Jan., Volume 9, No. (Serial No.79) Cinese Business Reiew, ISSN 537-56, USA Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns Wann-Jyi Horng, Yu-Ceng Cen, Weir-Sen Lin (Deparmen of Hospial and Heal Care Adminisraion, Cia Nan Uniersiy of Parmacy and Science, Tainan 77, Taiwan) Absrac: Tis paper discusses e model consrucion and e associaion beween e Ialy and e Germany s sock markes. Te period of sudy daa is from January 3, o June 3, 8. Tis paper also uilizes Suden s disribuion o analyze e proposed model. Te empirical resuls sow a e wo sock markes are muually affeced eac oer, and e dynamic condiional correlaion (DCC) and e biariae asymmeric-garch (, ) model is appropriae in ealuaing e relaion beween em. Te empirical resul also indicaes a Ialy and Germany s sock markes sow a posiie relaionsip. Te aerage alue of correlaion coefficien equals o.844, wic implies a e wo sock markes reurn olailiy ae a syncronized influence on eac oer. In addiion, e empirical resul also sows a ere is an asymmerical effec beween Ialy and e Germany s sock markes, and demonsraes a e good news and bad news of e sock reurns olailiy will produce e differen ariaion risks for Ialy and e Germany s sock price markes. Key words: sock marke reurns; GARCH model; asymmeric effec; GJR-GARCH model; biariae asymmeric GARCH model. Inroducion As is known o all, Germany is one of big eig indusrial counries in e global economical financial sysem and also as been ery influenial in e global economy. Germany is also a counry wi ig producion and in ig income leels, and is social welfare is exremely deeloped and e life is exremely wealy. For example, e domesic producion gross aciees o,49 billion Euros in 5, wic grows.9% compared wi in 4 (daa source: Te Federaion Saisics Bureau). In addiion, e expor alues of German enerprises are occupied /3 of e domesic producion gross. Wen e inesor as an inesmen in inernaional sock marke, e/se will usually care abou e inernaional capial, e moion siuaion, e inernaional poliics and e economical siuaion cange, in paricular, Ialy sock marke cange. Tere is a close relaionsip for Ialy based on e rade and e circulaion of capial wi Germany, bu Germany is also a powerful global economical naion. Terefore, e relaionsip beween Ialy s sock marke and Germany s sock marke is wor furer discussion. Wi e exisence of many reurn olailiy meods (e.g. auoregressie moing aerage (ARMA) model), researcers commonly used o inesigae e relaions beween wo sock markes. Engle (98) proposed e Wann-Jyi Horng, P.D., associae professor, Deparmen of Hospial and Heal Care Adminisraion, Cia Nan Uniersiy of Parmacy and Science; researc fields: saisics, economerics, daa analysis. Yu-Ceng Cen, P.D., associae professor, Deparmen of Hospial and Heal Care Adminisraion, Cia Nan Uniersiy of Parmacy and Science; researc fields: saisics, daa analysis, daa mining. Weir-Sen Lin, P.D., associae professor, Deparmen of Hospial and Heal Care Adminisraion, Cia Nan Uniersiy of Parmacy and Science; researc fields: eal care managemen, biosaisics. 3
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns auoregressie condiionally eeroskedasiciy (ARCH) model and Bollersle (986) proposed e generalized auoregressie condiionally eeroskedasiciy (GARCH) model. According o em, is kind of model is comparaiely beer a cacing e financial propery wile e condiional ariance does no ae e fixed caracerisic. Nelson (99) looked a sock price canges and discoers a ere are bo posiie and negaie relaionsips wi e fuure sock price olailiy. Te GARCH model supposes a e seled ime condiional ariance is a funcion of condiional ariance and an error erm square erm s ime lags. Terefore, error erm s posiie and negaie alues do no respond o is influence on e condiional ariance equaion. Te condiional ariance can only cange along wi e error erm s alue, bu canno go along wi e error erm s posiie and negaie canges. To improe is flaw, Nelson (99) presened an exponenial GARCH model and Glosen, Jagannaan and Runkle (993) gae a resold GARCH model. Tese models are so-called e models of asymmeric-garch. Teir models are adoped by many scolars, wile researcing on e issue of asymmeric problems suc as Horng (7), Brooks (), Poon and Fung (), Crisie (98), Frenc, Scwer and Sambaug (987), Campell and Henscel (99), Koumos and Boo (995) and Koumos (996). Researc on e relaion beween sock marke and e reurn olailiy meod, using muliariae GARCH model, as been growing like musroom. For examples, Yang (5), Yang and Doong (4), Granger, Hung and Yang (), Wang and Barre () and Bollersle (99) ae applied arious biariae GARCH models analyzing sock marke price. Te purpose of is paper is o examine e relaions of Ialy s sock marke and Germany s sock marke, using e DCC and e biariae asymmeric-garch model in consrucing e connecion of e wo sock markes. And using e posiie and negaie alues of sock rerurns olailiy are as e resold. Te organizaion of is paper is as follows: Secion descibes e series caracer of Ialy and Germany sock prices and eir reurns olailiy; Secion 3 inroduces e model of e DCC and e biariae GARCH; Secion 4 presens e asymmeric es of e DCC and e biariae-igarch model; Secion 5 presens e model of e DCC and e biariae asymmeric-garch and is parameers esimaion, and e analysis beween associaed of Ialy and Germany sock reurns; Finally, secion 6 summarizes e conclusions and suggesions of is sudy.. Daa caracerisics. Daa sources Te daa of is researc included e oil price, Ialy and Germany s sock price colleced beween January 3, and June 3, 8. Te source of e sock daa was e Taiwan Economic Journal (TEJ), a daabase in Taiwan. Ialy sock price refers o e MIBTEL sock index, and Germany s sock price refers o DX sock index. During e process of daa analysis, in case a ere was no sock marke price aailable on e side of Ialy s sock marke or Germany s sock marke due o olidays, e idenical ime sock price daa from one side was deleed. Afer is, e ree ariables samples are,4.. Reurns calculaion and rend cars To compue e reurn of Ialy sock marke, e auors adop e naural logarim difference, and ride again. Te reurn of Germany s sock marke also deried from e naural logarim difference, rides again. Fig. sows e rend cars of Ialy s sock price index (ITA) (see Fig. a), Germany s sock price index (GER) (see Fig. b), e rend cars of Ialy s sock price index reurn (RITA) (see Fig. c) and Germany s sock price 4
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns index reurn (RGER) (see Fig. d) in e sample period. 36 9 3 8 8 4 7 6 5 4 6 3 5 5 5 5 IT A Fig. a G E R Fig. b 8 6 4 - -4-6 -8 8 4-4 -8-5 5 5 5 R ITA R G E R Fig. c Fig. d Fig. Trend cars of Ialy and Germany s sock price index and is reurn As can be seen in Fig., in e seleced sample period, Ialy s sock price index and Germany s sock price index obiously sow e same direcion of e rend. Wen e flucuaion of Germany s sock price index grew bigger, Ialy s marke reurn olailiy degree will also became bigger. In addiion, e clusering of Ialy and Germany s sock price reurn olailiy sowed e same paern. I seems a e wo sock markes ae a cerain leel of releance. In oer words, e wo sock prices markes seemed o be inerdependen. Tis is also e main moie for discussing e relaionsips of Ialy and Germany s sock price reurns..3 Basic saisics Table presens e basic saisics of e analysis including e mean alues, sandard deiaions, skewed coefficiens, kurosis coefficiens and e Jarque-Bera normal disribuion es for e sampled period of e oil price olailiy, Ialy and Germany s sock marke reurns. Te kurosis coefficiens were wor menioning. Te wo reurn sequences kurosis coefficiens are bo bigger an 3, wic implies a e normal disribuion es of Jarque-Bera is no normal disribuion. Aloug e iolaion of normal disribuion is no uncommon for financial commodiy ariable, i is more appropriae o carry ou e analysis, using e eay ail disribuion and e GARCH model. Also e resuls from ADF and KSS uni roo ess indicaed a e wo sock markes reurn ariables were in a sable sequence. Te sable caracerisic analyzes e essenial condiion of e GARCH model..4 Uni roo es 5
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns Furermore, is sudy uses ADF (Augmened Dickey & Fuller, 979; Augmened Dickey & Fuller, 98) and KSS (Kapeanios, e al., 3) uni roo wen examining e U.S. sock price index and Canada s sock price index, and deciding weer e uni roo caracerisic, used o examine weer e ime series daa as sabiliy, no as for appears e false reurn (spurious regression). As sown in Table, e firs order difference afer e ime series daa was analyzed a e significance leel of. ( %). Te maerial e researcers used was in a sable condiion. In oer words, e sock reurns of Ialy and Germany are in saionary sequence. Table Daa saisics Saisics ITA GER RITA RGER Mean 5,335.38 5,35.87 -.999 -.36 S-D 5,3.4,59.8.3394.563838 Skewed -.7568.676 -.374 -.5883 Kurosis.873.845445 6.758 6.73558 J-B N (p-alue) 4.663 (.) 9.979 (.),7.86 (.) 847.6 (.) sample,4,4,4,4 Noes: J-B N is e normal disribuion es of Jarque-Bera; S-D denoes e sandard deiaion; p-alue< denoe significance ( %). Table Uni roo es of ADF and KSS for e reurn daa ADF ITA GER RITA RGER Saisic -.3367 -.448 -.69*** -9.6747*** Criical alue -3.963-3.49-3.79 (Significan leel) ( %) ( 5%) ( %) KSS ITA GER RITA RGER Saisic -.379 -.37 -.9386*** -7.345*** Criical alue -.8 -. -.9 (Significan leel) ( %) ( 5%) ( %) Noes: *** denoes significance a e leel %..5 Co-inegraion es Using Joansen s (99) co-inegraion es as illusraed in Table 3 a e significance leel of.5 ( 5%) does no reeal of λ max and Trace saisics. Tis indicaed a Ialy s sock marke and Germany s sock marke do no ae co-inegraed relaion. Aloug e wo sock markes do no seem o ae a long-erm co-inegraed relaion, e resuls implied a ere was a muual affec beween e wo markes in Table 4. Terefore, i is necessary o furer undersand e gearing relaion beween e wo markes. H Table 3 Joansen co-inegraion es (e lag of VAR is 5) λ max Criical alue ( 5% ) Trace Criical alue ( 5% ) None 6.454 6.87 9.338 8.7 A mos.8787 3.74.8787 3.74 Noes: Te lag of VAR is seleced by e AIC rule (Akaike, 973). 6
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns Table 4 Uncondiional correlaion marix of Ialy and Germany Coefficien ITA GER Coefficien RITA RGER ITA.958 RITA.886 GER.958 RGER.886.6 ARCH effec es Furer examinaion, using e ARCH effec es, was conduced o deermine weer e sock reurn olailiy as e condiionally eeroskedasiciy. Tis researc used e Ljung-Box (978) es meod, e Lagrange muliplier (LM) es meod proposed by Engle (98) and e F disribuion es meod proposed by Tsay (4). Tese meods were used o furer confirm residual error sequence ariance and decided weer ere was e ARCH effec. In case of e presence of e ARCH effec, e GARCH model would be used o mac suiably. Te ARCH effec es uses e pas q ime lags of e residual error square o carry ou e regression analysis. Te ARCH effec es is based on e AR (3) model in e equaion (4) and equaion (5) as below. Is maemaial form is as follows: a ˆ ˆ L ˆ + () d + d a + + d q a q Te auors es e null ypoeses H : d d L d q by equaion (). Wen H is rejeced, i implies a ere is no effec of ARCH, a is, we can use e model of e GARCH o fi i. LM, F and Ljung-Box (L-B) es meods were employed o examine e sock price dae reurn and examine weer ere was e condiionally eeroskedasiciy penomenon. Te examinaion resul of e ARCH effec es is lised in Table 5. As illusraed, Ialy and Germany s sock price reurn analysis model reealed a e series a e leel of.5 ( 5%) as e condiionally eeroskedasiciy penomenon. Tis suggesed a maced suiably analysis model may use e GARCH model. Table 5 ARCH effec es Ialy Engle LM es Tsay F es L-B es LB (3) LB (6) LB (7) Saisic 649.555 6.353 7.4734 4.3864 4.6694 (p-alue) (.) (.) (.) (.) (.) Germany Engle LM es Tsay F es L-B es LB () LB (3) LB (6) Saisic 765.83.98 5.499 6.769 5.477 (p-alue) (.) (.) (.) (.) (.) Noes: p-alue < denoes significance ( %). 3. GJR-GARCH and biariae GARCH models If only single ariable GARCH model analysis is conduced, en e sock reurn olailiy is only allowed o cange as necessary. In case like is, i is easy o neglec Ialy and e Germany s sock price reurn olailiy ariance srucure. I is likely o creae e esimae wiou e efficiency and e deducion arms. Two socks reurns olailiy condiional ariance bo faors canges as necessary. Te biariae GARCH model simulaneously considered wo sock markes olailiy on e ime dependence. Terefore, is paper uses e biariae GARCH model o discuss e impac a Ialy s sock marke reurn olailiy as on Germany s sock marke reurn and e relaion beween e wo sock prices markes. 7
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns 3. Inroducion of GJR-GARCH model Glosen, Jaganaan and Runkle (993) proposed e GJR-GARCH model. Tis model as e differen influence of e good and bad news on e maerial olailiy. Te general form of GJR-GARCH model may be esablised as follows: were wi a is wie noise, q + i D + D a,, a > denoes good news, and a i i if a if a p η + j > β () j j a denoes bad news. Regarding e GJR-GARCH model, under e good news and bad news, e influences of e condiion error square iem are dissimilar. Take an example wi q, wen ere appears e good news, e error square iems olailiy coefficien is ; Wen appears e bad news, e error square iems olailiy coefficien is +η. Wen η, e impac response of e condiion error square iem is symmerical; Wen η, e impac response of e condiion error square iem is asymmerical, a is ime, e effec is called e asymmeric effec. 3. DCC and biariae GARCH model From e inspecaion of e resuls from e aboe menioned ables, i is known a Ialy and Germany s sock reurn bo ae e condiionally eeroskedasiciy, lepokuric and e saionary sequence saisical caracerisic. Terefore, i is suggesed a e biariae GARCH model sould be used o analyze e relaions beween Ialy and Germany s sock marke reurns. In is paper, e DCC and biariae GARCH model proposed by Engle () and Tse and Tusi () are used o analyze e connecion beween Ialy and Germany s sock price reurns. Te resul of e normal disribuion es of Jarque-Bera sows a e sudy daa is no a normal disribuion. In addiion, e kurosis coefficiens are bigger an 3. We sould use disribuion of e eay ails and i is comparaiely suiable. Terefore, is paper uses e Suden s disribuion of eay ails, and uses e maximum likeliood algorim meod of BHHH (Bernd, e al., 974) o esimae e unknown parameers. Te biariae GARCH model may be consruced from equaion (4) o equaion (). Tis model is used as a baseline o discuss Ialy s sock price reurn olailiy and is impac on Germany s sock price reurn. Te GARCH (, ) models are saed as follows: a ( a,, a, ) n n RITA + φ j RITA j + φ j RGER j + a, j j φ (4) n n RGER + ϕ j RGER j + ϕ j RITA j + a, j j ϕ (5), + a, + a, + β, (6), + a, + a, + β, (7), ρ,, (8) ρ exp( q ) /(exp( q ) + ) (9) q + + ρ a, a, /,, () obey e biariae Suden s disribuion, is is, T (,( ) H / ), among (,) and (3) 8
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns,, H,,, densiy funcion of coefficien of a, and a,,,, and is e degree of freedom of Suden s disribuion. Te probabiliy a is referred in e book of Tsay (4). Te ρ is e dynamic condiional correlaion. 4. Model esimaion and analysis 4. Biariae GARCH model and is parameer esimaion Tis secion uses e DCC and biariae GARCH model, i.e., equaion (4) o equaion () o analyze e relaedness of Ialy and Germany s sock price reurn olailiies. Te empirical resuls sow a Ialy and Germany s sock price reurn olailiy may be based on e DCC and biariae IGARCH (, ) model. Is esimae resuls are in Table 6. Table 6 DCC and esimaion of e biariae IGARCH (, ) model Parameers φ φ 3 φ 3 ϕ ϕ 3 Coefficien.779.68 -.6.976 -.977 (p-alue) (.) (.56) (.4) (.) (.5) Parameers ϕ 3 β Coefficien.9.8.36.474.964 (p-alue) (.46) (.) (.38) (.79) (.) Parameers β Coefficien.58.583.55.96 6.6373 (p-alue) (.) (.9) (.396) (.) (.) Parameers Coefficien 7.484-6.74.35.8493 (p-alue) (.) (.4) (.799) (.) Noes: According o equaions: RITA φ + φ3rita 3 + φ3rger3 + a, ; RGER ϕ + ϕ3rger3 + ϕ 3RITA 3 + a, ; + + a, a, + β, ;, + a, + a, + β, ; q + + ρ a, a, /,, ;, ρ exp( q ) /(exp( q ) + ) ;, ρ,,. p-alue< denoes significance ( %, 5%, %); Te minimum esimaed alue of condiional correlaion ρˆ.7 and e maximum esimaed alue of condiional correlaion coefficien equals coefficien equals maximum likeliood funcion alue of naural logarim equals L -7.777. f ρ ρˆ.979; Te 4. Diagnosis analysis of asymmeric for e biariae IGARCH model Because of e parameer esimaion and e sandard residual error diagnosis in e below DCC and biariae IGARCH (, ) model, e examinaion can only ceck if e model maces up wi e suiable qualiy, bu i is acually unable o look up weer e model as an asymmerical penomenon. Terefore, Engle and Ng (993) deelop a diagnosis es in order o examine weer e model as asymmerical risk or no. Tis researc uses is diagnosis es o carry ou e examinaion. Engle and Ng (993) beliee a by obsering e ariables pas alue, i is possible o forecas e 9
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns sandardized residual error square ( a / σ ), σ ( ( ) / ) /. Howeer, if ere is no forecas paern of e ariables pas alue, en e expression model may be se up misakenly. Terefore, e examinaion meod of e model ypoeses as e following four examinaion meods: () Sign bias es: () Negaie size bias es: (3) Posiie size bias es: (4) Join es: ( a / ) b + b S + e () ( / ) b + bs ( a / ) a + e ( / ) b + b ( S )( a / ) a + e ( a / ) b + bs + bs ( a / ) + b3 ( S )( a / ) + e (4) were S is e dummy ariable, as a, en S ; a >, en S. Afer e aboe four of examinaion resuls, Table 7 asymmerically examines e resul for Ialy s sock price marke as: () e sign bias es reeals ( %); () e negaie size bias es reeals ( %); (3) e posiie size bias es reeals ( %); (4) e join es reeals ( %). And Table 7 also asymmerically examines e resul for e Germany s sock price marke as: () e sign bias es reeals ( %); () e negaie size bias es reeals ( %); (3) e posiie size bias es reeals ( %); (4) e join es reeals ( %). By e posiie size bias es and e join es, i sows a Ialy and Germany s sock price markes do ae e asymmery effecs. Table 7 Asymmeric es of e biariae IGARCH (, ) Ialy Sign bias es Negaie size bias es Posiie size bias es Join es F saisic.99 3.579 3.945.473 (p-alue) (.9) (.) (.) (.) Germany Sign bias es Negaie size bias es Posiie size bias es Join es F saisic 7.3966 7.337.875 3.8 (p-alue) (.) (.) (.) (.) Noes: p-alue < denoes significance ( %, 5%, %). 5. DCC and biariae asymmeric-garch model and model cecking 5. DCC and biariae asymmeric-garch model and parameer esimaion Based on e resuls of e posiie size bias es and e join es, we may use e GARCH model of asymmeric o discuss Ialy and Germany s sock price reurn olailiy process. Following e idea of GJR-GARCH model, e use of e posiie and negaie alue of Ialy and Germany s sock reurn olailiy is a resold, respeciely. Afer model process selecion, in is paper, we may use e asymmeric-garch (, ) model o discuss e olailiy model consrucion of e Ialy s and e Germany s sock price reurn, e model is illusraed as follows: RITA u φ + φ RITA + φ RGER + a ) + ( 3 3 3 3, u )( φ + φ RITA + φ RGER + a ) (5) ( 3 3 3 3, () (3) 3
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns RGER w ϕ + ϕ RGER + ϕ RITA + a ) + ( 3 3 3, w )( ϕ + ϕ RGER + ϕ RITA + a ) (6) ( 3 3 3 3,, u,, +, ( + a + a β ) + u )( a + β ) (7) (,, ( w )( a, + β, ( + a + a β ) + ) (8), w,, +, q, ρ,, (9) ρ exp( q ) /(exp( q ) + ) () + + ρ a, a, /,, (), if RITA, u, w if RGER (), if RITA >, if RGER > wi RCANA > and RUSA > denoe good news, RCANA and RUSA denoe bad news. Te wie noise of a ( a,, a, ) also obeys e biariae Suden s disribuion and is funcion form is defined as aboe. Tis secion uses e DCC and e biariae asymmeric-garch model, namely uses equaion (5) o equaion (), o discuss Ialy s and Germany s sock price reurn olailiies relaedness analysis. Parameers esimaion firsly considers a general model, and bases on e esimaed resuls. Ten, e auors delee some nonsignifican explanaion ariables, and finally obain a simplificaion model for Ialy and Germany s sock price reurn olailiies relaedness analysis. From e empirical diagnosis resul, we know a Ialy and Germany s sock price reurn olailiy may be consruced on e DCC and biariae asymmeric-garch (, ) model. Is esimae resul is saed in Table 8. Based on e esimaed resuls of e DCC and e biariae asymmeric-garch (, ) model in Table 8, e auors es e esimaed alue of parameers coefficien o be significan or no wi a p-alue. Under e bad news and e good news, e obseraion condiion s consan erm coefficien does ae significan influence under e % significance leel in Ialy. If e inesors ae a long-erm iew on an inesmen sock in Ialy, ey are able o obain a cerain degree of reurn. Under e bad news, Ialy s sock price reurn receies before 3 days impac of Ialy s sock marke reurn ( φ 3.7). Under e good news, Ialy s sock price reurn olailiy does also receie before 3 days influence of Germany s sock price reurn ( φ 3 -.645). Under e bad news, e obsered mean equaion of e esimaed coefficien demonsraes a e obseraion condiion s consan erm coefficien does ae significan influence under e % significance leel in Germany. If e inesors ae a long-erm iew on an inesmen sock in Germany, ey are able o obain a cerain degree of reurn. Under e bad news and good news, Germany s sock price reurn receies before 3 days impac of Ialy ( ϕ 3.657 and ϕ 3.7, respeciely). Under e bad news, Germany s sock price reurn receies before 3 days impac of Germany s sock marke reurn ( ϕ 3 -.593). On e oer and, e correlaion coefficien aerage esimaion alue ( ρˆ.844) of Ialy and Germany s sock price reurn olailiy is significan. Tis resul also sows a Ialy s sock price reurn olailiy is e posiie influence o Germany s sock price reurn s olailiy, and ey are precisely e syncronized muual influence. Wen e ariaion risks of Ialy s sock price reurn increases, e inesors risk of Germany s sock price reurn is able o increase. Likewise, wen e ariaion risks of Ialy s sock price reurn reduce, e inesors risk of e Germany s sock price reurn is also able o reduce. In addiion, e esimaed alue of e degree of freedom for e 3
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns Suden s disribuion is 6.7345, and is significan under e significance leel of. ( %). Tis also demonsraes a is researc daa as e eay-ailed disribuion. Tis resuls as aboe are consisen o e esimaed resuls of e biariae IGARCH (, ) model. Te obsered condiional ariance equaion of e esimaed coefficien, under e % significance leel, demonsraes a all e condiional ariance esimaed coefficiens are significan in Table 8. From e Table 8, e esimaed coefficiens of e condiional ariance equaion will produce differen ariaion risks under bad news and good news. We ae e resuls a + + β, + β. 898, + + β and + β.935. Tis resuls conforms e assumed condiions of e IGARCH model and GARCH model, respeciely. Tis resul also demonsraes a e DCC and e biariae asymmeric-garch (, ) model may cac Ialy and Germany s sock price reurn olailiies process. Bu is model also needs furer researc o carry on e diagnosic analysis of e sandard residual error, and e deail will be proided as below. Under e bad news, Ialy s sock marke as a fixed ariaion risk and Germany s sock marke as also e fixed ariaion risk. Besides, aking e good news as a sample, Ialy and Germany s sock marke reurns ae differen condiional ariable risks (respeciely, β. 78 and β. 834). Tis demonsraes a bo e good news and bad news of e sock reurns olailiy will produce e differen ariaion risks of Ialy and Germany s sock price markes. Based on e likeliood raio es, e es resul is also suppored e biariae asymmeric-garch (, ) model in Table 8. Terefore, e explanaory abiliy of e DCC and e biariae asymmeric-garch (, ) model is beer an e model of e DCC and e biariae IGARCH (, ). Table 8 Parameer esimaion of e DCC and e biariae asymmeric-garch (, ) model Parameers φ φ 3 φ 3 φ φ 3 φ 3 Coefficien.54.7 -.466.448.53 -.645 (p-alue) (.8) (.98) (.5) (.7) (.855) (.9) Parameers ϕ ϕ 3 ϕ 3 ϕ ϕ 3 ϕ 3 Coefficien.974 -.593.657.34 -.46.7 (p-alue) (.4) (.) (.5) (.569) (.9) (.975) Parameers β β Coefficien..8.367.745.6.78 (p-alue) (.) (.) (.) (.) (.) (.) Parameers β β Coefficien.97.96.3.7763.8.834 (p-alue) (.587) (.) (.) (.) (.3) (.) Parameers Coefficien -.99 5.5336.84 6.7345.844 (p-alue) (.4) (.) (.3) (.) (.) Noes: p-alue< denoes significance ( %, 5%, %); Te minimum esimaed alue of condiional ρˆ.6 and e maximum esimaed alue of condiional correlaion coefficien equals L -67.899 and -[ L - L ]56.357. () correlaion coefficien equals Te maximum likeliood funcion alue of naural logarim equals χ () 8.37, χ () 3.93..5. f f r ρ. ρˆ.; χ 5.987, 5. Model cecking of e sandard residual for e DCC and biariae asymmeric-garch model 3
Reurn resold model analysis of wo sock markes: Eidence sudy of Ialy and Germany s sock reurns To correc e inappropriaeness of e DCC and e biariae asymmeric-garch model, Ljung-Box es meod is used o furer examine e sandard residual error and a sandard residual error square iem and o see weer ere sill exiss auo-correlaion. Tables 9 sows e Q es of e sandard residual error and Q es of e sandard residual error square iem wi a p-alue. Clearly, is model does no ae e auo-correlaion. From Tables, we can see a e proposed model does no ae e ARCH effecs of sandard residual error square iem. Terefore, e DCC and biariae asymmeric-garch (, ) model maces quie suiably and is more appropriae. Table 9 L-B Q es of sandard residual and sandard residual square iem of e DCC and biariae asymmeric-garch (, ) Ialy L-B es LB () LB () LB (5) LB () LB () LB (5) Q saisic 8.76.97 3.9798.67 7.9849 8.55 (p-alue) (.5583) (.97) (.96) (.3877) (.5884) (.894) Germany L-B es LB () LB () LB (5) LB () LB () LB (5) Q saisic.86.964 5.58 9.449 4.9855 8.959 (p-alue) (.979) (.97) (.4345) (.49) (.777) (.8383) Noes: p-alue < denoes significance ( %, 5%, %). Table ARCH effec (L-B) es of e sandard residual of e DCC and biariae asymmeric-garch (, ) Ialy LB () LB () LB (3) Q saisic.8349.9.844 Saisic.75 (p-alue) (.439) (.833) (.776) (p-alue) (.8747) Germany LB () LB () LB (3) Q saisic.7583.35.67 Saisic.64 (p-alue) (.4484) (.756) (.958) (p-alue) (.934) Noes: p-alue < denoes significance ( %, 5%, %). F es F es 6. Conclusions Tere are many facors a mig ae grea influence on sock prices including oerall economic agens and oerall currency supplies, ineres rae, price and inflaion rae. Eac facor may ae influence on e sock price reurn. Tis researc discusses wo marke reurn olailiies influence of Ialy and Germany. e auors use daa from January 3, o June 3, 8. Te empirical resul sows a Ialy and Germany s sock price marke reurn s olailiy as an asymmeric effecs, and Ialy and Germany s sock price reurn olailiy may consruc in e DCC and e biariae asymmeric-garch (, ) model wi a resold of oil price olailiy. Tis model also passes roug a sandard residual error and e ARCH effec es. Tis siuaion demonsraes a e DCC and biariae asymmeric-garch (, ) model s fiing is appropriae. Te empirical resul also obains a e dynamic condiional correlaion coefficien alue ( ρˆ.844) of Ialy and Germany s sock price reurn olailiy is posiie. Tis resul demonsraes a Ialy s sock reurn olailiy is affecing Germany s sock reurn olailiy, and Germany s sock reurn olailiy is also affecing Ialy s sock reurn olailiy. Te empirical resul also discoers a Ialy and Germany s sock price marke reurns olailiy as an asymmerical penomenon. Te posiie and negaie alues of e sock reurn olailiy affec e ariaion risks of Ialy and Germany s sock 33
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