Integration at cost: Evidence from volatility impulse response functions

In eg a ion a a cos : E idence om ola ili y impulse esponse unc ions Eka e ini Panopoulou∗Theologos Pan elidis† Feb ua y 25, 2005 Abs ac We in es iga e he in e na ional in o ma ion ansmission be ween he U.S. and he es o he G-7 coun ies using daily s ock ma ke e u n da a co e ing he las 20 yea s. A p e-1995 and pos - 1995 analysis e eals ha he linkages be ween he ma ke s ha e changed subs an ially in he mo e ecen e a, sugges ing ha na ional ma ke s ha e become mo e in e dependen . In he majo i y o he coun ies unde sc u iny, we p o ide e idence o di ec ola ili y spillo e s, unning mainly om he US and poin ing o mo e apid in o ma ion ansmission du ing he ecen yea s. We u he unco e he dynamics o he ola ili y spillo e s be ween he in e na ional s ock ma ke s by means o a Vola ili y Impulse Response Analysis. Ou indings, based on h ee his o ical shocks ha ha e caused u bulence in he s ock ma ke s, sugges ha he pe sis ence o ola ili y shocks has inc eased subs an ially du ing he pos -1995 pe iod mainly due o inc eased pe sis ence and in e dependence in he ola ili y o all ma ke s. As a esul , ola ili y shocks in he in e na ional s ock ma ke s nowadays pe pe ua e o a signi ican longe pe iod compa ed o he p e-1995 e a. JEL classi ica ion: G15, C32 Keywo ds: ola ili y spillo e s, ola ili y impulse esponse unc ions, s ock ma ke , ARCH-BEKK Acknowledgmen s: Wea eg a e ul oT.Fla in,C.Ha ne andN.Pi is o help ulcommen s and sugges ions. The au ho s hank he EU o inancial suppo unde he “PYTHAGORAS: Fund- ing o esea ch g oups in he Uni e si y o Pi aeus” h ough he G eek Minis y o Na ional Educa ion and Religious Affai s. The usual disclaime applies. ∗Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, G eece and Depa men o Economics, Na ional Uni e si y o I eland Maynoo h. Co espondence o: Eka e ini Panopoulou, Depa - men o Economics, Na ional Uni e si y o I eland Maynoo h, Co.Kilda e, Republic o I eland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934. †Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, G eece. 1 In oduc ion In he wake o he s ock ma ke c ash o Oc obe 1987, he s udy o he ansmission o inancial shocks ac oss ma ke s o coun ies has eme ged as one o he mos in ensi e esea ch opics in he in e na ional inance li e a u e in ecen yea s. The i s con ibu ions in he so-called spillo e li e a u e came om Eun and Shim (1989) and Becke e al. (1990) who, based on ei he a VAR model o a se o single linea equa ions, ied o cap u e he dependence be ween in e na ional equi y e u ns. In a simila way, Koch and Koch (1991) in es iga ed he e olu ion o con empo aneous and lead/lag ela ionships among eigh s ock ma ke s and concluded ha egional in e dependence g ows o e ime and ha he in luence o he Japanese ma ke inc eases a he expense o he US ma ke . Howe e , hese s udies ocused on he e u n se ies and on how e u ns a e co ela ed ac oss ma ke s, i.e. hey conside ed only in e dependence h ough he mean o he p ocess. A second s and o he li e a u e, which is g owing apidly, explici ly ocuses on he ola ili y o equi y e u ns, sugges ing he exis ence o highe -o de dependence s emming om he second momen s. This amewo k is app op ia e when modeling high- equency inancial ime se ies and i s impo ance has been ecognized e e since Engle (1982) in o- duced he class o ARCH models. In his con ex , Hamao e al. (1990) employed uni a ia e GARCH models o examine he s ock ma ke s a ound he 1987 US s ock ma ke c ash. They ound e idence o signi ican p ice- ola ili y spillo e s om he US o he UK and Japan and om he UK o Japan o he pos -c ash pe iod. In con as , no such spillo e s a e ound in he p e-c ash pe iod. Thei esul s sugges ha shocks ha o igina e in he US a e la ge and mo e pe sis en han he UK and Japanese ones. Lin e al. (1994), using a signal ex ac ion model wi h GARCH p ocesses, ound a ecip ocal ela ionship be ween he p ice and ola il- i y o he US and Japanese ma ke s. Susmel and Engle (1994) analyzed he in e ela ionship be ween he US and he UK s ock ma ke s using hou ly e u ns and did no ind s ong e idence o ei he mean o ola ili y spillo e s be ween he wo ma ke s. Ka olyi (1995) examined he dynamic ela ionship be ween he US and Canadian s ock ma ke e u ns and e u n ola ili ies using a bi a ia e GARCH model. He ound ha he effec so shockso ig- ina ing in he US ma ke on he Canadian ma ke e u ns and ola ili y a e smalle and less pe sis en han hose measu ed wi h adi ional ec o au o eg essi e models. Theodossiou 1 and Lee (1993) s udied he ela ionship be ween he US, he UK, Canadian, Ge man and Japanese s ock ma ke s using a mul i a ia e GARCH-in-mean model and ound mean and ola ili y spillo e s be ween some o hose ma ke s. The au ho s also documen ed ha he US is he majo expo e o ola ili y. Mo e ecen ly, Kou mos and Boo h (1995) examined p ice ola ili y spillo e s o he US, he UK and Japan in he con ex o an ex ensi e mul i- a ia e Exponen ial GARCH model which can cap u e possible asymme ies in he ola ili y ansmission mechanism. The au ho s ound apa om p ice spillo e s, ex ensi e and ecip- ocal second momen in e ac ions, which a e asymme ic, i.e. nega i e inno a ions in a gi en ma ke inc ease ola ili y in he nex ma ke o ade mo e han posi i e inno a ions. The appea ance o he Asian inancial c isis in 1997 e i ed he in e es in he ma e and u ned he ocus away om he majo s ock ma ke s owa ds he eme ging ones (see o example Ng, 2000; Capo ale e al., 2001; He, 2001; Chen e al., 2002; Miyakoshi, 2003). In his s udy, we ocus explici ly on unco e ing he ola ili y dynamics be ween he US s ock ma ke and he emaining six o he G-7 coun ies using Vola ili y Impulse Response Func ions o mul i a ia e GARCH models in oduced by Ha ne and He wa z (2006). In his ein, we aim a es ablishing he pa e n o in o ma ion ansmission be ween hese coun ies. As indica ed by Ross (1989), he ansmission o in o ma ion o a ma ke is ela ed p ima ily o he ola ili y o an asse ’s p ice changes in an a bi age- ee economy, i.e. he second momen is mo e impo an han he i s one in he low o in o ma ion. In his ein, Engle e al. (1990) a ibu e mo emen s in ola ili y o he lag wi h which ma ke pa icipan s p ocess new in o ma ion. The p esen s udy makes a wo old con ibu ion. Fi s , we es ima e a bi a ia e GARCH model, o which a BEKK ep esen a ion is adop ed (see Engle and K one , 1995), o each o he six coun ies agains he US using daily e u ns o he las wen y yea s. This BEKK o mula ion enables us o e eal he exis ence o any “me eo showe s”, i.e. ansmission o ola ili y om one ma ke o ano he , as well as any “hea wa es”, i.e. inc eased pe sis ence in ma ke ola ili y (see Engle e al., 1990). Spli ing ou sample in o wo non-o e lapping sub-samples o equal leng h, we in es iga e whe he he effo s o mo e economic, mone a y and inancial in eg a ion ha e undamen ally al e ed he sou ces and in ensi y o ola ili y spillo e s o he indi idual s ock ma ke s. Second, by using a ecen ly de eloped echnique, we es ima e he co esponding Vola ili y Impulse Response Func ions (VIRFs) implied by he 2 speci ica ion o each model. We hen assess he impac o h ee his o ically obse ed shocks, i.e. he 1987 s ock ma ke c ash, he 1997 Asian Financial c isis and he 2001 e o is a ack on he ola ili y and co- ola ili y o he ma ke s. To he bes o ou knowledge, no o he s udy (excep o Ha ne and He wa z, 2006) has employed his inno a i e echnique o VIRFs o s udy ola ili y dynamics in any ma ke . Mo e impo an ly, he e a e se e al easons why VIRFs ep esen a con enien app oach o analyse ola ili y spillo e s. Fi s , his echnique allows he esea che o de e mine p ecisely how a shock o one ma ke in luences he dynamic adjus men o ola ili y o ano he ma ke and he pe sis ence o hese spillo e effec s. Second, VIRFs depend on bo h he ola ili y s a e and he unexpec ed e u ns ec o when he shock occu s. As a esul , he asymme ic esponse o ola ili y on nega i e and posi i e “news” ypically documen ed in he li e a u e (see e.g. Kou mos and Boo h, 1995) can easily be accommoda ed.1Thi d, con a y o ypical Impulse Response Func ions, his speci ic me hodology a oids ypical o hogonaliza ion and o de ing p oblems which would be ha dly easible in he case o highly in e ela ed and obse ed a high equencies inancial ime se ies. The only s udy ha is closely ela ed o ou s is he one by Leachman and F ancis (1996). The au ho s use a wo-s age p ocedu e, i.e. hey i s es ima euni a ia eGARCHmodels o he G-7 s ock ma ke e u ns and hen he es ima ed condi ional a iances a e used o cons uc a VAR sys em. This me hodology enables hem o employ he s anda d Impulse Response analysis and conduc Va iance Decomposi ions in o de o de e mine how a shock o one ma ke in luences he dynamic adjus men o ola ili y in he emaining ma ke s and he pe sis ence o hese ola ili y spillo e s. They can also quan i y he ela i e signi icance o each ma ke in gene a ing and ansmi ing luc ua ions o o he ma ke s. In e es ingly, he au ho s sugges ha a mul i a ia e GARCH app oach would gi e mo e efficien pa ame- e es ima es han hei wo-s age app oach bu would no enable he esea che o ob ain impulse esponse unc ions, as he la e a e no a ailable o GARCH p ocesses. I is his gap in he li e a u e ha we in end o b idge by es ima ing he VIRFs o he G-7 s ock ma ke e u ns accommoda ed by he a o emen ioned me hodology. Consis en wi h he inc eased in eg a ion o capi al ma ke s al eady documen ed in he li e a u e (see, 1Nega i e “news”, i.e. unexpec ed e u ns, in one ma ke can esul in a diffe en ola ili y p o ile han posi i e “news”, o he hings being equal. 3 o example, Ha ey, 1991; Bekae and Hod ick, 1992; Campbell and Hamao, 1992), ou esul s sugges ha equi y ma ke s ha e become mo e in e dependen in he pos -1995 pe iod compa ed wi h he p e-1995 pe iod. This g ea e in eg a ion esul ed in a signi ican inc ease in he pe sis ence o ola ili y shocks o all he coun ies a hand. The exis ence o bo h ele a ed “hea wa es” and “me eo showe s” effec s is depic ed in he pa e n and size o he VIRFs. The emainde o his s udy is o ganized as ollows. Sec ion 2 discusses he econome ic me hodology and Sec ion 3 desc ibes he da a and p esen s he empi ical indings o bo h he p e-1995 pe iod and he pos -1995 pe iod. Sec ion 4 offe s a summa y and some concluding ema ks. 2 Econome ic Me hodology In his sec ion, we i s p esen he model we employ o in es iga e he ola ili y spillo e s be ween he s ock ma ke s unde sc u iny and hen p o ide a b ie desc ip ion o he ola ili y impulse esponse me hod employed o analyse he pe sis ence o he ola ili y shocks in he in e na ional s ock ma ke s. 2.1 The BEKK Model The analysis is based on a bi a ia e VAR(1)-GARCH(1,1) model. Le Y =(y1 ,y 2 )0be he e u ns ec o , wi h y2 deno ing he US s ock ma ke and y1 one o he emaining G-7 coun ies. The condi ional mean o he p ocess is modeled as ollows: Y =C+M∗Y −1+E (1) whe e Cis a 2×1 ec o o cons an s and Mis a 2×2coefficien ma ix and E =(e1 ,e 2 )0 is he ec o o he ze o-mean e o e ms. We allow E o ha e a ime- a ying condi ional a iance, ha is Va (E |F −1)=H whe e F −1deno es he σ− ield gene a ed by all in o ma ion a ailable a ime −1. We u he assume ha he condi ional a iance, H , ollows a bi a ia e GARCH(1,1) model and we, speci ically, conside he ollowing BEKK 4 ep esen a ion, in oduced by Engle and K one (1995): E =H1/2 ∗Z H =Ω∗Ω0+A∗E −1∗E0 −1∗A0+B∗H −1∗B0(2) whe e Ω=[ωij],i,j=1,2is a 2x2 lowe iangula ma ix o cons an s, A=[aij]and B=[bij],i,j=1,2a e 2x2 coefficien ma ices and Z =(z1 ,z 2 )0∼iid(   0 0   ,   10 01   ). Ma ix Ameasu es he ex en o which condi ional a iances a e co ela ed wi h pas squa ed unexpec ed e u ns (i.e. de ia ions om he mean) and consequen ly cap u es he effec s o shocks on ola ili y. On he o he hand, ma ix Bdepic s he ex en o which cu en le els o condi ional a iances and co a iances a e ela ed o pas condi ional a iances and co a i- ances. Apa om displaying sufficien gene ali y, his model ensu es ha he condi ional a iance-co a iance ma ices, H =[hij, ],i,j=1,2,a eposi i ede ini e unde a he weak assump ions.2 Compa ed o al e na i e mul i a ia e GARCH ep esen a ions, he BEKK model is mo e con enien o es ima ion, because i in ol es ewe pa ame e s.Engle and K one (1995) p o e ha he BEKK model in (2) is second-o de s a iona y i and only i all he eigen alues o (A⊗A+B⊗B)a e less han uni y in modulus. In his case, he uncondi ional a iance o E ,Va (E ), can easily be calcula ed by: ec[Va (E )] = [I4−(A⊗A)0−(B⊗B)0]−1∗ ec(Ω0Ω) whe e ec is he ope a o ha s acks he columns o a squa e ma ix.3 Mo e in de ail, he condi ional a iance o each equa ion can be expanded o he bi- a ia e GARCH(1,1) as ollows: h11, =ω2 11 +a2 11e2 1 −1+2a11a12e1 −1e2 −1+a2 12e2 2 −1+(3) +b2 11h11, −1+2b11b12h12, −1+b2 12h22, −1 h22, =ω2 21 +ω2 22 +a2 21e2 1 −1+2a21a22e1 −1e2 −1+a2 22e2 2 −1+(4) +b2 21h11, −1+2b21b22h12, −1+b2 22h22, −1 2Engle and K one (1995) show ha H is posi i e de ini e i a leas one o Ωo Bis o ull ank. 3The momen p ope ies o mul i a ia e GARCH p ocesses a e also examined by Ha ne (2003). 5 h12, =ω11ω21 +a11a21e2 1 −1+(a11a22 +a12a21)e1 −1e2 −1+a12a22e2 2 −1+(5) +b11b21h11, −1+(b11b22 +b12b21)h12, −1+b12b22h22, −1 Suppose ha we es ima e a bi a ia e sys em o Canada and he US based on equa ions (1) - (2). In such a case, h11, and h22, deno e he condi ional a iance o Canada and he US espec i ely, while h12, deno es he condi ional co a iance be ween he se ies. Signi icance o any o bo h he elemen s a12,b 12 sugges s ha ola ili y in he Canadian ma ke is affec ed by de elopmen s in he ola ili y o he US ma ke h ough ei he he pas ola ili y o he US ma ke , h22, −1, o he pas squa ed inno a ions e2 2 −1(o e en he c oss p oduc s, e1 −1e2 −1, o pas inno a ions). Fu he mo e, indi ec eedbacks may exis h ough he pas alue o he condi ional co a iance h12, −1. When conside ing he e olu ion o he US ma ke ola ili y and i s dependence on he Canadian one, he easoning is simila and ollows di ec ly om equa ion (4). The con empo aneous co-mo emen in he ola ili y o he se ies is gi en by equa ion (5) and is a unc ion o pas squa ed inno a ions, c oss p oduc s o inno a ions, pas condi ional ola ili ies and na u ally pas condi ional co a iance. This ich pa ame e iza ion sugges s ha e en in he case ha condi ional ola ili ies be ween he se ies a e no linked di ec ly, i.e. b12 =b21 =0, he in e ac ions be ween he condi ional a iances is ensu ed by pas e u n inno a ions. To cope wi h he excess ku osis usually ound in he es ima ed s anda dised esiduals unde he assump ion o Gaussian inno a ions, we ollow Bolle sle (1987) and e alua e (and maximize) he sample log-likelihood unc ion unde he assump ion o (ν)−dis ibu ed inno a ions. In such a case, gi en a sample o Tobse a ions, a ec o o unknown pa ame e s θand a 2×1 ec o o e u ns Y , he bi a ia e BEKK model is es ima ed by maximizing he ollowing likelihood unc ion: L(θ)= T X =1 ln(l (θ)) (6) wi h l =Γ((T+ )/2) Γ( /2)[π( −2)]T/2|H |−1/2·1+ 1 −2E0 H−1 E ¸−(T+ )/2 (7) whe e νdeno es he deg ees o eedom o he −dis ibu ion and Γ(·)is he gamma unc ion. This log-likelihood unc ion is maximized using he Be nd , Hall, Hall and Hausman (1974) 6 algo i hm (BHHH).4 2.2 Vola ili y Impulse Response Func ions We now b ie ly desc ibe he Vola ili y Impulse Response Func ion (VIRF) in oduced by Ha ne and He wa z (2006). The au ho s de i e he VIRF based on an al e na i e mul- i a ia e GARCH ep esen a ion, namely he ec- ep esen a ion (in oduced by Engle and K one , 1995), gi en by: ech(H )=Q+R∗ ech(E −1∗E0 −1)+P∗ ech(H −1)(8) whe e Qis a 3×1ma ix o cons an s, while Rand Pa e 3×3coefficien ma ices. ech is he ope a o ha s acks he lowe iangula pa o a squa e ma ix. I is impo an o no e ha he ec- ep esen a ion gi en in (8) equi es he es ima ion o 21 pa ame e s, while he BEKK ep esen a ion gi en in (2) has only 11 pa ame e s. Thus, he BEKK model manages o educe subs an ially he numbe o pa ame e s, acili a ing he es ima ion p ocedu e. Ob iously, he ec-model is mo e gene al han he BEKK model, since he BEKK model educes he numbe o pa ame e s by imposing some speci ic es ic ions on he ec-model. In gene al, any gi en BEKK model has a unique equi alen ec- ep esen a ion (Engle and K one 1995), while he con e se is no ue.5,6In summa y, by employing he BEKK model we achie e he educ ion o he numbe o pa ame e s wi h i ually no cos in e ms o he gene ali y o he model. The de i a ion o he unique equi alen ec- ep esen a ion o a BEKK model is s aigh o wa d.7In he es o his pape , we assume ha (8) is he equi alen ec- ep esen a ion o (2). Assume ha a ime =0 he condi ional a iance is a an ini ial s a e H0and an ini ial 4Susmel and Engle (1994) sugges ha in he case o high- equency inancial da a using he -dis ibu ion gene a es a mo e efficien es ima ion o condi ional e o s han he no mal dis ibu ion. 5Two GARCH ep esen a ions a e equi alen i e e y sequence o e o s {E }gene a es he same sequence o condi ional ola ili ies {H } o bo h ep esen a ions. 6I is possible ha a ec-model has no equi alen BEKK ep esen a ion. Mo eo e , i he e is an equi alen BEKK ep esen a ion o a ec-model, his BEKK ep esen a ion is no unique. 7The necessa y assump ions o he equi alence o he wo ep esen a ions a e he ollowing: Q=   ω2 11 ω11ω21 ω2 21 +ω2 22  ,R=  a2 11 2a11a12 a2 12 a11a21 a11a22 +a12a21 a22a12 a2 21 2a21a22 a2 22  and P=  b2 11 2b11b12 b2 12 b11b21 b11b22 +b12b21 b22b12 b2 21 2b21b22 b2 22  . 7 shock Z0=(z1,0,z 2,0)0occu s. The VIRF, V (Z0),is hende ined as ollows: V (Z0)=E[ ech(H )|F −1,Z 0]−E[ ech(H )|F −1] The i s and hi d elemen s o V (Z0)(deno ed as 1, and 3, espec i ely) ep esen he eac ion o he condi ional a iance o he i s and second a iable espec i ely o he shock, Z0, ha occu ed pe iods ago. Simila ly, he second elemen o V (Z0)(deno ed as 2, ) ep esen s he eac ion o he condi ional co a iance o he shock, Z0, ha occu ed pe iods ago. The VIRF can easily be compu ed ecu si ely based on he ollowing ela ions: V1(Z0)=R∗{ ech(H1/2 0Z0Z0 0H1/2 0)− ech(H0)}(9) V (Z0)=(R+P)∗V −1(Z0), >1 The VIRF has wo impo an diffe ences compa ed o he adi ional Impulse Response Func ion (IRF) in he condi ional mean. Fi s , he VIRF is an e en unc ion o he ini ial shock, ha is V (Z0)=V (−Z0), con a y o he IRF ha is an odd unc ion o he ini ial shock. Second, he IRF is a linea unc ion, i.e. IRF(k∗Z0)=k∗IRF(Z0),while heVIRF is no homogeneous o any deg ee. Be o e p esen ing he empi ical esul s o his s udy, we b ie ly desc ibe he beha io o he VIRF. Fi s o all, le Ψ=[ψi,1]:= ech(H1/2 0Z0Z0 0H1/2 0)− ech(H0)whe e i=1,2,3. I is ob ious ha he elemen s o Ψa e unc ions o he elemen s o he ini ial s a e H0and he elemen s o he shock Z0. The ollowing h ee cases a e o in e es : Case I: Diagonal BEKK model (i.e. a12 =a21 =b12 =b21 =0) In his case, bo h Rand P(and hus R+P) a e diagonal ma ices (see oo no e 7). I is easy o show ha : 1,1=a2 11ψ1,1and 1, =(a2 11 +b2 11) −1 1,1 o >1 2,1=a11a22ψ2,1and 2, =(a11a22 +b11b22) −1 2,1 o >1 3,1=a2 22ψ3,1and 3, =(a2 22 +b2 22) −1 3,1 o >1 The e o e, in his pa icula case he e a e no ola ili y spillo e s, since bo h 1, and 3, 8 10−4,2.03 ×10−4)0 espec i ely o he Canada-US model, In his case, he ini ial shock is es ima ed o be b Z0=(b H1/2 )−1b E =(−9.74,−14.04)0. The co esponding ini ial shocks o he emaining i e models a e calcula ed in a simila way. The second shock we conside is he Asian inancial c isis in 1997. Mo e speci ically, we calcula e he ini ial shock based on he es ima ed models (Table 3, Panel B) o Oc obe 27, 1997. The las shock we conside is he one associa ed wi h he e o is a ack o he Twin Towe s in Sep embe 2001. Since he i s ading day o he US s ock ma ke a e he a ack was he Sep embe 17, 2001, he ini ial shocks a e calcula ed based on his day. The es ima ed ini ial shocks o hese h ee his o ical shocks wi h espec o ou es ima ed models a e epo ed in Table 5. Apa om he es ima ed pa ame e s o he BEKK models and he co esponding ini ial shocks, he calcula ion o he VIRFs equi es he ini ial s a e o ola ili y, H0,assugges ed by equa ion (9). To make ou indings in a ian o he choice o ini ial s a e, we selec he las day o ou sample, i.e. Oc obe 8, 2004 and employ his es ima ed condi ional a iance- co a iance ma ix in bo h sub—pe iods.15 This allows a di ec compa ison o he VIRFs be ween he wo sub-pe iods unde conside a ion. We i s in es iga e he size o he effec o each shock on he condi ional a iance o he se ies unde examina ion. Table 7 epo s he maximum alue and he 1-s ep ahead alue o he VIRF di ided by he ini ial condi ional a iance. As expec ed, he effec o he 1987 c ash on he condi ional ola ili y dynamics is subs an ially g ea e han he co esponding effec s s emming om he o he wo shocks conside ed in his analysis. Fo example, in he case o he US, he c ash o 1987 induces a ise in ola ili y ha is 6.57 and 17.18 imes he ini ial ola ili y o he p e-1995 and pos -1995 pe iod espec i ely.16 The co esponding igu es o he Asian inancial c isis a e 1.06 and 2.78 o he pe iods examined. E en milde effec s a e p e alen when he hi d shock is conside ed.17 The inc eased in ensi y o ola ili y spillo e s du ing he ecen yea s is easily shown when 15The ini ial s a es employed o each pai o coun ies a e p esen ed in Table 6. Al e na i ely, he es ima ed uncondi ional a iance ma ix o E could be employed as an ini ial s a e. In such a case, ou esul s would be quali a i ely simila o he ones epo ed. 16The analysis o he US is based on he Canada-US model, al hough quan i a i ely simila esul s a e d awn om he es o he bi a ia e models. 17In his case, i a simila shock occu ed in he p e-1995 pe iod, he inc ease in he US ola ili y would be jus 0.53 imes he ini ial ola ili y, while in he case o he pos -1995 pe iod, he ola ili y inc ease would be 1.38 imes he ini ial ola ili y. 15 he pa h o he impulse esponses in he ola ili y o each coun y is conside ed. Figu es 2-4 plo he VIRFs o he h ee shocks espec i ely. In mos cases, he VIRF is maximised he day a e he shock. Howe e , in some cases he effec o he ini ial shock g adually inc eases, eaching i s maximum alue a e many days o e en weeks. In gene al, he impulses a e declining s a ing om a high le el o ola ili y. In some cases, howe e , he e is e idence o an ini ial shock ampli ica ion which inc eases u he he ini ial effec . E en ually, in all cases he VIRFs esume hei declining pa h owa ds ze o. We now ocus on he es ima ed hal -li e o he ola ili y shocks, which a e epo ed in Table 8 (Panels A, B and C o he h ee shocks espec i ely) o all six pai s o coun ies and he wo sub-pe iods.18 Appa en ly, he hal -li es o ola ili y shocks pain a simila pic u e poin ing o mo e pe sis en shocks in he mo e ecen e a. Fo example, o he p e-1995 pe iod and o he 1987 c ash, he es ima ed hal -li es o he US, he coun y om which he c ash o igina ed, ange om 48 o 91 days, while i he shock occu ed in he pos -1995 pe iod, he espec i e igu es would be 98 days o 219 days. The hal -li es o he es o he coun ies a e lowe han he US in he i s sub-pe iod anging om 13 days (UK and F ance) o 41 days (Japan). Su p isingly, ou indings om he ecen e a sugges ha a simila o he “1987 c ash” shock would induce ola ili y spillo e s ha would las o signi ican ly longe pe iod nowadays compa ed o he p e-1995 pe iod. Ou esul s o he o he wo shocks a e quali a i e simila o hose o he i s shock, so we do no discuss hem sepa a ely o sa e space. In summa y, he empi ical indings o his ola ili y impulse esponse expe imen sugges ha he inc eased in eg a ion o he in e na ional s ock ma ke s du ing he pos -1995 pe iod has also caused an inc ease in he pe sis ence o ola ili y shocks. As a esul , simila ola ili y shocks can pe pe ua e o a signi ican longe pe iod nowadays compa ed o he p e-1995 e a. 4 Conclusions The e is ex ensi e empi ical wo k in he li e a u e wi h espec o in e dependencies be ween inancial ma ke s and mo e speci ically, na ional s ock ma ke s. This pape ocuses on second- 18No e ha he hal -li es in Table 8 a e calcula ed a e he Ini ial Shock Ampli ica ion has been deduc ed. 16 o de in e dependencies, i.e. linkages h ough he condi ional a iances o he se ies. The analysis was pe o med using daily closing s ock index da a om he G-7 s ock ma ke s o helas 20yea s. Byadop ingabi a ia eBEKK ep esen a ion and spli ing ou sample in o wo 10-yea sub-samples, we i s examined whe he s ock ma ke linkages be ween he US and he emaining o he G-7 coun ies ha e changed du ing he ecen yea s. As a second s ep, we employed a new echnique de eloped by Ha ne and He wa z (2006) and es ima ed he Vola ili y Impulse Response Func ions (VIRFs) ela ed o each pai o ou coun ies. This echnique enabled us o quan i y he size and he pe sis ence o h ee his o ical shocks ha ha e caused u bulence in he s ock ma ke s. Fu he mo e, he signi ican ly diffe en s uc u e o s ock ma ke s in he p e- and pos -1995 pe iods allowed compa isons ha shed some ligh in o he cu en beha io o s ock ma ke s. Ou empi ical indings can be summa ised as ollows. We con i med he es ablished iew ha he US s ock ma ke is he majo ola ili y expo e coun y. Speci ically, he e is e idence o signi ican ola ili y spillo e s om he US o Canada, F ance and Ge many du ing he p e-1995 pe iod. Fo he same pe iod, he es o he G-7 coun ies, i.e. I aly, Japan and he UK appea secluded and in ulne able o shocks o igina ing in he US. On he o he hand, ou indings o he mo e ecen pe iod poin o inc eased in eg a ion be ween he ma ke s. Speci ically, he smalle o he G-7 coun ies, i.e. Canada, F ance, Ge many and I aly mainly impo ola ili y om he US. A mo e impo an inding, howe e , is he e idence in a o o bidi ec ional ola ili y spillo e s be ween he US and Japan, as well as he US and he UK. Ou esul s sugges ha shocks o igina ing in he UK affec posi i ely he US s ock ma ke while he Japanese ones in luence he US ma ke nega i ely, inducing lowe le els o ola ili y. Ou VIRFs analysis o h ee his o ical shocks, namely he 1987 c ash, he 1997 Asian inancial c ash and he 2001 e o is a ack p o ided use ul insigh s wi h espec o he size and pe sis ence o ola ili y shocks. We speci ically ound e idence in a o o inc eased ampli ude and du a ion o ola ili y spillo e s in he pos -1995 sample compa ed o he p e-1995 one. This in ensi y o shocks mainly s ems om he inc eased in e dependence and pe sis ence o he equi y ma ke ola ili ies documen ed in he ecen e a. Consequen ly, had a shock simila o he one o he 1987 c ash occu ed in he mo e ecen yea s, he ime equi ed o his shock o die ou would ha e been ex emely longe nowadays compa ed o he p e-1995 pe iod. 17 The me hod employed he e can also be applied o o he cases ha in ol e high equency da a, mainly inancial da a, o examine linkages and unco e he ola ili y dynamics be ween he se ies unde examina ion. Vola ili y spillo e s be ween exchange a e ma ke s o be ween s ock ma ke s and exchange a es can be de ec ed and quan i ied h ough he VIRFs. An- o he p omising ou e o u he in es iga ion may be he ex ension o his bi a ia e analysis o a highe o de one, allowing o in e ac ions among h ee o mo e coun ies. Bo h hese ex ensions will be he objec o ou u u e wo k. Re e ences [1]Becke , K.G., J.E. Finne y and M. Gup a (1990). The in e empo al ela ion be ween he U.S. and Japanese s ock ma ke s. Jou nal o Finance, 45, 1297-1306. [2]Bekae , G. and R.J. Hod ick (1992). Cha ac e izing p edic able componen s in excess e u ns on equi y and o eign exchange ma ke s. Jou nal o Finance, 47, 467-470. [3]Be nd , E.K., B.H. Hall, R.E. Hall and J.A. Hausman (1974). Es ima ion and in e ence in non-linea s uc u al models. Annals o Economic and Social Measu emen , 69, 542-547. [4]Billio, M. and L. Pelizzon (2003). Vola ili y spillo e s be o e and a e EMU in Eu opean s ock ma ke s. Jou nal o Mul ina ional Financial Managemen , 13, 323-340. [5]Bolle sle , T. (1987). A condi ional he e oskedas ic ime se ies model o specula i e p ices and a es o e u n. Re iew o Economics and S a is ics, 69, 542-547. [6]Campbell, Y. and Y. Hamao (1992). P edic able s ock e u ns in he Uni ed S a es and Japan: A s udy o long- e m capi al ma ke in eg a ion. Jou nal o Finance, 47, 43-69. [7]Capo ale, G.M., N. Pi is and N. Spagnolo (2001). Vola ili y ansmission and inancial c ises. DP02-2001, Cen e o Mone a y and Financial Economics, Sou h Bank Uni e si y, London, o hcoming a he Jou nal o Economics and Finance. [8]Chen, G., M. Fi h and O.M. Rui (2002). S ock ma ke linkages: E idence om La in Ame ica. Jou nal o Banking and Finance, 26(6), 1113-1141. 18 [9]Cheung Y.M. and L.K. Ng (1996). A causali y-in- a iance es and i s applica ion o inancial ma ke p ices. Jou nal o Econome ics, 72, 33-48. [10]Engle, R.F. (1982). Au o eg essi e condi ional he e oskedas ici y wi h es ima es o he a iance o U.K. in la ion. Econome ica, 50, 987-1008. [11]Engle, R.F., T. I o and W.L. Lin (1990). Me eo showe s o hea wages? He e oskedas ic in a-daily ola ili y in he o eign exchange ma ke . Econome ica, 58, 525-542. [12]Engle, R.F. and K.F. K one (1995). Mul i a ia e simul aneous gene alized ARCH. Econome ic Theo y, 11, 122-150. [13]Eun, C. and S. Shim (1989). In e na ional ansmission o s ock ma ke mo emen s. Jou nal o Financial and Quan i a i e Analysis, 24, 241-256. [14]Fla in T., M. Hu ley and F. Rousseau (2002). Explaining s ock ma ke co ela ion: A g a i y model app oach. The Manches e School, 70, 87-106. [15]Ha ne , C.M. (2003). Fou h momen s uc u e o mul i a ia e GARCH models. Jou nal o Financial Econome ics, 1, 26-54. [16]Ha ne , C. and H. He wa z (2006). Vola ili y Impulse Response Func ions o Mul i a i- a e GARCH Models: An Exchange Ra e Illus a ion. Jou nal o In e na ional Money and Finance, o hcoming. [17]Hamao, Y., R. Masulis and V. Ng (1990). Co ela ions in p ice changes and ola ili y ac oss in e na ional s ock ma ke s. Re iew o Financial S udies, 3, 281-307. [18]Ha ey, R. (1991). The wo ld p ice o co a iance isk. Jou nal o Finance, 46, 111-158. [19]He, L.T. (2001). Time a ia ion pa hs o in e na ional ansmission o s ock ola ili y — US s. Hong Kong and Sou h Ko ea. Global Finance Jou nal, 12(1), 79-93. [20]Ka olyi, A. (1995). A mul i a ia e GARCH model o in e na ional ansmission o s ock e u ns and ola ili y. Jou nal o Business, Economics and S a is ics, 13, 11-25. [21]Ka olyi, A. and R.M. S ulz (1996). Why do ma ke s mo e oge he ? An in es iga ion o US-Japan s ock e u n como emen s. Jou nal o Finance, 51, 951-986. 19 [22]Koch, P.D. and T.W. Koch (1991). E olu ion in dynamic linkages ac oss daily na ional s ock indexes. Jou nal o In e na ional Money and Finance, 10, 231-251. [23]Kou mos, G. and G.G. Boo h (1995). Asymme ic ola ili y ansmission in in e na ional s ock ma ke s. Jou nal o In e na ional Money and Finance, 14, 747-762. [24]Leachman, L.L. and B. F ancis (1996). Equi y ma ke e u n ola ili y: Dynamics and ansmission o he G-7 coun ies. Global Finance Jou nal, 7(1), 27-52. [25]Lin, W.-L., R.F. Engle and T. I o (1994). Do bulls and bea s mo e ac oss bo de s? In e na ional ansmission o s ock e u ns and ola ili y. Re iew o Financial S udies, 7 (3), 507-538. [26]Miyakoshi, T. (2003). Spillo e s o s ock e u n ola ili y o Asian equi y ma ke s om Japan and he US. In e na ional Financial Ma ke s, Ins i u ions and Money, 13, 383-399. [27]Ng, A. (2000). Vola ili y spillo e effec s om Japan and he US o he Paci ic-Basin. Jou nal o In e na ional Money and Finance, 19, 207-233. [28]Ross, S.A. (1989). In o ma ion and ola ili y: The no-a bi age Ma ingale app oach o iming and esolu ion i ele ancy. Jou nal o Finance, 44, 1-17. [29]Susmel, R. and R.F. Engle (1994). Hou ly ola ili y spillo e s be ween in e na ional eq- ui y ma ke s. Jou nal o In e na ional Money and Finance, 13(1), 3-25. [30]Theodossiou, P. and U. Lee (1993). Mean and ola ili y spillo e s ac oss majo na ional s ock ma ke s: Fu he empi ical e idence. Jou nal o Financial Resea ch, 16, 337-350. 20 21 Table 1: Summa y Desc ip i e S a is ics Panel A: Full Sample (31/12/84-8/10/04) Canada F ance Ge many I aly Japan UK US Mean 0.00025 0.00035 0.00028 0.00029 9.59E-05 0.00044 0.00034 Median 0.00049 0.00046 0.00032 0.00037 0.00000 0.00055 0.00025 Maximum 0.08874 0.08289 0.08769 0.07099 0.12883 0.07231 0.09095 Minimum -0.12111 -0.08430 -0.11494 -0.10678 -0.13823 -0.14047 -0.22899 S d. De . 0.00960 0.01355 0.01453 0.01304 0.01602 0.01150 0.01093 Skewness -1.17403 -0.22157 -0.29519 -0.36396 0.11682 -0.59935 -2.07463 Ku osis 17.7069 5.88741 7.16838 6.90276 7.63023 10.6913 47.1517 Panel B: Fi s subsample (31/12/84-31/12/94) Canada F ance Ge many I aly Japan UK US Mean 0.00016 0.00044 0.00031 0.00027 0.00048 0.00054 0.00033 Median 0.00037 0.00049 0.00000 0.00034 0.00053 0.00054 0.00029 Maximum 0.08874 0.08289 0.08769 0.07099 0.12883 0.07231 0.09095 Minimum -0.12111 -0.08430 -0.11494 -0.10678 -0.13823 -0.14047 -0.22899 S d. De . 0.00800 0.01317 0.01351 0.01397 0.01560 0.01179 0.01045 Skewness -2.07996 -0.36377 -0.50435 -0.39156 -0.01657 -1.01165 -4.80774 Ku osis 43.4971 7.11751 10.3723 7.59009 10.1313 15.5090 108.379 Panel C: Second subsample (1/1/95-8/10/04) Canada F ance Ge many I aly Japan UK US Mean 0.00034 0.00028 0.00027 0.00029 -0.00025 0.00035 0.00035 Median 0.00064 0.00041 0.00053 0.00045 -0.00043 0.00056 0.00017 Maximum 0.04690 0.06198 0.06837 0.05592 0.12354 0.05797 0.05574 Minimum -0.09033 -0.07362 -0.08559 -0.07543 -0.06592 -0.05886 -0.07114 S d. De . 0.01088 0.01389 0.01542 0.01213 0.01639 0.01124 0.01136 Skewness -0.80306 -0.10832 -0.16263 -0.31626 0.22749 -0.16387 -0.10826 Ku osis 8.96719 4.94645 5.24439 5.42687 5.72985 5.29419 6.25458 22 Table 2: Un es ic ed Es ima ed GARCH(1,1)-BEKK Models Panel A: 1s subsample (31/12/84-31/12/94) Panel B: 2nd subsample (1/1/95-8/10/04) c 11 α11 α12 b11 b 12 d. . c11 α11 α12 b11 b 12 d. . c 21 c 22 α21 α22 b21 b 22 Eigen- alues (s.e.) c21 c 22 α21 α22 b21 b 22 Eigen- alues (s.e.) Canada 0.0013* 0.2596* -0.0173 0.9387* 0.0149* 0.9885 4.8333* Canada 0.0007* 0.2125* 0.0314 0.9747* -0.0074 0.9963 7.3849* (0.0001) (0.0291) (0.0183) (0.0116) (0.0060) 0.9710 (0.3160) (0.0001) (0.0183) (0.0185) (0.0043) (0.0050) 0.9961 (0.5860) 0.0004* 0.0006* 0.0656* 0.1355* -0.029* 0.9938* 0.9692 LL 0.0005* 0.0006* 0.0344 0.2301* -0.0074 0.9705* 0.9940 LL (0.0001) (0.0002) (0.0331) (0.0193) (0.0128) (0.0062) 0.9625 17066.3 (0.0002) (0.0001) (0.0208) (0.0213) (0.0054) (0.0055) 0.9939 17029.1 F ance 0.0036* 0.2614* 0.0545* 0.9213* -0.0012 0.9890 5.6514* F ance 0.0013* 0.2167* -0.0271 0.9692* 0.0110 0.9977 8.4343* (0.0004) (0.0280) (0.0221) (0.0160) (0.0078) 0.9458 (0.4033) (0.0002) (0.0189) (0.0235) (0.0057) (0.0071) 0.9886 (0.8219) 0.0004 0.0007* -0.0110 0.1533* -0.0019 0.9830* 0.9425 LL -0.0003 0.0008* 0.0106 0.2315* 0.0018 0.9682* 0.9883 LL (0.0002) (0.0001) (0.0146) (0.0130) (0.0073) (0.0026) 0.9214 15138.7 (0.0002) (0.0001) (0.0164) (0.0186) (0.0051) (0.0053) 0.9798 15977.8 Ge many 0.0028* 0.2738* 0.0423* 0.9339* 0.0044 0.9881 5.2204* Ge many 0.0007* 0.2205* 0.0384 0.9733* -0.0055 0.9997 8.4185* (0.0003) (0.0257) (0.0207) (0.0109) (0.0067) 0.9593 (0.3353) (0.0002) (0.0165) (0.0227) (0.0043) (0.0069) 0.9932 (0.8173) -0.0001 0.0008* -0.0064 0.1415* 0.0041 0.9828* 0.9566 LL -0.0003 0.0009* 0.0017 0.2415* 0.0021 0.9656* 0.9931 LL (0.0001) (0.0001) (0.0137) (0.0123) (0.0055) (0.0027) 0.9423 15197.8 (0.0002) (0.0001) (0.0122) (0.0162) (0.0034) (0.0047) 0.9869 15921.2 I aly 0.0021* 0.2436* 0.0132 0.9584* -0.0044 0.9896 5.6541* I aly 0.0017* 0.2409* 0.0068 0.9572* 0.0027 0.9964 8.6927* (0.0003) (0.0223) (0.0163) (0.0076) (0.0046) 0.9786 (0.4018) (0.0002) (0.0205) (0.0180) (0.0074) (0.0053) 0.9863 (0.8834) 0.0002 0.0007* 0.0082 0.1477* -0.0027 0.9836* 0.9784 LL 0.0001 0.0007* 0.0236 0.2293* -0.0067 0.9718* 0.9855 LL (0.0001) (0.0001) (0.0107) (0.0121) (0.0036) (0.0022) 0.9780 14978.5 (0.0002) (0.0001) (0.0180) (0.0165) (0.0064) (0.0042) 0.9745 16219.0 Japan 0.0025* 0.3437* 0.0593* 0.9281* -0.0104 0.9898 5.2258* Japan 0.0020* 0.2072* 0.0069 0.9696* 0.0041 0.9946 8.3958* (0.0002) (0.0235) (0.0279) (0.0089) (0.0074) 0.9808 (0.3588) (0.0003) (0.0170) (0.0249) (0.0050) (0.0063) 0.9902 (0.8265) 0.0002 0.0007* 0.0243* 0.1537* -0.008* 0.9827* 0.9648 LL -0.0002 0.0007* -0.026* 0.2308* 0.0049 0.9709* 0.9893 LL (0.0002) (0.0001) (0.0100) (0.0122) (0.0038) (0.0024) 0.9634 14890.7 (0.0002) (0.0001) (0.0132) (0.0153) (0.0039) (0.0038) 0.9837 15242.6 UK 0.0031* 0.2693* 0.0061 0.9239* 0.0057 0.9864 6.0113* UK 0.0013* 0.2186* -0.095* 0.9574* 0.0320* 0.9976 9.0356* (0.0004) (0.0304) (0.0250) (0.0164) (0.0073) 0.9497 (0.4041) (0.0001) (0.0170) (0.0191) (0.0065) (0.0073) 0.9776 (0.8716) 0.0004 0.0008* -0.0049 0.1656* -0.0020 0.9796* 0.9485 LL -0.000* 0.0008* 0.0565* 0.2343* 0.0003 0.9623* 0.9649 LL (0.0002) (0.0001) (0.0188) (0.0135) (0.0090) (0.0033) 0.9281 15438.0 (0.0002) (0.0002) (0.0182) (0.0209) (0.0075) (0.0072) 0.9506 16512.5 No es: S anda d e o s a e epo ed in pa en heses. An as e isk indica es signi icance a he 5% le el. d. . e e s o deg ees o eedom o he -dis ibu ion. LL e e s o he alue o he log-likelihood unc ion. 23 Table 3: Res ic ed Es ima ed GARCH(1,1)-BEKK Models Panel A: 1s subsample (31/12/84-31/12/94) Panel B: 2nd subsample(1/1/95-8/10/04) c 11 α11 α12 b11 b 12 d. . c11 α11 α12 b11 b 12 d. . c 21 c 22 α21 α22 b21 b 22 Eigen- alues (s.e.) c21 c 22 α21 α22 b21 b 22 Eigen- alues (s.e.) Canada 0.0010* 0.2161* 0.9567* 0.0099* 0.9923 5.0970* Canada 0.0007* 0.1896* 0.0495* 0.9796* -0.0116* 0.9968 7.3827* (0.0001) (0.0170) (0.0073) (0.0026) 0.975 (0.3232) (0.0001) (0.0132) (0.0164) (0.0028) (0.0042) 0.9956 (0.5843) 0.0007* 0.1580* 0.9835* 0.975 LL 0.0006* 0.0007* 0.2555* 0.9652* 0.9939 LL (0.0001) (0.0125) (0.0022) 0.9619 17065.9 (0.0002) (0.0001) (0.0169) (0.0044) 0.9939 17026.8 F ance 0.0036* 0.2692* 0.0424* 0.9218* 0.9886 5.6243* F ance 0.0015* 0.2108* 0.9696* 0.0064* 0.9962 8.4791* (0.0004) (0.0263) (0.0197) (0.0143) 0.9459 (0.3983) (0.0002) (0.0162) (0.0047) (0.0020) 0.9900 (0.8214) 0.0002* 0.0008* 0.1465* 0.9834* 0.9459 LL 0.0008* 0.2375* 0.9694* 0.9900 LL (0.0001) (0.0001) (0.0122) (0.0023) 0.9221 15137.2 (0.0001) (0.0148) (0.0036) 0.9846 15975.4 Ge many 0.0028* 0.2667* 0.0545* 0.9373* 0.9881 5.2190* Ge many 0.0009* 0.2233* 0.0187* 0.9726* 0.9964 8.4130* (0.0003) (0.0221) (0.0152) (0.0089) 0.9603 (0.3334) (0.0002) (0.0145) (0.0075) (0.0033) 0.9959 (0.8164) 0.0009* 0.1445* 0.9835* 0.9603 LL 0.0009* 0.2358* 0.9700* 0.9959 LL (0.0001) (0.0109) (0.0022) 0.9496 15196.3 (0.0001) (0.0146) (0.0036) 0.9957 15919.6 I aly 0.0021* 0.2426* 0.9596* 0.9898 5.6196* I aly 0.0017* 0.2335* 0.9597* 0.0044* 0.9964 8.6295* (0.0003) (0.0216) (0.0072) 0.9796 (0.3938) (0.0002) (0.0193) (0.0068) (0.0017) 0.9859 (0.8451) 0.0008* 0.1435* 0.9845* 0.9795 LL 0.0008* 0.2336* 0.9705* 0.9859 LL (0.0001) (0.0121) (0.0022) 0.9795 14977.0 (0.0001) (0.0154) (0.0037) 0.9755 16217.8 Japan 0.0025* 0.3386* 0.9317* 0.9891 5.1422* Japan 0.0021* 0.2112* 0.9682* 0.0060* 0.9936 8.4674* (0.0003) (0.0231) (0.0085) 0.9827 (0.3418) (0.0003) (0.0171) (0.0052) (0.0025) 0.9893 (0.8384) 0.0008* 0.1569* 0.9821* 0.9681 LL 0.0008* -0.0115* 0.2323* 0.9712* 0.9874 LL (0.0001) (0.0128) (0.0025) 0.9681 14885.1 (0.0001) (0.0058) (0.0151) (0.0036) 0.9874 15240.8 UK 0.0028* 0.2601* 0.9355* 0.9851 6.0111* UK 0.0014* 0.2192* -0.0943* 0.9575* 0.0317* 0.9976 9.0840* (0.0004) (0.0270) (0.0130) 0.9583 (0.3949) (0.0002) (0.0168) (0.0190) (0.0063) (0.0070) 0.9781 (0.8752) 0.0003* 0.0009* 0.1631* 0.9791* 0.9583 LL -0.0006* 0.0008* 0.0561* 0.2347* 0.9626* 0.9658 LL (0.0001) (0.0001) (0.0130) (0.0028) 0.9428 15437.0 (0.0002) (0.0002) (0.0145) (0.0160) (0.0043) 0.9513 16511.2 No es: See Table 2. 24 Table 4: Likelihood Ra io Tes s Canada F ance Ge many I aly Japan UK 1s subsample LR-s a . 0.8529 3.1034 3.0371 2.8405 11.2143 2.0793 d. . 6 6 7 8 8 7 p- alue 0.9906 0.7958 0.8815 0.9440 0.1898 0.9553 2nd subsample LR-s a . 4.4864 4.8151 3.1584 2.4012 3.6086 2.6975 d. . 5 5 5 6 6 2 p- alue 0.4817 0.4389 0.3969 0.8794 0.7295 0.2596 No es: The null hypo hesis es ed is: Res ic ed Model p e e ed o Un es ic ed Model. Table 5: His o ical Shocks Canada F ance Ge many I aly Japan UK C ash 1987 Z10 -9.74 -3.99 -2.46 -3.63 -7.28 -8.63 Z20 -14.04 -16.85 -16.97 -17.39 -17.32 -15.74 Asian C isis Z10 -8.83 0.68 -0.41 -0.82 -1.37 0.96 Z20 -4.24 -7.47 -7.07 -6.82 -6.85 -7.05 Twin Towe s Z10 1.16 0.68 -0.41 -2.37 -1.97 2.79 Z20 -5.27 -7.47 -7.07 -4.65 -4.88 -5.76 Table 6: Ini ial S a e H0 Canada F ance Ge many I aly Japan UK h11,0 0.7390 1.0380 1.0517 0.5925 1.4174 0.5321 h12,0 0.3397 0.4019 0.4491 0.1299 0.2504 0.1942 h22,0 0.5724 0.5587 0.5553 0.5486 0.5272 0.5993 No es: Figu es a e exp essed in 10-4.