ֻ19जֻ5௹࠹აྐ༏ંฆ୍9ᄅ Sept.,2004 ࠹ႋႨ࣮ ᇏݓܢ൧թᄝ ჿೣڏ ིႋગ? 对我国股票市场的实证分析马 丹(༆ଲҍࣜն࿐࠹࿐ჽ,ඹԫӮ610071)ᅋ ေ: ჿೣིႋ ࠧӉ࠺ၫྟ,൞ᆷܢௐࡎ۬թᄝӉ௹ӻ࿃ა٤ᇛ௹֥࿖ߌགྷའbູਔؓݓᆣಊ൧ӆ֥Ӊ࠺ၫྟቔбࢠಆ૫֥ٳ༅,໓ᅣ࿊౼ഈᆣሸކᆷඔބധᎪӮٳᆷඔ,ٳࢨ؍০ႨR/SٚمaARFIMAݖӱট്љ൬ၭੱ֥࠺ၫหᆘ,ѩႨFIGARCHଆটख़߂ѯ֥࠺ၫหᆘbٳ༅ؿགྷ,hurstᆷඔၛࠣARFIMAଆіૼ൬ၭੱਙթᄝбࢠັ֥Ӊ࠺ၫหᆘ,ط০ႨFIGARCHଆᄵؿགྷਙ֥ѯթᄝࢠ఼ູਛ֥Ӊ࠺ၫྟbܱՍ:Ӊ࠺ၫ;R/Sٳ༅;ARFIMAଆ;FIGARCHଆᇏٳোݼ: ໓ངѓ്:A ໓ᅣщݼ:1007-3116(2004)05-0068-05 20ൗࡀੂ୍սણ֣غ҃અห( ᆀሹॖၛ۴ऌݖಀ֥ྐ༏ᄝ၂קӱ؇ഈҩໃট֥delbrot)ؓႵི൧ӆࡌඪิԛਔ఼Ⴕ৯֥็ᅞb൬ၭ,ၹՎӉ࠺ၫ֥թᄝགྷսࣁವࠎെ Ⴕིؿགྷ൬ၭੱ֥ٳ҃൞ࡕڂແ֥,ط൬ၭੱਙ൧ӆࡌഡ(EMH)ӞָാϧbߎӯགྷӉ௹ཌྷܱ,ྟѩऌՎิԛਔܢௐࡎ۬ ֥୶1968୍M1]andelb[rotᄝषԷྟ֥۽ቔᇏ൮ིႋ (NoahEffect)ބ ჿೣིႋ (JosephEffect)bՑႄࣉਔٳඔ҃ᄎࠣٳྙ֥קၬ,קਔӉ࠺෮ ໌୶ིႋ ൞ᆷܢௐࡎ۬غ߶ؿള҂৵࿃aၫٳ༅֥ࡔൌ֥ඔ࿐ࠎԤb֞80୍ս,࠹ਈࣜ࠶࿐ؿྟ֥ն๋ᄁ,ѩᄝ၂۱ն๋ᄁުӈ۵ሢ၂۱նࡅૌषᇿၩ֞Ӊ࠺ၫ࣮ᄝࣜ࠶ࣁವ֩ਵთ֥ᇗ๋ᄁ,ᄝ၂۱ཬ๋ᄁު૫ӈ۵ሢ၂۱ཬ๋ᄁ,ᆃ֝ᇁնቔႨb80୍սԚ,GrangerandJoyeux(1980)andܢௐ൬ၭ֥ٳ҃ԛགྷࡕڂިແ֥གྷའ; ჿೣིႋ Hosking(1981[2])֩ದؓԮ֥ARMAଆࡆၛ൞ᆷܢௐࡎ۬թᄝӉ௹ӻ࿃ა٤ᇛ௹֥࿖ߌགྷའ,ঔᅚ,ิԛਔٳඔྙླྀᆜ֥ARFIMAଆ,ؓऎᆃ֝ᇁ൬ၭթᄝӉ௹ཌྷܱྟbᆃਆ۱ིႋ֥ؿགྷൌႵٳඔົ֥ൈࡗਙ࣮ࣉೆ၂۱ྍࢨ؍b1996࠽ഈࢣषਔਆোൈࡗਙ࣮֥ٚم֥ଞbఃᇏ୍,Baillie,BollerslevandMikkelsen[3]ᄝEngle֥ᆭ၂൞ض۬غ֥ARCHଆ,ൌᆣ࣮іૼᆃোଆARCHଆࠎԤᆭഈ,ิԛਔّ႘ѯੱӉ࠺ၫྟ൞ѽሚ ୶ིႋ ֥མ۽ऎbਸ਼၂۱ᄵ൞ၛٳ֥FIGARCHଆ,ᆃննิۚਔ࠹ਈࣜ࠶ٚمؓᆜሱ݂߭၍नଆູսі֥۲োٳᆜଆbऎႵӉ࠺ၫหᆘ֥ࣁವ൧ӆ֥ख़߂৯؇b一a研究背景ؓᆣಊ൧ӆ֥Ӊ࠺ၫٳ༅൞୍࣍টࢠູಣ֥߅ีbٳ༅ٚمޓ؟Їওѓ؇ંބ۲ᇕӉ࠺ၫଆൈࡗਙ֥Ӊ࠺ၫྟ൞ᆷਙᇏཌྷएࢠჹ֥ൈbఃᇏѓ؇ં൞࣮ࣁವگᄖྟ໙ี֥ᇗေࡗࡗۯऎႵཁᇷ֥ሱཌྷܱT,ྟࠧlim | ( ંބٚم,္൞ࣁವ۽ӱྍ֥࣮ज़ีb۴ऌѓ؇)|= bT =1ೂݔሧӁ൬ၭੱऎႵࢠӉ֥࠺ၫྟ,ପહඌٳ༅҂эྟॖၛฐ෬ᆣಊ൧ӆӉ௹ѯ֥ܿ,ੰR/Sٚمࣼ൞ఃᇏ֥၂ᇕ[4]bՖଢభট,ुၘႵ֥࣮൬۠ರ௹:2004-02-18ቔᆀࡥࢺ:ઔ օ(1979-),୯,ඹԫസၒџ൧ದ,ණൖളb࣮ٚཟ:ࣁವඔऌٳ༅;൧ӆטҰაყҩb68
ઔ օ:ᇏݓܢ൧թᄝ ჿೣڏ ིႋગ?ࢲંಏරެ҂࣐ཌྷbႵ࣮іૼ:ᆣಊ൧ӆ҂թӻࣲྟ֥ඣॖၛ๙ݖHა֥ҵ֥նཬট؇ᄝӉ࠺ၫྟหᆘ(Hiemstra&Jones,1997);္ႵਈbHurstᆷჟொ,іૼܢௐࡎ۬э֥ཌྷܱ࣮ಪູರ൬ၭੱaᇛ൬ၭੱമᇀᇛ൬ᄅ൬ၭੱनթྟჟն,ྐ༏ّႋൈᇌჟӉ;Hჟ࣍Ⴟ,іૼܢᄝࢠӉ֥ཌྷܱྟ[Barkoulas&Baum(1996),Baumௐࡎ۬э֥ཌྷܱྟჟཬ,ྐ༏ّႋൈᇌჟ؋,൧ӆ&Travlos(2000[5]),Sadique&SilvapulleႵིྟჟ఼b(2001[6])]b(ؽ)AFIMAଆ࣐ܵଢభؓӉ࠺ၫ֥ٳ༅ٚمၛರӮඃ,R/Sٚم൞၂ᇕбࢠࡥь്֥љӉ࠺ၫྟ֥ٚ൞ն҆ٳٳ༅ࣇࣇअཋႿӮඃ֥ᆣಊ൧ӆ(หљ൞مb൞ൌ࠽ഈ෮ླေ֥҂ࣇࣇ൞ᆩ֡൞ڎթᄝӉૅݓᆣಊ൧ӆ,ؓྍྖ൧ӆ(ECM)֥ٳ༅бࢠ࠺ၫྟ,ߎ༐ຬࡹ৫ॖၛख़߂ᆃᇕหᆘ֥ଆ,Ֆطഒ[7]bაӮඃ൧ӆཌྷб,ྍྖ൧ӆ၂ϮऎႵܿଆॖၛؓൈࡗਙቔԛбࢠఞ֥֒ყҩbARFIMAཬaੀྟҵaѯྟ఼ၛࠣሧᆀؓྐ༏ّ႘ࢠતଆ൞ଢభᄎႨࢠ؟֥ଆᆭ၂,ؓႿܴҳᆴਙ֩หׄbᆃུหׄॖିྍྖ൧ӆ֥ྐ༏Ԯ־ٚൔ{xt},ೂݔડቀ:აӮඃ൧ӆႵ෮҂bቋ୍࣍ࠫ,ݓଽႵ࿐ᆀؓ (L)(1-Ld)(Xt-u)= (L) tݓᆣಊ൧ӆ֥Ӊ࠺ၫྟቔਔٳ༅,൞ᆃུٳ༅ࠎᄵ{xt}ڛՖٳᆜሱ݂߭߁नଆ,࠺ູARFI ЧഈીႵྙӮ၂֥ࢲંbMA(p,d,q)ଆbఃᇏLູᇌުෘሰ, ູxt֥नູਔؓݓܢௐ൧ӆ֥Ӊ࠺ၫྟቔбࢠಆ૫֥ᆴ,{ t}ູϢᄮലਙ,|d|<,(1-L)ູٳඔҵٳ༅,гᆀ࿊౼ഈᆣሸކᆷඔބധᎪӮٳᆷඔ,০Ⴈٳෘሰb2P (L)=1- 1L- 2L- - LPູpࢨሱR/SٚمaARFIMAݖӱট്љ൬ၭੱ֥࠺ၫหᆘ݂߭ᇌުෘሰ؟ཛൔb (L)=1- 1L- 2L2- -,ႨFIGARCHଆটख़߂ѯ֥࠺ၫหᆘbQLqqູqࢨ߁नᇌުෘሰ؟ཛൔbᆃ (L)二a分析方法ა (L)܄ၹሰ, (L)ބ (L)֥ਬׄಆᄝگ૫ֆ໊ჵ|z|=1ᆭຓ,ၛЌᆣ໗ྟbҵٳෘሰ(1(၂)R/Sٳ༅ ᇗѓࠞҵٳ༅م(rescaledrangeanalysis,R/S)-Ld)οؽཛൔᅚषູ(1-Ld)= Cjd(-Lj),֒0j=0൞Hurst(1951)ᄝ࣮ඣ໓࿐ൈ൮༵ิԛট֥b<d<ൈ,{xt}൞Ӊ࠺ၫݖӱbMandelbrot&Waills(1969)ࡼR/Sٳ༅ႨႿҩਈൈؓARFIMAଆ֥ࢲܒѐ്აҕඔܙ࠹ႋ࣐ࡗਙӉӱཌྷ఼ܱ֥؇,طުR/Sٳ༅ФܼٗႋႨॖିֹ০ႨԮ֥ARMAଆࡹଆᇏ֥ٚم۽ऎbႿؓࣁವൈࡗਙӉӱཌྷܱ֥ٳ༅ᆭᇏ,ఃࠎЧනაԮ֥ARMAଆཌྷб,ARFIMAଆ֥ࡹਫ਼൞ؓႿൈࡗਙ{x1}:৫ေބگᄖ֤؟bᄝ০Ⴈරಖݦඔܙ࠹ሱླྀٚ R(T)ҵൈ,ࣚಒරಖܙ࠹ٚمმ֞ਔ࠹ෘഈ֥TT=max{ X[Sowell(1992)۳ԛਔࠞնරಖܙ࠹مऎุ֥࠹ෘj-E[X]}-min{ Xj-E[X]}0 j Tj=10 j Tj=1ఃᇏT൞ሰࡗ֥Ӊ؇ٚم]b,R(T)൞T௹ࡗഈ֥ࠞҵ()FIGARCHଆ,ᆃR(T)ෛT֥ᄹնطᄹն(Feder,1988)bູбࢠ҂ো֥ൈࡗਙ,HurstႨܴҩᆴ֥ѓൌ࠽ഈ,ॖၛϜFIGARCHଆ֥නམुቔ൞ሙҵಀԢࠞҵRARFIMAଆනམᄝARCHଆቂᇏ֥ഥbԮ(T)֤֞:R֥ARCHଆ൞ࡹ৫ᄝਙીႵֆ໊۴֥భิ(T)=H( T)S^(T)ᆭഈ,֥ೂݔऎႵᆜඔࢨֆ໊۴ᄵေࡼਙࣉྛS^(T)൞T௹ࡗഈ֥ѓሙҵ,a൞ӈඔ,H൞ތ໗߄ԩ(IGARCH),ၹູᆜඔࢨֆ໊۴֥ཋקݖථหᆷඔ,0 H 1(Mandelbrot,1972)bތථหႿ۬აधؓbູਔ࣮ऎႵӻ࿃ѩ٤Ⴅჹ࿃ᆷඔႵᇕ҂ো:֒H=ൈ,ჰਙ൞ѓሙ֥ѯэ߄,Baillie,BollerslevބMikkelsen(1996)ෛࠏႳሼ,֥གྷᄝ҂߶႕ཙࡼট,ࠧჰਙಌكӉ௹ิԛਔࢺႿGARCHაIGARCHᆭࡗ֥FIGARCH֥࠹ཌྷܱ;֒0 H<ൈ,ჰਙऎႵّӻࣲଆ(fractionallyintegratedGARCH)bFIGARCH,ྟࠧਙ൞नᆴ߭گ֥,ݖಀ֥ᄹਈაໃট֥ᄹਈଆ֥іղൔॖཿ:ູڵཌྷ;ܱ֒<H 1ൈ,ჰਙऎႵӻࣲ,ྟࠧݖ (L)(1-Ld) 2t= 0+[1-B(L)u2t]ಀ֥ᄹਈაໃট֥ᄹਈ൞ᆞཌྷܱ֥(Hurst,1951)bູਔᆰّܴ႘่ࡱٚҵཛ,၂Ϯཿູ:69
࠹აྐ༏ંฆ 2t= 0[1-B(L-1)]+{1-[1-B(L-1)] (L)ರ֥ഈᆣሸކᆷඔބധᎪӮٳᆷඔູဢЧbᄝҐဢ (1-Ld)} 2௹ࡗЇওնࣷ൧ծീ֥ԛaࢌၞᇅ؇ڿ۪aರᅨt= 0[1-B(L-1)]+ (L) 2יږཋᇅaݓႵܢࡨӻၛࠣPTᇅ؇ᇔࢲ֩ᇗնtఃᇏ ൎ൙ࡱbູਔٳ༅ޡܴᆟҦؓᆣಊ൧ӆ֥႕ཙ,ࡼ0 d 1, (L)= KLK, K 0, k=1,2,K=1ဢЧࡗ߃ٳູਆ۱ࢨ؍:1992୍2ᄅ1ರ~1996 ,ၛЌᆣ 2t٤ڵbFIGARCHّ႘ਔຓ҆Ԋࠌ୍ؓ12ᄅ16ರֻູ၂ࢨ؍;1996୍12ᄅ17ರၛު่ࡱٚҵऎႵӻ࿃ྟ,ѩߏત༯ࢆbֻູؽࢨ؍bቔᆃဢ߃ٳ֥ჰၹᇶေ൞1996୍12FIGARCHଆ֥ܙ࠹бࢠ,ࠞնරಖܙ࠹ᄅ16ರԛᅨיږ҂ӑݖ10%֥ཋᇅᆟҦؓᆣಊཌྷؓбࢠࡥֆ,ѩିູࢠ؟ದ෮ࢳބႋႨbෙಖ൧ӆႵࢠն႕ཙ,Վު֥ඔऌѯࡗэ֤༮ᅎФࣁವൈࡗਙສສ൞٤ᆞٳ҃,ऎႵࡕڂިແห෪ᄝ(,)ᆭࡗ,ᆃࡼ႕ཙᆇൌ֥ඔऌളӮᆘ,൞BollerslevބWooldridge(1992)ᆷԛ:ಯಖݖӱ,ೂݔ҂ࡆၛٳ૧Ⴕࢠն֥༂ҵbॖၛ০Ⴈᆞٳ҃ቔරಖܙ࠹,ᆞٳ҃ܙ࠹ࢲݔ(၂)R/Sٳ༅ࢲݔऎႵਗ਼Ͽྟbູਔࣉྛරಖܙ࠹,౫ࢨᇌުෘሰႮႿཌྟ၇ঠྟ߶Hurstᆷඔொ,ູਔཨсྶФࡥჿູႵཋࢨᇌުཛ,၂Ϯটඪ500~1000Ԣჰඔऌሱཌྷܱ֥႕ཙ,сྶؓჰඔऌࣉྛԩࢨࠧॖbᆃဢ,֒ tڛՖᆞٳ҃ൈ,රಖݦඔ:ູb๙ݖ౼AR(1)֥җҵ,ॖၛࢆ֮ொӱ؇ѩ༐ logL(Xt/ t-1;I0; )ຬႮՎࢆ֮ࢲݔ֥҂ཁᇷྟӱ؇bՎݖӱ္ࣼ൞ყTT 2t=(2 ) log Ϣᄮലԩbؓರ൬ၭੱrtࣉྛAR(1)݂߭ಀוt=1t=1 2tఃᇏI0൞Ԛ่ࡱbਙ֥ཌྟཌྷܱ֤җҵਙ{xt}bࡼ{xt}ਙ֩ٳູA۱Ӊ؇ཌྷ֥֩ሰࡗ,ૄ۱ሰࡗٳљ࠺ູ三a我国证券市场长期Ia,ૄ۱Iaഈ֥xt࠺ູxk,a,ؓૄ۱ሰࡗ࠹ෘ࠹记忆特征的实证分析ொҵ,ၛࠣૄ۱ሰࡗഈ֥ࠞҵ:,Ⴈ(ሰࡗѓሙҵ)ಀԢᆭު࠹ෘෘඌनඔ֤֞bቋު֤݂֞߭ гᆀ࿊ᄴ1992୍2ᄅ1ರ~2002୍12ᄅ30ൔ(࠹ෘࢲݔі1,࠹ෘ֤֥֞log-log1)b1 ഈݚധᎪR/S(1992~2002)і1 Hurstᆷඔ࠹ෘࢲݔіၫྟѩ҂൞ٳԛbਆ൧ཌྷбࢠ,Ֆ1992୍2ᄅൈࡗ؍HurstᆷඔE(H)ѓሙҵᇀ1996୍12ᄅ,ഈ൧֥HurstᆷඔۚႿധ൧,ᆃ၂1992\02\01~2002\12\ࢲݔაགྷൌ֥൧ӆሑঃ൞ཌྷ໖ކ֥b90୍սԚ௹ഈݚ1992\02\01~1996\12\൞ݓ௵תषؿᅞࣉ֥ൈ௹,ᆃ၂ൈ௹ӯ1996\12\17~2002\12\གྷԛૼཁ֥ധ఼,ഈᆣᆷඔӮູᆜ۱൧ӆ֥ڄ1992\02\01~2002\12\ཟѓbՖ1996୍12ᄅၛ,ުཐ݂֥ۖ߭ყ௹ڿэ.ധᎪ1992\02\01~1996\12\ਔᆃ၂ሑঃ,Վ௹ࡗധᆣ֥Hurstᆷඔّݖটૼཁ1996\12\17~2002\12\ӑݖਔഈ൧,ၛധؿᅚູսі֥݂߭ۀܢ֤֞ਔ൧ӆ֥௴ђಪbՖі1ॖၛुԛ:ં൞ᆜ۱ൈࡗ؍ߎ൞ٳൈ(ؽ)ARFIMAଆࢲݔࡗ؍ഈݚሸކᆷඔაധᎪӮٳᆷඔ֥HurstᆷඔनնႿ,іགྷԛ၂ק֥Ӊ࠺ၫหᆘ,൞ᆃᇕӉ࠺гᆀ০ႨEMLٚمؓഈݚሸކᆷඔაധᎪӮ70
ઔ օ:ᇏݓܢ൧թᄝ ჿೣڏ ིႋગ?ٳᆷඔ൬ၭੱၛࠣཌྷႋ֥धؓ൬ၭੱࣉྛܙ࠹,ఃࢲݔі2bі2 ARFIMA(p,d,q)ܙ࠹ࢲݔіൈࡗ؍SH(1992~2002)SH(1996~2002)SH(1992~2002)SZ(1992~1996)SZ(1996~2002)SZ(1992~2002)ଆARFIMAARFIMAARFIMAARFIMAARFIMAARFIMA|R|ܙ࠹ࢲݔ(1,d,1)(1,d,1)(2,d,1)(2,d,1)(1,d,2)(2,d,1)**************ଆARFIMAARFIMAARFIMAARFIMAARFIMAARFIMARܙ࠹ࢲݔ(2,d,0)(1,d,0)(0,d,1)(0,d,1)(1,d,1)(1,d,1)*************ᇿ:*іൕᄝ10%֥ඣ༯࠹ཁᇷ;**іൕᄝ5%֥ඣ༯࠹ཁᇷ;***іൕᄝ1%֥ඣ༯࠹ཁᇷb Ֆၛഈܙ࠹ࢲݔॖၛुԛ:ં൞ഈᆣߎ൞ധ໗ྟဒaARCHིႋဒbгᆀؓ෮Ⴕඔऌࣉྛ൧ఃܢᆷ൬ၭੱਙ֥Ӊ௹ཌྷܱྟٳັ,ࠫެਔADFဒ,ؿགྷ൬ၭੱ൞໗֥bطؓਙࣉྛཬჅ10%bطPetersᄻࣜࡹၰHurstᆷඔაdᆭၳٚҵဒؿགྷᆰ֞ۚࢨၛުಯಖթᄝࢠ఼֥ࡗ֥ܱ༢ູd=,ᆃࠎЧഈ֤֞ਔႆᆣbഈARCHིႋ,іૼGARCHଆ൞ൡ֥֒bູਔॉݚބധᎪܢ൧൬ၭੱਙdᆴෙಖޓཬ,൞ՖሱҳӉ࠺ၫྟ,۴ऌBBMิԛFIGACHଆ֥Мࣟ,ཌྷܱݦඔഈܴҩ֞ສສᇌުࠫ௹֥ሱཌྷܱݦඔ৵࿃ؓ2rt֥ሱཌྷܱݦඔࣉྛਔٳ༅bఃٳ༅іૼ2:rູᆞࠇູڵ,ཁಖ҂ડቀෛࠏႳሼࡌק,൧ӆႵིྟਙ֥ሱཌྷܱݦඔӯགྷԛ၂ק֥ܿੰ,ྟࠧສສᄝ၂бࢠbൈ္ؿགྷՖ1996୍ၛު൬ၭੱ֥ሱཌྷ۱бࢠӉ֥ൈࡗٓຶଽႵཌྷ֥ژݼ,ѩఃधܱؓྟѩીႵམყ௹֥ପဢ༯ࢆbཌྷّ,1996୍ުധᆴߏતֹࡨഒ,ѩᆰ֞іૼ֒భᇌު2100௹r൧֥Ӊ࠺ၫྟරެ֤֞ਔᄹ఼bᆃᇕགྷའѩ҂ିඪਙ֥ሱཌྷܱݦඔಯಖᄝ2Пѓሙ༂ᆭຓbᆃіૼ֒ૼޡܴᆟҦാི,ᆺିՖඔऌหᆘؿളڿэഈࢳbభ֥э߄ေࣜݖбࢠӉ֥ൈࡗҌିཨാ,طᇀഒႵႮႿ1996୍ၛ,ުඔऌࠎЧഈФ෪ᄝ(,၂҆ٳѯ൞ॖၛყҩ֥bഡקFIGARCHଆऎ)ᆭࡗ,֤ඔऌᆭࡗᄝژݼa౼ᆴٓຶഈ۷ࡆႵೂ༯ྙൔ:ࢤ࣍,ၹՎඔऌᆭࡗ֥৳༢Ⴕॖି۷ࡆࣅૡbหљyt=m+ t t| t-1~N(0, 2t)൞భ૫ิ֥֞ࠫࡱն൙,नႵॖି࠺ၫྟࡆ఼bqd(a1L+ aqL)(1-L) 2t=w+[1-1-b1L- p] 2t()FIGARCHଆܙ࠹ࢲݔbpLࡹ৫ARCHোଆ၂Ϯটඪႋھ൮༵ࣉྛі3ਙԛਔ০Ⴈࠞնරಖܙ࠹مܙ࠹֥ࢲݔbі3 FIGARCHଆܙ࠹ࢲݔіDataSH(1992-1996)SH(1996-2002)SH(1992-2002)SZ(1992-1996)SZ(1996-2002)SZ(1992-2002)Resultsd ႨAICaSICሙᄵّگбࢠ۲۱ଆ,ቋުಒקթᄝӉ࠺ၫหᆘbѩෛሢൈࡗ၍,dᆴႵбࢠp,q֥ࢨඔनູ1bູਔࡥ߄,ᄝՎᆺਙԛਔӉ࠺ၫૼཁ֥༯ࢆ൝,ࠧӉ࠺ၫྟࡨbႮFIGARCHҕඔd֥ܙ࠹ࢲݔބཌྷႋ֥t࠹ਈb۴ऌܙ࠹ࢲଆӁള่֥ࡱनᆴყҩᆴ၂Ϯбఃଆն,ݔॖၛुԛ:ᄝିಒקdᆴཁᇷ֥౦ঃ༯߶ᄹࡆڄགყҩ֥Ϝֻ၂,Ԣਔ൧ሸކᆷඔၛຓࠫެ෮Ⴕਙ֥؇bdᆴնႿ,ѩन࠹ཁᇷ,ඪૼൈ֥ѯֻؽ,FIGARCHଆܙ࠹ࢲݔაARFIMAଆ71
࠹აྐ༏ંฆႵ෮҂bᆃ൞ႮႿARFIMAଆൈᆌؓनᆴᆃུቋᇔ๙ݖ൧ӆࢌၞࠃّ႘ᄝܢࡎᆷඔഈ,ٚӱط֥bٳ༅֥ଢ֥൞ູਔّ႘r֥Ӊ࠺ၫห֤ܢࡎᆷඔ෮ܒӮ֥ൈࡗਙӯགྷԛ٤ཌྟbᆘbطFIGARCHଆᇏ֥dᆴ൞ؓ 2tط,ख़߂ൈгᆀߎؿགྷѩಪູ:ޡܴᆟҦ֥ቔႨѩીႵ֤֥൞ӻ࿃ѩ٤Ⴅჹ࿃֥ѯэ߄่ؓࡱनᆴ֥൬ၭੱӉ࠺ၫྟ༯ࢆ,ّطႵ෮ᄹ఼bႮႿᅨיږ႕ཙbཋᇅᆟҦ֤ඔऌ౼ᆴٓຶնն෪ཬ,ೂݔᄝ၂۱ֻ,гᆀᇿၩ֞d֥ܙ࠹ࢲݔؓൈࡗ؍ٳ୩෪֥ॢࡗᇏ౼ᆴ,ପહඔऌᆭࡗ֥ܱ৳ྟ൞ॖିૹۋbೂݔϜᆃࠫ۱ࢨ؍ᄜ༥ٳ,ᄵࢲݔ߶Ⴕ෮҂ᄹ఼֥b൞ࠎЧഈनնႿᆃඪૼᆣಊ൧ӆෙಖູ(ؽ)ഈݚބധᎪܢ൧धؓ൬ၭੱਙ{|rt|}ބൌᆣٳ༅ิ܂ਔپڶ֥ඔऌটჷ,൞࣐ܵඔऌটٚ൬ၭੱਙ2{rt}ऎႵޓ఼֥Ӊ࠺ၫྟሱ၂۱ሹ,ุႮႿႨൈࡗࡼሹุ߃ٳູྸ؟ൈႨARFIMAଆؓ{|rt|}ܙ࠹֥dᆴࠎЧഈࠢࡗ؍Ґဢൈ,۲۱ဢЧ֥սіྟႵ෮҂b࠹ෘࢲᇏᄝቐႷbط{rt}֥ሱཌྷܱݦඔਙᄵߏત༯ݔ֥ҵၳᆺି۴ऌ۲۱ൈࡗ؍ᆣಊ൧ӆྛູหᆘটࢆ,ᆰ֞ۚࢨߎႵࢠ఼֥ཌྷܱྟbࢳb()ഈݚބധᎪܢ൧֥ѯྟऎႵӉ࠺ၫྟა四a结ӻ࿃ྟ 论ᄝ1992~1996୍ᆭࡗ,ႮFIGARCHଆܙ࠹Ч໓০ႨR/Sٳ༅aARFIMAၛࠣFIGARCH֥dᆴࠎЧഈնႿ,ѩ࠹ཁᇷbط1996୍ଆٳ༅ᇏݓᆣಊ൧ӆ֥Ӊ࠺ၫྟหᆘ,Ֆܢ൧൬ၛު,dᆴཁᇷ༯ࢆമᇀ֮Ⴟᆃඪૼࡹ൧ᆭၭੱაѯྟਆ۱ٚ૫ٳࢨ؍ٳ༅ა࣮ഈݚބധԩ,ഈݚބധᎪܢௐ൧ӆ֥ѯऎႵӉ௹࠺ၫྟ,֒Ꭺܢ൧֥Ӊ࠺ၫྟbఃࢲݔіૼ:ൈࢤ൳֥֞ྐ༏ᄝఃФࢤ൳֞ᆭު࿃ᄝޓӉ၂؍(၂)ഈݚބധᎪܢ൧൬ၭੱਙ{rt}֥R/Sൈࡗଽ႕ཙໃটbط1996୍ၛު,dᆴ༯ࢆӉ࠺ၫ࠹ਈࢤ࣍,ARFIMAଆ֥dᆴࢤ࣍0,ሱཌྷܱྟᇯࡶࡨമᇀཨാ(ೂഈݚܢ൧),ᆃඪૼޡܴᆟྟбࢠҦ࣐ܵીႵཨԢ൬ၭੱЧദ֥Ӊ࠺ၫྟ,ᇅਔ࣐ܵཌྷܱྟѩ҂఼,ᄝ၂קӱ؇ഈඪૼᇏݓఃѯ֥Ӊൈ௹ઢ,,ѯ֥৯؇ննࡨ,ᄝܢௐ൧ӆѩીႵӯགྷԛෛࠏႳሼ֥ห,ྟѩ҂൞၂ܿٓބטࢫܢ൧ਅݺᄎྛٚ૫ཁൕӮིbطᄝ۱৫ݖӱ,ط൞іགྷԛཌྷ၇թ֥ܱ༢bఃჰၹ1996୍ᆭު,൧ӆؓܢ൧ѯ֥ཨ߄ି৯ᄹ఼,൧ᄝႿྐ༏ၛ٤ཌྟ֥ٚൔӯགྷ,ದૌ္ၛ٤ཌྟ֥ӆྟၹᄹࡆbٚൔؓྐ༏ቔԛّႋ,ܢࡎѯ္ӯགྷ٤ཌྟ,෮Ⴕҕॉ໓ང[1] (ૅ),fractionalBrowniannoisesandapplications[J].SIAMReview,1968,(10):422-437.[2] (ૅ)[J].Biometrica,1981,(68):165-176.[3] (ૅ)BaillieRT,BollerslevT,[J].Journalofeconometrics,1996,(74):3-30.[4] Ray,BK,-rangedependenceindailystockvolatilities[J].JournalofBusiness&EconomicStatistics,2000,(18):254-262.[6] (ૅ)SadiqueS,-termmemoryinstockmarketreturns:internationalevidence[J].InternationalJournalofFinanceandEconomics,2001,(6):59-67.[7] (ૅ)BarkoulasJT,BaumCF,[J].AppliedFinancialEconomics,2000,(10):177-184.(ᄳщࠠ:ݒൂ)72
