls Table 3 repors he esimaion resuls of he DCC MV-GARCH model obained from he maximizaion of Eq. (6) for each pair of currencies (euro/pound serling and euro/swiss franc). Firs, Table 3 shows a srong GARCH effec in he condiional volailiies of all wih he mixure disribuion hypohesis, which suggess ha when we approximae he volailiy shows a GARCH process (Anderson, 1996). Since he Ljung-Box es saisics indicaes a serial correlaion of he squared sandardized residual, we also ha includes firs- and second-order ARCH erms in each case and confirm ha i does no subsanially change our findings below (he resuls are available upon reques). Therefore, we develop he following discussion based on he models in Eqs. (1)-(5). Table 3. he currencies. This finding is consisen wih he exan empirical lieraure and also sochasic process of arrival informaion wih auoregressive process, he reurn esimae a model Secondly, we observe he spillover effec from he euro o boh pound serling and he Swiss franc in he firs and second momens. In he reurn equaion of boh pound serling and he Swiss franc, he parameer b euro, 2, he spillover effec in mean equaion, shows a posiive value and is saisically significan. This indicaes ha here is a no subsiuion effec from he euro o eiher of hese wo currencies. We also observe he spillover effec in he condiional volailiies from he euro o boh pound serling and he Swiss franc. The effecs are calculae d wih a value of β euro, 2 in Eq. (3). The esimaed euro 2 β, shows a posiive value and is saisically significan in boh he pound serlin g and Swiss franc volailiy equaions. To show ha effec visually, we calculae an impulse response funcion from Eq. (3). Le h = ( h, h ) represen he 2 1 vecor of condiional volailiies in period, and euro, i, le 2 ( 2 2 ) e = e, e be he 2 1 vecor of squared innovaions of Eq. (1) in period. Noe euro, i, E 2 [ e Φ ] = E [ h]. We can obain he following s sep ahead of predicions: ( ) s h+ s= ω + A+ B h, (7) 7

9 h h + s = ( A + B) s ω α β 1 β euro euro 0 euro, i, 1 ω = A= B=. ω 0 α β β i i euro, 2 i, 2 The superscrip * means an expeced value in period 1. Prime (" ") indicaes a ransporaion marix. Using Eq. (8) and esimaed parameers in Table 3, we obain impulse responses of pound serling and he Swiss franc volailiies o a volailiy shock in he euro in period. (8) Figure 2. The doed line in Figure 2 is he esimaed wo-sandard error boundary. We obain he sandard errors by linear approximaion (see Appendix). Figure 2 shows ha he impac of shock in he reurn volailiy of he euro on each currency reaches is peak afer 11 (pound serling, abou 2 hours) and 6 (Swiss franc, 1 hour) periods, respecively. This implies ha since a volailiy shock in he euro brings an uncerainy o he pound serling and Swiss franc markes, hese markes become volaile for he firs several periods afer ha shock. We also confirm ha he impac of he euro volailiy on each currency is no shor-lived. Therefore, we conclude ha he volailiy spillover effec from he euro o boh pound serling and he Swiss franc is subsanial and is impac long-lived. Finally, we examine he dynamics of he condiional correlaion beween he euro and each currency. The c ondiional correlaion parameers appearing in Table 3 are saisically significan for each pair of currencies (euro/pound serling and euro/swiss franc), consisen wih he hypohesis ha he condiional correlaion of each pair is ime varian. Figure 3. Figure 3 shows he averaged condiional correlaion of each currency pair for each 10-minue inerval. We confirm high level correlaion in all inervals, providing empirical evidence for he inerdependence beween he euro and each currency. This implies ha hese hree FX markes are highly inegraed, leading us o suppose ha such high level inegraion means ha he markes share he same informaion ha 8

10 affecs he FX raes. Moreover, from he resuls of he Granger causaliy es (Table 2) and he DCC MV-GARCH esimaion (Table 3), i is naural o infer ha informaion relevan o he euro also has an impac on pound serling and he Swiss franc. To examine he validiy of his inference, we model he dynamics of he cross correlaion as follows: q 23 i pρi p nhourdn p= 1 n= 1 ˆ ρ = τ + γ ˆ + λ + δnewseur,,, (9) where ˆ ρ i, is a cross correlaion beween he euro and currency i obained by he esimaion in Table 3. Since we model an auoregressive process of a cross correlaion in Eq. (5), lagged erms are included in Eq. (9). Lag lengh q is seleced by he AIC crierion. Evans and Lyons (2002) asser ha order flows, whic h are defined as he ne of buyer-iniiaed rades, convey informaion on aggregae porfolio shifs and, herefore, have a subsanial explanaory power o he dynamics of FX raes. Here, we define as news an unexpeced componen of he order flow of he euro as newseur. in Eq. (9) is calculaed from he squared residuals of he ARMA(1,1) model of he euro order flow (see Table 4A). hourd is a dummy variable which akes uniy a he n h GMT hour and n oherw ise zero. Figure 3 shows a seasonali y of he cross correlaions, which corresponds o he opening imings of he regions of hree major markes, namely, he Tokyo, London and New York markes. To measure he pure effec of euro news on he inerdependence, we remove he seasonaliy by inroducing he GMT variable hourd n. Table 4. hour dummy Table 4B repors he esimaion resul of Eq. (9). The number in parenheses is he sandard error obained from he Newey and Wes variance-covariance marix. In boh cases, he esimaed news EUR δ is posiive and saisically significan. This resul is consisen wih our inference ha here is informaion spillover from he euro o pound serling and he Swiss franc. I is reasonable o assume ha unexpeced selling of he euro enables marke paricipans o infer aggregae porfolio shifs from he euro counries and also from he Unied Kingdom (UK) and Swizerland: Since a negaive 9

11 economic shock o he euro area also has a negaive impac on he UK and Swizerland, raders shif heir asses from hese areas. Consequenly, unexpeced selling of he euro induces marke paricipans o sell hese currencies accompanied by porfolio reshuffling. Therefore, unexpeced selling of he euro can also have a negaive impac on pound serling and he Swiss franc. This inference is consisen wih he sign of δ in Table 4B. The above confirmaion is no very surprising. The euro counries, he UK and Swizerland share common economic and poliical backgrounds due o heir geographic proximiy. Moreover, smaller Swizerland heavily relies on is neighboring euro counries and is affeced by he economic siuaion of hose counries. The UK, which is bigger han Swizerland, is also affeced by he euro area. The resuls of Figures 2 and 3 indicae ha he euro and he pound serling markes are relaively less inegraed han he euro and Swiss franc markes. 5. Conclusion The findings of his paper provide wo major conribuions: Firs, he euro, pound serling and Swiss franc markes are highly inegraed, he laer wo currencies being subsanially affeced by he euro. A volailiy shock in he euro brings abou uncerainy o he pound serling and Swiss franc markes for several inervals. The resul of he empirical approach implies ha news of he euro spills over ino he pound serling and he Swiss franc markes and, consequenly, he euro and he wo currencies (pound serling and Swiss franc) show highly posiive co-movemen. This is explained by he common economic and poliical backgrounds which he euro counries, he UK and Swizerland share due o heir geographic proximiy. Secondly, alhough he level of inegraion beween he euro and pound serling markes is high, hey are less inegraed han he euro and Swiss franc markes. If such high inegraion in he euro, pound serling and Swiss franc is universal, he UK and Swizerland would have lile incenive o join he European Moneary Union because hey can enjoy he degree of freedom in execuing heir moneary policy ha would be los by giving up heir own currencies. 10

12 Appendix s s Denoing ha D( Ξ ) = ( A+ B), Ξ= [ α euro, β euro 1 β i 1 α i β euro 2 β i 2 ],,,,,,,, and ˆΞ is a se of esimaed parameers, we obain he firs order linear approximaion of D( Ξ ) s around ˆΞ as follows: ( ˆ s s ˆ s D Ξ) D( Ξ) D ( Ξ ) + ( Ξ Ξˆ) Ξ s 1 ˆ s ˆ s ˆ s 1 i ˆ i vec[ D( Ξ)] vec[ D( Ξ ) ] = vec [ D( Ξ ) ] + [ D( Ξ)] D( Ξ) ˆ ( Ξ Ξ ), i= 0 Ξ (A1) where " vec " creaes a column vecor by appending he columns of a marix o each oher. is he Kronecker produc. y z resuls in a marix in which every elemen in y has been muliplied by marix resul of Lükepohl (1993, p.471) s vec[ D( Ξ ) ] : z. The second line in Eq. (A1) is derived from he Wih Eq. (A1), we obain he following variance-covariance marix of ˆ s vec[ ( ) ] vec[ ( ˆ ˆ ˆ ) ] Var(vec[ ( ) ]) Var( ) s s D Ξ D Ξ D Ξ = Ξ Ξ Ξ (A2) where Ξˆ Ξˆ s s 1 vec[ D( ) ] ˆ s 1 i ˆ i vec[ D( )] = [ D( Ξ) ] D( Ξ) i= 0 Ξ, where ˆΞ and Var( Ξ ˆ ) are obained from he maximizaion of Eq. (6). Ξ 11

13 References Anderson, T.G., Reurn volailiy and rading volume: an informaion flow inerpreaion of sochasic volailiy. Journal of Finance 51(1), Baillie, R., Bollerslev, T., Inra-day and iner-marke volailiy in foreign exchange raes. Review of Economic Sudies 58, Chiang, T.C., Jeon, B.N., Li, H., Dynamic correlaion analysis of financial conagion: Evidence from Asian markes. Journal of Inernaional Money and Finance 26, Engle, R., Dynamics condiional correlaion: A simple class of Mulivariae generalized auoregressive condiional heeroskedasiciy models. Journal of Business and Economic Saisics 20(3), Engle, R., Kroner, K., Mulivariae simulaneous GARCH. Economeric Theory 11, Evans, M.D.D., Lyons, R.K., Order flow and exchange rae dynamics. Journal of Poliical Economy 110(1), Lükepohl, H., Inroducion o muliple ime series analysis. 2nd ed. Springer-Verlag, Berlin, Germany Inagaki, K., Tesing for volailiy spillover beween he Briish pound and he euro. Research in Inernaional Business and Finance 21(2), Io, T., Hashimoo, Y., Inraday seasonaliy in aciviies of he foreign exchange markes: Evidence from he elecronic broking sysem. Journal of he Japanese and Inernaional Economies 20, Malik, A.K., European exchange rae volailiy dynamics: an empirical invesigaion. Journal of Empirical Finance 12(1), Melvin, M., Melvin, B.P., The global ransmission of volailiy in he foreign exchange marke. Review of Economics and Saisics. 85(3), Nikkinen, J., Sahlsröm, P., Vähämaa, S., Implied volailiy linkages among major European currencies. Journal of Inernaional Financial Marke, Insiuions & Money. 16, Takayama, A., Mahemaical economics. 2nd ed. Cambridge Universiy Press, Cambridge, UK. 12

14 Tse, Y.K., Tsui, A.K., A mulivariae generalized auoregressive condiional heeroskedasiciy model wih ime-varying correlaions. Journal of Business and Economic Saisics 20(3), Wh ie, H., Maximum likelihood esimaion of misspecified models, Economerica 50(1)

15 Table 1 Summary of saisics Variable Mean S.D. Firs order serial correlaion LB(6) R euro *** R gbp *** R chf *** R 2 euro *** R 2 gbp *** R 2 chf *** X euro *** X gbp *** X chf *** Noe: LB(6) is he Ljung-Box saisics wih six lags. R, R 2 and X are he firs and second momens of reurns, and order flow of each currency (euro, pound serling [gbp] and Swiss franc [chf]). *** indicaes 1 percen level of significance. S.D.: sandard deviaion

16 Table 2 Granger χ 2 causaliy es 2A. Granger χ 2 causaliy es of firs momen of reurns Direcion of causaliy Euro Pound serling Pound serling Euro Direcion of causaliy Euro Swiss franc Swiss franc Euro Crierion Lag Sum of ζ 2 χ 2 sa p-value Sum of η 1 χ 2 sa p-value Crierion Lag Sum of ζ 2 χ 2 sa p-value Sum of η 1 χ 2 sa p-value AIC (.000) (.611) AIC (. 000) (.808) SIC (.000) (.271) SIC (. 000) (.664) HQ (.000) (.442) HQ (. 000) (.649) 2B. Granger χ 2 causaliy es of second momen of reurns Direcion of causaliy Euro Pound serling Pound serling Euro Direcion of causaliy Euro Swiss franc Swiss franc Euro Crierion Lag Sum of κ 2 χ 2 sa p-value Sum of ν 1 χ 2 sa p-value Crierion Lag Sum of κ 2 χ 2 sa p-value Sum of ν 1 χ 2 sa p-value AIC (.030) (.008) AIC (.001) (.641) SIC (.016) (.011) SIC (.000) (.788) HQ (.016) (.011) HQ (.000) (.788) Noe: The regression forms for he causaliy es of he firs and he second momens of he reurns are as follows: q R = cons + ζ R + η R euro, 1, p euro, p 1, p i, p p= 1 p= 1 q R = cons + ζ R + η R. i, 2, p euro, p 2, p i, p p= 1 p= 1 q q q q euro, = cons + κ1, p euro, p + ν1, p i, p p= 1 p= 1 R R R q q i, = + κ2, p euro, p+ ν2, p i, p p= 1 p= 1 R cons R R, where i=gbp (pound serling), chf (Swiss franc). Lag lengh q is seleced by each crierion. The Granger χ 2 es saisics (χ 2 sa) is calculaed wih he Newey and Wes variance-covariance marix. The lag of he Newey and Wes variance-covariance marix is T 1/4, where T is he sample size.

17 Table 3 Esimaion resuls of DCC MV-GARCH model Pair of reurns: R euro, and R gbp, Euro Pound serling (gbp) Esimaes Esimaes a euro.000 (.002) a gbp.012 *** (.004) b euro, ** (.010) b euro, *** (.012) b gbp,2.125 *** (.013) d euro.163 *** (.006) d gbp.089 *** (.007) ω euro.029 *** (.010) ω gbp.062 *** (.017) α euro.036 *** (.006) α gbp.064 *** (.010) β euro,1.932 *** (.019) β euro,2.114 *** (.041) β gbp, (.010) β gbp,2.765 *** (.051) ρ.734 *** (.009) θ *** (.053) θ *** (.005) Ρ Ρ.004 Ρ Ρ LB(6).048 LB(6) * LB(6) *** LB(6) *** Pair of reurns: R euro, and R chf, Euro Swiss franc (chf) Esimaes Esimaes a euro.013 (.012) a chf.019 ** (.009) b euro, *** (.011) b euro, *** (.014) b chf,2.154 *** (.012) d euro.069 *** (.006) d chf.011 ** (.006) ω euro.029 (.022) ω chf.078 ** (.033) α euro.035 ** (.016) α chf.056 *** (.016) β euro,1.934 *** (.039) β euro,2.315 *** (.119) β chf,1 - β chf,2.555 *** (.150) ρ.901 *** (.005) θ *** (.024) θ *** (.006) Ρ.011 Ρ.007 Ρ Ρ LB(6) LB(6) LB(6) *** LB(6) *** Noe: The number in parenheses is he robus sandard error suggesed by Whie (1982). ***, ** and * indicae 1, 5 and 10 percen levels of significance, respecively. Ρ and Ρ 2 are he firs order serial correlaions of he sandardized residual and he squared sandardized residual, respecively. LB(6) and LB(6) 2 are he Ljung-Box es saisics wih six lags for serial correlaion in he sandardized residual and he squared sandardized residual, respecively.

18 Table 4 Dynamics of condiional correlaion 4A. Resuls of ARMA(1,1) of order flow X euro Esimaes cons.013 * (.008) µ.592 *** (.208) ξ ** (.219) σ *** (.007) X = cons + µ X + ξυ + υ euro, euro, 1 1 υ N (0, σ 2). 4B. Esimaion of regression of condiional correlaion Cross correlaion beween he euro and he pound Cross correlaion beween he euro and he Swiss franc Esimae Esimae τ *** (.00311) τ *** (.00319) γ *** (.01028) γ *** (.01331) γ *** (.01344) γ *** (.01673) γ *** (.01234) γ *** (.01334) γ *** (.01263) γ *** (.00902) γ *** (.00807) λ (.00056) λ * (.00076) λ (.00056) λ * (.00096) λ ** (.00057) λ ** (.00094) λ *** (.00058) λ *** (.00099) λ (.00060) λ ** (.00094) λ (.00056) λ (.00084) λ (.00057) λ (.00082) λ ** (.00058) λ (.00084) λ ** (.00055) λ (.00088) λ *** (.00063) λ (.00093) λ (.00056) λ (.00091) λ (.00058) λ *** (.00073) λ ** (.00053) λ *** (.00074) λ *** (.00052) λ *** (.00078) λ (.00053) λ ** (.00078) λ (.00052) λ (.00081) λ (.00061) λ (.00080) λ (.00054) λ (.00092) λ *** (.00059) λ *** (.00099) λ *** (.00062) λ *** (.00099) λ *** (.00063) λ *** (.00108) λ ** (.00063) λ *** (.00117) λ *** (.00059) λ *** (.00101) δ *** (.00004) δ *** (.00007) Noe: The number in parenheses in Table 4A is he robus sandard error suggesed by Whie (1982). The number in parenheses in Table 4B is he sandard error calculaed wih he Newey and Wes variance-covariance marix. ***, ** and * indicae 1, 5 and 10 percen levels of significance, respecively.

19 Figure 1 Seasonaliy of second momens of he euro, pound serling and Swiss franc Averaged squared reurns of he euro Five inerval moving average :00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 GMT 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23: Averaged squared reurns of pound serling Five inerval moving average :00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 GMT 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23: Averaged squared reurns of he Swiss franc Five inerval moving average :00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 GMT 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Noe: The verical axis shows he averaged second momens of he reurns in each inerval. The horizonal axis is Greenwich Mean Time (GMT).

20 Figure 2 Impulse response funcion responding o a shock in euro volailiy Inerval Series of responses of he pound volailiy o a shock in euro volailiy Inerval Series of responses of he Swiss franc volailiy o a shock in euro volailiy Noe: The doed line is he esimaed wo-sandard error boundary. We obained he sandard errors by linear approximaion (see Appendix). The horizonal axis shows each 10-minue inerval (1 is one 10-minue inerval).

21 Figure 3 Averaged cross correlaion in each inerval :00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Averaged cross correlaion beween he euro and pound serling :00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Averaged cross correlaion beween he euro and Swiss franc Noe: The verical axis shows he averaged cross correlaion in each inerval. The horizonal axis is Greenwich Mean Time (GMT).