뿄ꙍ뻷듁뚡늼돸륓궷쁉뙋ꓴ뭐뙓귈껄ꩇRisk Premium and Depreciation Effect inStock Returns over the Asian Financial Crisisꓨꓥ뫓∗(WenShwo Fang)멋굮ꖻꓥꙢGARCH-M볒ꮬ걛멣ꑗꅁ꣏ꗎ뉛뭜걷뿄ꙍ뻷ꪺꓩ룪껆ꅁ맪쏒놴끑궷쁉뙋ꓴ뭐덱덦뙓귈Ꙣꕸ왗ꖫ돸륓륌땻꒤ꪺꛦ결ꅃ뿄ꙍ뻷ꓞ땯ꖫꩩ냊뭐ꕸ맴뙓귈ꅁꖻꓥ쏒맪뿄ꙍ뻷듁뚡ꅁꕸ왗ꖫ돸륓륌땻꙳Ꙣ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴ뭐굴ꪺ뙓귈껄ꩇꅁ땍ꛓ궱맯걷뿄ꙍ뻷ꓞ끟ꪺ뿄ꖫ돵꒣쎭ꥷꅁ궷쁉뙋ꓴꣃꖼ쁈ꖫ돵궷쁉ꪺ뱗ꕛꛓ뱗ꕛꅆꙐ껉ꅁꕸ맴뙓귈뮤꣏룪ꑈꕈ낪돸륓ꪺ과꒸룪늣듀ꕎ늼ꅁ뙩ꑀꡂ궰ꝃ늼믹껦뭐돸륓ꅃꖻꓥ뗽뻚엣ꗜ꒣쎭ꥷꪺꕾ뛗ꖫ돵뷄삻ꖫ돸륓뭐ꩩ냊ꅁꙝꚹꅁ덱덦뙓귈ꓞ땯ꪺ늼ꖫ돵룪궷쁉ꅁ삳걏군릺룪ꕸ왗ꖫꪺ(냪꒺냪믚냲롧뉺ꑈꡍ떦ꪺ)ꑀ귓궫굮뗻꛴굮ꗳꅁ룪ꡍ떦뛈ꛒ뱻늼ꖫ돵ꛛꢭꪺ볐ꅁꦿ늤ꕾ뛗ꖫ돵뇸ꗳꅁꕩ꿠뻉교낾뭾ꪺꝐ쉟ꅃ쏶쇤꙲ꅇ걷뿄ꙍ뻷ꅁ늼돸륓ꅁ궷쁉뙋ꓴꅁ뙓귈껄ꩇꅁGARCH-M볒ꮬꅃAbstractUsing GARCH-M models, this paper investigates the behavior of risk premiumand currency depreciation in Taiwan stock return process over the Asian financialcrisis, characterized by unstable stock and foreign exchange markets since July daily data as an example, the evidence documents significantly a time-varyingrisk premium and a negative depreciation effect. Nevertheless, the increased volatilitycaused by the financial crisis has not raised stock holders to require larger riskpremium for compensation. Meanwhile, domestic currency depreciation shifts assetholdings from stocks to foreign exchanges (. the US dollars), leading to a furtherdecline in stock returns. The evidence for the negative depreciation effect in the stockreturn process suggests that domestic investors and international-funds managers whoplan to invest Taiwan stock market have to evaluate situations in stock and foreignexchange markets simultaneously to avoid biased : Asian Financial Crisis, Stock Returns, Risk Premium, DepreciationEffect, GARCH-M Model. ∗ꓨꓥ뫓(WenShwo Fang)Ⱐ덻ꗒꑪ뻇롧샙꡴냆뇐뇂ⰠAssociate Professor, Department of Economics,Feng Chia University, Taichung,
1. ꭥꢥ꫱꙾꣓ꅁꩆꙨ볆냪깡ꪺ냪믚뙔꧶롧녠녢ꕘ뉻끦깴ꅂꕾ뛗꙳꦳꒣ꢬꅂꕾ뛅륌Ꙩꅂ롧샙냲ꖻ궱ꪺ뽮깺꒣꺶떥ꙝ꿀ꅁ뻉교과꒸Ꙣꩆꖫ돵ꪺ녪뛕ꅁ꧳1997꙾7ꓫꅁ궺ꗽꙢ껵냪ꕾ뛗ꖫ돵ꕘ뉻썥ꑪꪺ뻷꧊ꕾ뛗(과꒸)뙒뵌ꅁ껵맴ꖨ뙓ꅁ뙩ꛓꓞ땯늼ꖫ돵ꪺ녙뙞ꅁꚹꑀ궷볉뙩ꑀꡂ뛇뻉ꛜꑪꙨ볆ꪺꩆ냪깡ꅁꚨ꧒뿗ꪺ걷뿄ꙍ뻷(Asian financial crisis)ꅃ쇶땍ꕸ왗롧샙냲ꖻ궱ꙮꅁꙢ걷뿄ꙍ뻷듁뚡ꅁ꒴ꚳ뗛ꕏꑈꙌ뙈뉠꣨ꪺ낪ꯗ롧샙ꚨꅝ1997꙾맪뷨롧샙ꚨ뉶결ꉈꅁ1998꙾결ꉈꅁ1989-1998ꪺ10꙾ꖭꞡ맪뷨ꚨ뉶결ꉈꅞꅁꙐ껉ꅁ롧샙꯹쓲꧊ꪺ낪ꚨ냪믚뙔꧶롧녠녢ꪺ곕빬ꅁꕸ왗닖뽮ꑆꖨ썂ꪺꕾ뛗꙳꦳(1998꙾꦳곹결920믵과꒸ꅁ결ꕀ곉닄ꑔꛬꅁ뛈ꚸ꧳ꓩꖻ뭐꒤냪ꑪ뎰)ꅁ땍ꛓ꣼꣬걷뿄궷볉ꪺ뷄삻ꅁ늼뭐ꕾ뛗ꖫ돵꒴걏ꕘ뉻쑙궫ꪺ끉끨뭐ꩩ냊ꅃꕈꕸ왗땯ꛦ뙱ꕛ앶믹볆ꅝTAIEXꅞꫭꗜꪺ늼ꖫ돵믹껦ꅁ녱1997꙾7ꓫ꣬1998꙾12ꓫꪺꑕ뙞ꉈꅁ걏꣤뚡믹볆뒿녱1997꙾7ꓫ돌낪ꪺ10,066쉉ꅁ궫뙞꣬Ꙑ꙾10ꓫꪺ7,313쉉ꅁ뙞둔결ꉈꅑꙐ듁뚡ꅁꕸ맴맯과꒸ꪺ뛗뉶쇶ꖼꖨ둔빟샺ꅁꕘ뉻꯹쓲ꪺ뙓귈ꅁ뛗뉶녱1997꙾7ꓫꫬꪺ꒸ꑗꛜ1997꙾꦳ꪺ꒸ꅁꕸ맴뙓귈ꉈꅆꪽ꣬1998꙾9ꓫ1ꓩꅁꕸ맴ꑾ녱꒸ꪺ믹ꛬꅁ몥ꚸ쎭ꥷꅂꙞꛜ1998꙾꦳ꪺ꒸ꅃ늼뭐ꕾ뛗결룪ꑈ뉺끝ꪺ궫굮ꑵ꣣ꅁꓗ꣤걏꫱꙾꣓ꅁ쁈뗛곬ꪺ뙩ꡂꅂ냪꒺뿄ꖫ돵ꪺꛛꗑ꓆뭐냪믚꓆ꅁꕈꖻ냪ꕈꕾ냪덦맴ꫭꗜꪺ쏒꣩(꙰늼ꅂ뛅꣩ꅂ덱덦떥)곛꒬뚡ꑶꚨ결ꙮꪺ듀ꕎ끝(substitutes)ꅁ룪ꑈ꒣Ꙣ띎꯹ꚳꪺꚳ믹쏒꣩냪ꝏꅁ쏶ꩠꪺ걏룪볐ꪺ걏ꝟ륆꣬륷듁ꪺ돸륓ꅁꚹ뫘때냪ꝏ깴늧ꪺ뿯뻜ꅁꣃ꒣ꕎꫭꕈꖻ냪덦맴ꫭꗜ뭐ꕈꕾ냪덦맴ꫭꗜꪺ쏒꣩룪돸륓곛Ꙑꅁ귬ꙝ걏룪ꑈꙢ뙒ꅂ뷦꒣Ꙑ덦맴결군믹돦ꛬꪺ쏒꣩껉ꅁ뛗뉶ꕩ꿠꒣Ꙑꅃꑀ꿫꣓뮡ꅁ꣤ꕌ뇸ꗳ꒣엜ꅁ꙰ꩇ륷듁ꖻ냪덦맴뙓귈ꅁꭨꕈꕾ냪덦맴ꫭꗜꪺ룪늣ꪺ돸륓뱗ꕛꅁ룪ꑈ녎엜룪닕Ꙙꅁ뱗ꕛꕾ뛗ꕈꕾ냪덦맴ꫭꗜꪺ쏒꣩ꅁ듮ꓖꕈꖻ냪덦맴ꫭꗜꪺ쏒꣩룪ꓱ꣒ꅁ덹ꚨ냪꒺쏒꣩믹껦뭐돸륓ꑕ덬ꅃ걷뿄ꙍ뻷듁뚡ꅁꕸ맴ꪺ꯹쓲뙓귈뭐ꕛ앶믹볆ꪺꑕ뙞꣤ꩩ냊(volatility)ꪺ뱗ꕛꝥ뉻ꓨꙖꪺ늾냊(냑빜맏1)ꅁꖻꓥ낲덝냪꒺뿄ꖫ돵꒤ꪺ늼뭐과꒸결쏶ꭙꙮꪺ듀ꕎ끝ꅁ걷뿄ꙍ뻷듁뚡ꅁ곛맯꧳녪뛕ꪺ과꒸ꅁꕸ맴꯹쓲뙓귈ꓞ땯룪ꑪ늳ꪺ뙓귈륷듁ꅁ뮤꣏룪ꑈ낾ꙮ꯹ꚳ낪돸륓2
ꪺ과꒸ꅂ듮ꓖ꯹ꚳ늼ꅁꕛ궫늼돸륓ꪺꑕ뙞ꖫ돵ꩩ냊ꪺ둔ꯗꅑꕴꕾ뿄ꙍ뻷듁뚡ꅁ꒤ꖡ믈ꛦ결뵷ꥍꫀ라ꑀ꿫ꑪ늳맯띳ꕸ맴뙓귈ꪺ륷듁ꓟ뉺ꅁ쁗쁗ꑺ륷ꕾ뛗ꖫ돵ꅁ끶ꛭ과꒸ꅁꚹꑀ걆떦ꑺ륷ꅁ뫲셙ꖫ돵룪ꅁꕩ꿠뙩ꑀꡂ삣ꝃ늼돸륓뭐쉘ꑪꖫꩩ냊1ꅃꖻꓥ쉘깩뛇닎ꪺGARCH-M볒ꮬꅝEngle ,Lilien and Robins, 1987ꅞꅁ맪쏒놴끑걷뿄ꙍ뻷듁뚡ꅁꕸ왗늼ꖫ돵돸륓ꅂ궷쁉뙋ꓴ(risk premium)뭐ꖻ냪덱덦뙓귈뚡ꪺ쏶ꭙꅃ ꖻꓥ닄ꑀ론결ꭥꢥꅁ뇔굺곣ꡳ냊뻷뭐ꗘꪺꅑ닄ꑇ론결늼뭐ꕾ뛗ꖫ돵쏶셰꧊ꪺ뉺뷗뭐맪쏒ꓥ쑭Ꙟ압ꅆ닄ꑔ론결곣ꡳꓨꩫꅁꙢ꯹쓲뙓귈뱶암늼ꖫ돵돸륓뭐ꩩ냊ꪺ왛쉉ꑗꅁ뇀뻉ꣃꯘꗟꖻꓥꪺGARCH-M볒ꮬꅆ닄ꕼ론결꣏ꗎ룪껆ꪺ냲ꖻ꽓뱸뭐ꫬꡂ꓀꩒ꅆ닄꒭론결볒ꮬ꛴군뭐떲ꩇ꓀꩒ꅆ닄꒻론결떲뷗뭐ꯘ쒳ꅃ2.늼뭐ꕾ뛗ꖫ돵Ꙣ뉻ꕎ뙽꧱롧샙엩꡴꒤ꅁꑀ냪늼뭐ꕾ뛗ꖫ돵곛꒬뱶암ꅁ꙳Ꙣ녋꒣ꕩ꓀ꪺ쏶셰ꅃ꣥ꮬꪺ늣ꭾꖫ돵뗛ꓢꩫ(Dornbusch and Fischer, 1980)Ꙣꑀ냪뙔꧶롧녠녢ꪺ왛쉉ꑗꅁꕄ녩덱맴뙓귈뱗ꕛꖻ냪늣ꭾꪺ냪믚ꖫ돵쑶ꪧꑏ뭐뙔꧶빬썂ꅁ뒣럭듁뭐ꖼ꣓늣ꕘ뭐맪뷨꧒녯ꅁꛓ늼ꖫ돵삳뱴냓ꖼ꣓뉻걹ꑊꪺ뉻귈ꅁ셰쎴ꖼ꣓꧒녯뭐럭듁룪ꡍ떦ꅁ덱덦뙓귈녡냊ꖼ꣓꧒녯뱗ꕛꪺ륷듁ꅁ뱗ꕛ늼뉻귈뭐룪ꅁꭐꚨ믹ꪺꑗ몦ꅃꚳ믹쏒꣩빬썂뉺뷗(Bransonand Henderson, 1985)ꭨꙢ룪ꖻ녢ꪺ왛쉉ꑗꅁ뭻결뛗뉶걏ꖭ뿅ꙕ뫘룪늣꣑ꅂ믝ꪺꑀ귓궫굮ꙝ꿀ꅁꙝ결뿄룪늣ꪺ믹귈ꗑꕌ귌ꪺꖼ꣓뉻걹ꑊꪺ뉻귈ꡍꥷꅁ덱덦믹귈ꪺ륷듁뱶암뿄룪늣믹껦ꅁꓗ꣤걏Ꙣ뉻꒵냪믚꓆ꪺ뿄ꖫ돵샴맒ꑕꅁ냪꒺ꅂꕾ룪곒ꕩ룪꯹ꚳꕈꖻ냪ꕾ냪덦맴ꫭꗜꪺ뿄룪늣ꅁ뛗뉶ꪺ엜냊녎덹ꚨꚳ믹쏒꣩닕Ꙙꪺ궫띳꓀끴ꅁꓞ땯늼믹껦ꪺ뷕뻣ꅃꖻꓥꙢꚳ믹쏒꣩빬썂ꪺ뉺뷗볒ꮬ걛멣ꑗꅁ놴끑룪늣ꖫ돵꒤ꪺ덱덦뙓귈맯늼돸륓ꪺ뱶암ꅃꚳ믹쏒꣩빬썂볒ꮬ쏶ꩠ뷑꙰냪꒺덦맴ꅂ꙳듚ꅂ꒽뛅ꅂ늼ꅂꕾ뛗떥ꑀ꡴ꙃ룪늣ꪺ믝ꡄ2ꅁꗴꑀ룪늣믝ꡄ결Ꙣ럭듁ꥷ끝둉ꑕꅁꚹꑀ룪늣뭐꣤ꕌꙕ귓룪늣ꕥ셠끝둉ꓱ꣒Ꙩꓖꪺ끴롭냝썄ꅁ궷쁉덗쇗(risk averse)ꪺ룪ꑈꪺ 1ꓨꓥ뫓떥(1998)ꧺ뵔ꕘꕎꫭꖫ룪ꪺ꽕롱덦맴(M1)듮ꓖꅁ녎덹ꚨ믹볆ꅂꚨꗦ뙱ꚨꗦ귈ꪺꑕ궰ꅃ꒤ꖡ믈ꛦꑺ륷ꕾ뛗ꖫ돵ꪺ놹걉ꅁ뫲셙ꖫ돵룪ꅁ꒣ꝑ꧳늼ꖫ돵ꪺꫭ뉻ꅃ2ꚹꑀ뇔굺쇴뉛끝둉꧒ꚳꑈꙢ뿯뻜ꕌ귌ꪺ뿄룪늣닕Ꙙ껉ꅁ꒣ꛒ뱻ꕌ귌꧒꯹ꚳꪺꭄ뿄꧊룪늣(꙰뛀ꅂ꧐ꙡ늣떥)ꅃ3
ꗘ볐결뿯뻜ꑀ꽓ꥷꪺ룪늣닕Ꙙꕈ랥ꑪꖼ꣓뫖ꝑ3ꅁ꣤ꕌ뇸ꗳ꒣엜ꅁ럭ꑀ룪늣ꪺ돸륓뱗ꕛꅁ믝ꡄ띕ꑪꅁ꯹ꚳꓱ꣒띕낪ꅃꚳ믹쏒꣩빬썂뉺뷗ꕄ녩Ꙣ뉻ꚳꪺ끝둉ꓴ럇ꑕꅁꙕ귓룪늣ꪺ믝ꡄ꓀ꝏ떥꧳꣤꣑떹꙳뙱껉ꅁ뿄ꖫ돵륆꣬ꞡ뿅ꅃ굙ꕏꖻ냪ꑈꗁ꯹ꚳꑔ뫘룪늣ꅇꖻ냪덦맴(M)ꅁꖻ냪늼(S)ꕈ과꒸ꫭꗜꪺꕾ뛗(F)ꅁꭨꗴꑀ껉뚡쉉ꕈꖻ냪덦맴ꫭꗜꪺꙗꗘ끝둉ꅝWꅞ결ꅇ W=M+S+E⋅F(1)꣤꒤뛗뉶(E)결ꕈꖻ냪덦맴ꫭꗜꪺ과꒸믹껦ꅃꑔ귓룪늣ꪺꖫ돵ꞡ뿅ꓨ땻ꚡ꓀ꝏ결ꅇe∂m M∂m=m(R,e)ꅁ<0ꅁ <0 (2)∂R∂ee∂s S=(Res,e)ꅁ∂s>0ꅁ <0 (3)∂R∂ee∂f EF=e f(R,e)ꅁ<0ꅁ∂f >0 (4)ꙕ귓ꚡꑬꪺꖪ쏤ꕎꫭ룪늣꣑떹ꅁ∂Rꕫ쏤ꕎꫭ룪∂ee늣믝ꡄꅁ꣤결늼돸륓(R)뭐과꒸돸륓e(e)ꪺ꣧볆4ꅆee결ꖻ냪덱덦ꪺ륷듁뙓귈뉶ꅁꙢ뉺꧊륷듁(rationalexpectations)낲덝ꑕꅁ륷듁뙓귈떥꧳맪믚뙓귈(e)ꅃꑀ뚥낾뻉볆닅뢹ꕎꫭ꧒ꚳ룪늣결ꓲ듀ꕎꅁꗴꑀ룪늣믝ꡄ뭐ꖻꢭ돸륓결ꖿ곛쏶ꅁ뭐꣤ꕌ룪늣돸륓결굴곛쏶ꅁꕂꖻꢭ돸륓껄ꩇꑪ꧳ꗦꑥ돸륓껄ꩇꪺ떴맯귈5ꅃ굙륷듁ꕸ맴뙓귈ꅁꭨꕾ뛗룪늣돸륓뱗ꕛꅁ궷쁉덗쇗ꪺ룪ꑈꗟꝙ궫띳꓀끴ꕌ귌ꪺꚳ믹쏒꣩닕Ꙙꅁ뒣낪꯹ꚳ돸륓뱗ꕛꪺꕾ뛗ꅂ듮ꓖ늼떥꣤ꕌ룪늣ꪺ꯹ꚳꓱ꣒6ꅁꙢꥷ끝둉ꪺ궭꣮ꑕꅁꗴꑀ돸륓뉶엜냊맯꧒ꚳ룪늣ꪺ뷄삻껄ꩇꪺ셠ꥍ결륳7ꅃꙢꖻꓥꑔ귓룪늣ꪺ볒ꮬ꒤ꅁ껚뻚ꕛ셠뇸ꗳ(adding-up condition)ꅁ럭늼뭐ꕾ뛗꣢귓ꖫ돵륆꣬ꞡ뿅ꅁ룪늣ꖫ돵ꝙ결ꞡ뿅ꅁꙝꚹ귌녍ꩠ꧳늼뭐ꕾ뛗ꖫ돵ꪺ끑뷗ꅃ륷듁ꕸ맴뙓귈(뛗뉶ꑗ)ꅁ뱗ꕛꕈꖻ냪덦맴ꫭꗜꪺ과꒸ 3뫖ꝑꝙ걏롧샙뉺뷗꒤ꪺ껄ꗎ(utility)ꅃꑀ꿫Ꙑ띎ꅁ룪늣믝ꡄ꣧볆꣤ꓞꗓ삳ꗎ걏 룪ꑈ랥ꑪ껄ꗎꛦ결ꪺ떲ꩇ(냑빜Branson and Henderson 1985)ꅃ4낲덝ꖻ냪덦맴ꪺꙗꗘ돸륓결륳ꅃ5ꚹꝙ∂s∂s+>0ꅁ∂f∂f+>0ꅃ∂R∂ee∂R∂ee6굙결궷쁉꒤ꗟꅁ결륳궷쁉뙋ꓴꅁꙕ귓룪늣뚡결ꞹꗾ듀ꕎꅁꭨ룪ꑈ녎늾신 ꧒ꚳ끝둉ꅁ뛈꯹ꚳ룻낪돸륓ꪺꕾ뛗룪늣ꅃ7꣒꙰굙럭과꒸룪늣돸륓뱗ꕛꅁꭨ∂m∂s∂f++=0∂e∂eeee∂e4
룪늣믹귈ꅁꙢꑷꪾꪺ과꒸꙳뙱ꑕꅁꚡ(1)ꫭꗜꪺ끝둉뱗ꕛꅁ굙꧒ꚳ룪늣곒결ꖿ녠끝ꅁꚹꑀ끝둉껄ꩇ녎뒣늼뭐ꕾ뛗떥룪늣ꪺ믝ꡄꅃꕴꑀꓨ궱ꅁꕸ맴뙓귈뷄삻ꚡ(3)늼ꖫ돵뭐ꚡ(4)ꕾ뛗ꖫ돵ꪺꞡ뿅ꅁꕘ뉻듀ꕎ껄ꩇꅇꕸ맴뙓귈뒣낪과꒸룪늣ꪺ돸륓뉶ꅁ룪ꑈ녎뱗ꕛ꯹ꚳ과꒸ꕾ뛗룪늣ꅂ듮ꓖ꯹ꚳ늼ꅁ꙳Ꙣꗦ뒫ꅝtrade-offꅞ쏶ꭙꅃ뙓귈껄ꩇ결끝둉뭐듀ꕎ껄ꩇꪺ셠Ꙙꅁ끝둉뭐듀ꕎ껄ꩇꭏ쏒덱덦뙓귈륷듁녎뱗ꕛꕾ뛗믝ꡄꅁ걏뙓귈맯늼믝ꡄꪺ뱶암ꭨ꒣뵔ꥷꅁ굙듀ꕎ껄ꩇꑪ꧳끝둉껄ꩇꅁꭨ늼믝ꡄ듮ꓖꅁ믹껦뭐돸륓ꑕ뙞ꅆ꒧ꅁꭨ늼믝ꡄ뱗ꕛꅁ믹껦뭐돸륓ꑗꅃ뙓귈돌ꯡ라뱗ꕛꅂ듮ꓖ늼믹껦뭐돸륓결ꑀ맪쏒냝썄ꅃꑀ꿫꣓뮡ꅁꕘ뉻ꕾꗍ뷄삻(꣒꙰걷뿄ꙍ뻷ꅁꕀ곉꧊ꪺ뿄뉖뛃ꅁ꒤냪ꑪ뎰ꪺ걆ꩶꅂ굸ꅂ궸뱵ꯂ꿙떥)ꅁꓞ땯ꖻ냪덦맴뙓귈ꪺ륷듁ꅁꙢꗟꝙ(immediate)룻땵(intermediate)ꪺ껉뚡꒺ꅁ듀ꕎ껄ꩇ룻결엣뗛ꅁ덱덦뙓귈뭐늼돸륓ꚨ굴Ꙗ쏶ꭙꅆ끝둉꓀끴껄ꩇ믝굮룻껉뚡ꪺ뷕뻣ꅁꙝꚹ껉뚡꧔ꅁ꣢ꕩ꿠ꚨꖿꙖ쏶ꭙꅃ놴끑늼뭐ꕾ뛗ꖫ돵쏶셰꧊ꪺ맪쏒ꓥ쑭꒣Ꙩꅁꗧ꿊ꕆꑀ교ꪺ떲뷗ꅃMaand Kao(1990)꣏ꗎꓫ룪껆ꅁ땯뉻ꕘꑦ뻉Ꙗ냪깡ꅁ냪꒺덱덦뙓귈뭐믹ꚨꖿꙖ쏶ꭙꅆ뙩ꑦ뻉Ꙗ냪깡꣢ꭨꚨꙖ쏶ꭙꅃSolnik(1987)땯뉻ꑋ귓ꑵ띾꓆냪깡ꪺ늼ꥵ돸륓뭐덱덦뙓귈ꚨꖿꙖ쏶ꭙꅆ굙꣏ꗎꓫ룪껆ꅁꙢ꒣Ꙑ룪껆듁뚡ꅁ꣢엜볆ꭨꕘ뉻굴Ꙗ쏶ꭙꅃJorion(1990)왛맮덱덦뙓귈맯룳냪ꗸ띾늼돸륓ꪺ뱶암ꅁꕌ땯뉻뽮랥녱냪ꕾ겡냊ꪺ뱴냓ꅁ꣤늼돸륓뭐뙓귈곒ꚨꖿ곛쏶ꅆ걏Knoo(1994)땯뉻뛗뉶엜냊맯뽄걷쑱띾늼돸륓ꪺ뱶암ꯜ걏뮴띌ꅃꝑꗎ럭ꕎꪺꙀ뻣Ꙙ꓀꩒(cointegration analysis)ꅁRatner(1993)땯뉻과냪믹볆ꪺꓫ룪껆뭐꒻귓ꑵ띾냪깡ꪺ싹쏤뛗뉶뛈꙳Ꙣ룻ꑰꕂ꒣엣뗛ꪺ굴Ꙗ쏶ꭙꅁꡓꚳꙀ뻣Ꙙ쏒뻚ꅆ걏Mukherjee and Naka(1995)ꅁꙐ볋꣏ꗎꓫ룪껆ꅁ땯뉻ꓩꖻꪺ믹볆뭐뛗뉶(꣤ꕌ셠엩엜볆)꙳Ꙣ엣뗛ꪺ듁Ꙁ뻣Ꙙ쏶ꭙꅁꓩ꒸뙓귈뒣ꓩꖻ늼돸륓ꅃꕴꑀꓨ궱ꅁAjayi and Mougoue(1996)꣏ꗎꓩ룪껆ꅁ땯뉻ꑋ귓ꑵ띾꓆냪깡꒤ꑃ귓냪깡ꪺ덱덦뙓귈맯룓냪ꪺ늼ꖫ돵곒꙳Ꙣꅂ땵듁ꪺ굴궱뱶암ꅃꕴꕾꅁꙢ뛗뉶ꩩ냊궷쁉ꪺ왛쉉ꑗꅁJorion(1991)땯뉻과냪늼ꖫ돵꒣꣼ꕾ뛗궷쁉ꪺ뱶암ꅆ걏ꅁKoutoulas andKryzanowski(1996)땯뉻뛗뉶뭐ꑵ띾늣ꕘꩩ냊걏덹ꚨꕛ꺳ꑪꖫꓫ돸륓ꩩ냊ꕄ굮ꙝ꿀ꅆKearney(1998)땯뉻뛗뉶ꩩ냊걏뱶암ꑰ냪(ꕈ띒몸쓵결꣒)ꖫꓫꩩ냊돌궫굮ꪺꙝ꿀ꅃꙢ냪믚뿄ꖫ돵띕쇍뻣Ꙙꪺ샴맒ꑕꅁ늼뭐ꕾ뛗ꖫ돵곛꒬쏶셰삳걏꒣5
ꪧꪺ맪ꅁꑗ굺맪쏒ꓥ쑭ꕘ뉻꒣ꑀ교ꪺ떲뷗ꕩ꿠ꪺ귬ꙝꕝ걁ꅇꅝ1ꅞ꣏ꗎꓩꅂꓫꅂꥵ룪껆ꪺ깴늧ꅆꅝ2ꅞ냪깡(뱴냓)맯ꕾ뙽꧱땻ꯗꪺꑪꑰꅆꅝ3ꅞ뿩ꕘ뿩ꑊꕄ뻉ꪺ냪깡ꅆꅝ4ꅞ곣ꡳꓨꩫ뭐볒ꮬ덝ꥷꪺ꒣Ꙑꅃꥵ룪껆떹꒩늣ꭾꖫ돵룻ꪺ뷕뻣껉뚡ꅁ덱덦뙓귈뛉Ꙗ꧳뒣낪늼믹껦ꅆꙁ녱룪늣믝ꡄꪺꢤꯗ꣓곝ꅁ뿄늣ꭾꖫ돵뷕뻣Ꟗ덴ꅁꥵ룪껆뒣꣑뙓귈ꢬ냷ꪺ껉뚡ꅁ엽ꖿꪺ끝둉껄ꩇꑪ꧳굴ꪺ듀ꕎ껄ꩇꅁꕾ뛗뭐늼ꖫ돵ꕘ뉻ꖿꙖ쏶ꭙꅃꕴꕾꅁꑰ냪걏룪랽롛뷡룻꿊ꕆꪺ냪깡ꅁ덱녠맯ꕾ뙽꧱땻ꯗ룻ꑪꅁ꧶꧳땯뉻늼뭐ꕾ뛗ꖫ돵쏶셰ꪺ쏒뻚ꅆ굙결ꕘꑦꕄ뻉ꪺ냪깡ꅁ뙓귈뭐믹ꝥ뉻ꖿ곛쏶ꅁ뙩ꑦꕄ뻉ꪺ냪깡ꅁ꣢ꭨ결굴곛쏶ꅃ돌ꯡꅁ꒣Ꙑꪺ곣ꡳꓨꩫꅂ볒ꮬ걏ꝟꛒ뱻꣤ꕌꪺ룑쓀엜볆ꅂ걏ꖼꛒ뙱엜볆ꪺ껉뚡륌땻꽓뱸(꣒꙰엜볆ꪺꥷ꧊(stationarity))ꅁꕩ꿠뻉교꒣Ꙑꪺ떲뷗ꅃꖻꓥ꣏ꗎꕸ왗늼뭐ꕾ뛗ꖫ돵ꪺꓩ룪껆ꅁ왛맮뿄ꙍ뻷듁뚡ꅁꕸ맴뙓귈걏ꝟ뱶암늼돸륓ꅃꕸ왗결ꑀꑰꮬ뙽꧱롧샙ꫀ라ꅁꓩ룪껆ꪺ꣏ꗎ낾궫꧳늼뭐ꕾ뛗꣢귓뿄ꖫ돵늣ꭾꪺ쑶ꪧ꧊듀ꕎ껄ꩇꅁ꣢뚡럭꙳Ꙣ굴Ꙗ쏶ꭙꅁꕸ맴뙓귈꣤륷듁뮤꣏룪ꑈ뱗ꕛ꯹ꚳ룻낪돸륓ꪺꕾ뛗ꅁ뇆삽늼룪룪ꅁ뻉교늼믹껦뭐돸륓ꪺꑕ뙞ꅃꖻꓥꝑꗎGARCH-M볒ꮬ샋엧ꚹꑀ낲뮡ꅁꣃ뻚ꕈ뒣ꕘꯘ쒳ꅁꝀ결곛쏶뉺끝룪ꡍ떦ꪺ냑ꛒꅃ3. GARCH-M볒ꮬ늼룪ꑈ꒣뛈쏶ꩠ늼돸륓ꅁꟳ쏶ꩠ늼꯹ꚳ듁뚡( holding period )ꪺ궷쁉ꅁ낪륷듁늼돸륓녎뱗ꕛ늼ꪺ꯹ꚳꅑꕴꑀꓨ궱ꅁꕎꫭ늼돸륓궷쁉ꪺ돸륓엜늧볆(variance)뱗ꕛꅁ궰ꝃ돸륓륷듺ꪺ뫫뵔꧊ꅁ녎듮ꓖ늼ꪺ꯹ꚳꅃMerton(1980)ꯘ쒳륷듺늼돸륓껉ꅁ삳ꛒ뱻ꕎꫭ늼꯹ꚳ듁뚡궷쁉ꪺ늧뷨엜늧볆(heteroscedasticity)ꅑChou (1988)뭻결ꛛ1960꙾ꕎꕈ꣓ꅁ과냪ꖫꪺꑕ껀ꅁꕄ굮걏늼ꖫ돵ꩩ냊꧊ꪺ뱗ꕛꅁ낪늼돸륓ꩩ냊쇴ꝴꪺ궷쁉ꅁ궰ꝃ룪ꑈ꯹ꚳ늼ꪺ띎쑀ꅁ뻉교늼믹껦ꪺꑕ뙞ꅃ쏶꧳뿄냓ꭾ돸륓뭐꣤ꩩ냊ꪺ맪뗽볒ꮬꓥ쑭ꅁꕩ냑빜Bollerslev, Chou, and Kroner(1992)뭐Bera and Higgins(1993)랥꣣ꕎꫭ꧊ꪺꙞ압뷗ꓥꅃEngle(1982)ꪺꛛ끪쉫뇸ꗳ늧뷨엜늧볆볒ꮬ(autoregressive conditionalheteroscedasticity modelꅁ슲뫙 ARCH)ꅁꙐ껉꛴군늼돸륓뭐ꕎꫭ궷쁉ꕂ쁈껉뚡엜냊(time-varying)ꪺ뇸ꗳ엜늧볆ꅑ쁈ꯡBollerslev (1986)ꟳꛒ뱻ꭥ듁ꪺ뇸ꗳ엜늧볆ꅁ쉘ꕒARCH볒ꮬꚨ결ꑀ꿫꓆ꛛ끪쉫뇸ꗳ늧뷨엜늧볆볒ꮬ(generalized autoregressive conditional heteroscedasticity modelꅁ슲뫙6
GARCH)ꅁꙢ떲멣덝ꥷꑗꟳ꣣뱵꧊ꅁꙐ껉ꑝ꣏녯Ꙣ냑볆꛴군껉ꟳꕛ뫫슲ꅃGARCH볒ꮬꑶꚨ결뿄롧샙뻇꒤ꅁ꓀꩒륷듺늼ꖫ돵돸륓뭐궷쁉ꪺ볐럇ꓨꩫꅃꖻꓥꙢGARCH-M 볒ꮬ(Engle ,Lilien and Robins, 1987ꅞ걛멣ꑗꅁ놴끑ꕸ왗Ꙣ걷뿄ꙍ뻷듁뚡ꅁ뙓귈맯늼돸륓꣤ꩩ냊ꪺ뱶암ꅁ맪뗽떲ꩇ땯뉻Ꙣ꒣쎭ꥷꪺ뿄ꖫ돵샴맒ꑕꅁ뙓귈걏늼돸륓꣤ꩩ냊ꪺ궫굮룑쓀엜볆ꅃGRACH-M볒ꮬ녪뷕궷쁉덗쇗ꪺ룪ꅁ굮ꡄ룉쁶꣤꯹ꚳ늼ꪺ궷쁉ꅁ늼돸륓ꕝ걁ꕎꫭ궷쁉ꪺ뇸ꗳ엜늧볆ꅁ뇸ꗳ엜늧볆ꪺ뱗ꕛꖲ뚷뱗ꕛ궷쁉룉쁶ꅁ뮤꣏룪ꑈ쑾쓲꯹ꚳ뮼뱗궷쁉ꪺ늼ꅃꕏR결t−1듁ꛜt듁ꪺt늼돸륓ꅁΩ−1결ꛜt−1듁결ꓮꪺ꧒ꚳ끔꺧뚰Ꙙ(information set)ꅁꙢꚹꑀꑶtꪾ뇸ꗳꑕꅁe결Rꪺ뇸ꗳꖭꞡ귈ꪺ뷄삻(shocks)ꅁh결Rꪺ뇸ꗳ엜늧볆ꅑttttꭨ볐럇ꪺGARCH (p,q) -M볒ꮬ결ꅒR=at0+bh+e(5)t teΩ1~N(0,h)(6)tt−tpqh=bt0+∑bh2−+ce(7)iti∑jt−j꣤꒤i=1j=1e꒣꙳Ꙣꛛ곛쏶(autocorrelation)ꅂꖭꞡ볆결륳ꕂ뇸ꗳ엜늧볆결hꪺttꕾꗍ뷄삻ꅁb0,b,c곒결ꭄ굴볆ꅑ+ i j∑bi∑c뿅뙱ꗴꑀ뷄삻맯뇸ꗳ엜늧볆jꪺ꯹쓲꧊(persistence)ꅁ꣤ꥍꖲ뚷ꑰ꧳1ꅁꕈꭏ쏒볒ꮬꪺ쎭ꥷꅑ뇸ꗳꖭꞡ귈ꓨ땻ꚡ꒤ꪺbh결쁈껉뚡엜냊ꪺ궷쁉뙋ꓴꅁ굙륷듁돸륓궷쁉뱗ꕛꅁꭨꖲ뚷t뱗ꕛ륷듁돸륓ꕈ결궷쁉룉쁶ꅁ걇ꛓꕎꫭ궷쁉뭐돸륓뚡ꧨ뒫쏶ꭙꪺ냑볆b귈ꑪ꧳륳ꅃꙢ뉻ꕎ곬덎뙩ꡂꅂ끔꺧뛇벽Ꟗ덴ꪺ뿄샴맒꒤ꅁ귌둘ꕇꕩꕈꗟꝙ샲녯뛗뉶덱덦뙓귈ꪺ끔꺧ꅁ꯹쓲뙓귈녎ꓞ땯뙩ꑀꡂꪺ뙓귈륷듁ꅁ뮤꣏룪ꑈ뷕뻣꣤룪늣닕Ꙙꅁꕈ룻낪돸륓ꪺꕾ뛗듀ꕎ늼ꅁ뱶암럭듁늼돸륓뭐ꩩ냊ꅃꙢꚹꑀ뇔굺ꑕꅁ늼돸륓뭐륷듁뙓귈꙳Ꙣꑕ굺쏶ꭙ:R=he−1e(8)tttt꣤꒤h결꣣ꚳꥷ엜늧볆s2ꪺꗕ뺸궵뭾깴(white noise error)ꅆee룪tt−1결tꑈꙢt−1듁껉맯t귈ꪺ뙓귈륷듁ꅁꭥ듁맯럭듁ꪺ뙓귈륷듁뱶암럭듁ꪺ늼돸륓ꅃeeꕩ왛듺ꪺ엜볆ꅁꙢt−1결꒣뉺꧊륷듁낲덝ꑕꅁ룪ꑈꝑꗎt−1듁꧒tꚳ끔꺧륷듁t듁뙓귈ꅁeet−1떥꧳뙓귈뻷뉶꓀끴ꪺ볆뻇듁뇦귈ꅁꑝ둎걏t듁ꪺt맪믚뙓귈ꅃ껚뻚뉺꧊륷듁낲덝ꅁ(8)ꚡ엜결ꅇ7
R=he(9)ttte결ꕈꖻ냪덦맴ꫭꗜꪺꕾ냪덦맴믹껦ꪺ맪믚뙓귈뉶8ꅃ꙰ꩇ뙓귈ꡓꚳt엜ꅁꚹꝙe=et−1=ett−2…=녠볆ꅁꭨꖫ돸륓R결ꑀ엜늧볆ꥷꪺꗕ뺸궵t륌땻ꅆ럭ꕘ뉻꯹쓲뙓귈ꅁꭨ꣼궭꧳eꪺ늼돸륓꒧뇸ꗳ엜늧볆(conditionaltvariance)결ꅒVar(Re)=s22(e)(10)ttt뙓귈ꧺ엣뱶암늼돸륓ꪺ뇸ꗳ엜늧볆ꅁ뙓귈띕ꑪ(ꑰ)ꅁꭨ늼돸륓ꪺ엜늧볆녎쁈꒧뱗ꕛ(듮ꓖ)ꅃ꙰ꩇ뙓귈ꢬꕈ룑쓀늼돸륓ꪺꩩ냊ꅁꭨ꣤득깴귈엜늧볆결ꥷꅃꛒ뱻뙓귈껄ꩇꪺGARCH-M볒ꮬ결ꅒR=a+bhs+ae+e s=1 , 1(11)t0t tt 2eΩ~(0,)tt−1Nh(12)th=bbh2cet0+∑it−1+∑(13)jt−j꣤꒤i=1j=1s결꛴군뇸ꗳꖭꞡ돸륓껉ꪺh냑볆ꅁ굙꣏ꗎ뭾깴뚵ꪺ엜늧볆꛴군볒ꮬꅁꭨs=1ꅑ굙꣏ꗎ볐럇깴꛴군ꅁꭨs=12ꅃ결ꑆꭏ뗽볒ꮬꪺ쎭ꥷ뭐엜늧볆결ꖿ귈ꅁꖲ뚷Ꙑ껉몡ꢬb0>0ꅁb≥0ꅁiꇢ1,2,…pꅁc≥0ij ,j=1,2,…qꅁ∑b<1ꅁi∑c<1ꅁ(j∑b+i∑c)<1떥궭꣮뇸ꗳꅃ늼돸륓jꓨ땻ꚡ꒤ꪺi=1j=1a0+bhsꫭꗜ궷쁉뙋ꓴꅁ꣤꒤b>0ꅁhꗑꚡ(13)ꡍꥷꅃ볒ꮬ꒤꧒ttꚳ냑볆(a0,b,ꍜ,bc)걏ꕈ돌ꑪ랧꛴군ꩫ(max 0,b,imum likelihood i jestimation techniques)ꡄ룑셰ꗟꓨ땻ꚡ닕ꛓ녯ꅃGARCH-M볒ꮬ꒤ꪺ궷쁉뙋ꓴ꣣ꚳ쁈껉뚡엜냊ꛓ엜ꪺ꽓꧊ꅁ꙰ꩇ뇸ꗳ엜늧볆걏녠볆(ꚹꝙb=c=0)ꅁꭨ볒ꮬ끨꓆ꚨ궷쁉뙋ꓴ결ꥷ귈ꪺ뛇닎낲ij덝ꅑ럭b=0껉ꅁ볒ꮬ신꓆결GARCH(p,q)볒ꮬꅝBellerslev 1986ꅞꅑ럭p=0ꅁ볒ꮬ신꓆결ARCH-M볒ꮬꅑ럭p=0ꅁb=0껉ꅁꭨ볒ꮬ신꓆결ARCH볒ꮬ(Engle 1982ꅞꅃGARCH-M볒ꮬ꒣뛈쇴ꝴ득깴뚵꣣ꚳARCH껄ꩇꅁ꒹덜ꭥ듁ꪺ뇸ꗳ엜늧볆뱶암럭듁뇸ꗳ엜늧볆ꅁꙐ껉ꖭꞡ귈ꓨ땻ꚡꟳꕛꑊ뇸ꗳ엜늧볆결궷쁉룑쓀엜볆ꅑꙝꚹꅁGARCH-M볒ꮬꪺ덝ꥷꟳ결ꑀ꿫꓆ꅁꕩ뙩ꑀꡂ왛맮뿄엜볆걏ꝟ꣣ꚳ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴꅃꖻꓥ덝ꥷGARCH-M볒ꮬꪺ늼돸륓ꓨ땻ꚡꅁ꒣뺨ꕝꝴ궷쁉뙋ꓴꅁꟳ뻉ꑊ뙓귈엜볆ꅁ걏ꚳꝏ꧳꙳Ꙣꓥ쑭볒ꮬꪺꕄ굮꽓쉉ꅃ룪ꑈ궱맯ꖻ냪덱덦 8맪믚뙓귈ꪺꥷ롱결ꅇ††††?e=100×[log(E)−log(E−1)]?꣤꒤E결ꝙ듁뛗뉶ꅃtttt8
뙓귈ꅁꕾ뛗룪늣돸륓뱗ꕛꅁ결끬ꡄꚳ믹쏒꣩닕Ꙙꪺ돸륓랥ꑪꅁ녎궰ꝃꖻ냪룪늣(꙰늼)ꪺ꯹ꚳꅁ신늾룪꣬ꕈꕾ냪덦맴ꫭꗜꪺ룪늣(꙰ꕾ뛗)ꑗꅁꚹꑀꛦ결녎꣏늼ꖫ돵ꪺ믝ꡄ듮ꓖꅂ꣑떹뱗ꕛꅁ뻉교늼믹껦ꑕ뙞ꅂ돸륓궰ꝃ뭐ꖫ돵ꩩ냊ꪺ뱗ꕛꅃ귌뭻결걷뿄ꙍ뻷듁뚡ꅁꕸ맴꯹쓲뙓귈ꓞ땯ꪺ룪늣궫꓀끴걏늼돸륓ꑕ궰꣤엜늧볆뱗ꕛꪺꑀ귓귬ꙝꅃ?⸠룪껆냲ꖻ꽓뱸ꖻꓥ꣏ꗎ룪껆결ꕸ왗늼뭐ꕾ뛗ꖫ돵ꪺꓩꚬ뵌믹ꅁꕝ걁ꕸ왗ꕛ앶믹볆뭐ꕈ띳ꕸ맴ꫭꗜꪺ과꒸믹껦ꪺ뛗뉶ꅝ띳ꕸ맴/과꒸ꅞꅑ룪껆꣓랽결꒤ꖡ믈ꛦ뇐뎡륱ꑬ군뫢뻷꒤ꓟEPS/AREMOS롧샙닎군룪껆깷ꅃꖻꓥ룪껆꓀결ꑔ귓곣ꡳ듁뚡:ꑀ걏ꛛ1995꙾1ꓫꫬꛜ1998꙾12ꓫ꦳ꅁꕝꝴ걷뿄ꙍ뻷ꕘ뉻ꭥꯡ듁ꪺꗾ냏뚡ꅁꙀꚳ1,128귓ꓩ왛듺귈ꅑ결ꓱ룻걷뿄ꙍ뻷ꪺ뱶암ꅁꖻꓥꙁ녎ꗾ냏뚡꓀돎결ꑇ귓볋ꖻꑪꑰ곛꫱ꪺꑬ뚰Ꙙꅁꑀ걏ꛛ1995꙾ꫬꛜ1996꙾꦳걷뿄ꙍ뻷땯ꗍꭥꪺ닄ꑀ볋ꖻ냏뚡ꅁꙀꚳ573귓ꓩ왛듺귈ꅑꕴꑀ걏ꛛ1997꙾ꫬꛜ1998꙾꦳꣼걷뿄ꙍ뻷뱶암ꪺ닄ꑇ볋ꖻ냏뚡ꅁꙀꚳ555귓ꓩ왛듺귈ꅃ꣢귓ꑬ볋ꖻꕄ굮걏ꗎ꣓ꓱ룻걷뿄ꙍ뻷걏ꝟ뱶암늼돸륓륌땻ꅈ걏ꝟ꙳Ꙣ뙓귈껄ꩇꅈ걏ꝟ쉘ꑪꖫꩩ냊궷쁉뭐굮ꡄꟳꙨꪺ궷쁉뙋ꓴꅈꖻꓥꥷ롱닄tꓩ늼돸륓ꅁRꅁ결ꖼ롧ꝑ뷕뻣ꪺꓩꚬ뵌믹볆ꪺt맯볆깴꓀(logarithmic differenceꅞꅁꙁ궼ꑗ100ꅁꚹꝙꅒR=100×[log(TAIEX)−log(TAIEXttt−1)]꣤꒤TAIEX결닄tꓩꪺꕸ왗땯ꛦ뙱ꕛ앶믹볆ꪺꚬ뵌믹껦ꅃꫭ1ꙃꕘꑔt귓볋ꖻ냏뚡ꪺ늼돸륓껉뚡볆ꙃꪺ냲ꖻ뇔굺닎군뙱ꅃꫭ1꒤ꑔ귓볋ꖻ듁뚡ꪺ늼ꖭꞡ돸륓(mean returns)곒결굴귈ꅁꕂꭄ녠놵꫱륳ꅆ둎볋ꖻꪺ볐럇깴(standard deviations)ꛓꢥꅁ걷뿄ꙍ뻷땯ꗍꭥ(1995-1996ꪺ닄ꑀꑬ볋ꖻ냏뚡)ꪺꖫ돸륓ꩩ냊(볐럇깴=)ꑰ꧳걷뿄ꙍ뻷땯ꗍ듁뚡(1997-1998ꪺ닄ꑇꑬ볋ꖻ냏뚡)ꪺꖫ돵ꩩ냊(볐럇깴=)ꅑ맏1ꛜ맏6꓀ꝏ쎸ꕘꑔ귓볋ꖻ냏뚡ꪺ믹볆뭐뛗뉶늼돸륓뭐뙓귈ꪺ껉뚡쇍뛕맏ꅁ맏1ꅂ2ꅂ3ꧺ엣곝ꕘ뿄ꙍ뻷듁뚡ꅁ믹볆뭐뛗뉶ꝥ뉻곛ꓨꙖꪺꢫ뛕ꅁ뛗뉶낪(ꕸ맴뙓귈)ꅁꭨ믹ꝃꅆ맏2ꅂ4ꅂ6꒤ꪺ늼돸륓ꩩ냊ꅁꛛ1997꙾10ꓫꕈꯡꅁꧺ엣ꑪ꧳뿄ꙍ뻷땯ꗍꭥꪺꖭ쁒껉듁ꅃꑔ귓늼돸륓껉뚡볆ꙃꪺ낾멁(skewness)ꭙ볆곒걏굴귈ꅁꝥ뉻ꭄ맯뫙꧊ꪺꖪ낾꓀끴ꅆꛓꑔ귓늼돸륓껉뚡볆ꙃꪺ깰멁(kurtosis)ꭙ볆ꞡꑪ꧳9
3ꅁ꓀ꝏ뙗ꕘ곹 34,29,20귓볐럇깴ꅁꝥ뉻낪꽕깰꓀끴(leptokurticdistribution)8ꅃJarque-Bera 녠멁꓀끴샋ꥷ(normality test)Ꙑ껉ꛒ뱻ꑀ볆ꙃꪺ낾멁뭐깰멁ꪺ녠멁꧊ꅁ꣤닎군뙱결ꅒT−KS2+1K2[(−3)]꣤꒤64T결볋ꖻ볆ꅁS결낾멁ꭙ볆ꅁK결깰멁ꭙ볆ꅃꚹ닎군뙱결ꑀꛛꗑꯗ(degree of freedom)결2ꪺc2꓀끴ꅃꫭ1꒤룻ꑪꪺ녠멁꓀끴샋ꥷ귈(J-B N)ꕘꅁꙢ5ꉍꪺ엣뗛ꓴ럇ꑕꅁ꓀ꝏ떴ꑔ귓볋ꖻ돸륓꓀끴결녠멁ꪺ뗪때낲덝ꅃꛛ곛쏶샋ꥷꗎ꣓샋듺껉뚡볆ꙃ엜볆ꪺ껉뚡곛꧊(temporaldependence)ꅁꑀꭨꕩꕈ엽귌ꑆ룑엜볆ꪺ꽓뱸ꅁꕴꭨꟳ걏볒ꮬ덝ꥷꪺ냑ꛒꅃꑀ꿫꣓뮡ꅁ믹볆꣤돸륓ꅁꙢ둘귓덳쓲ꪺꗦ꧶ꓩ(껉)꒺ꅁꕩ꿠꙳Ꙣꛛ곛쏶ꅃꖻꓥꕈLjung-Box Q(L-B Q)귈샋ꥷ늼돸륓볆ꙃꓴ럇뚵{R}꣤ꖭꓨ귈{R2}볆ꙃꪺ낪뚥ꛛ곛쏶(꣒꙰L-B Q(24)ꅂL-B2 Q(24ꅞꪺtt뢨뿰듁볆결24듁)ꅃL-B Q닎군귈결ꅒQ(k)=T(T+2)∑꣤꒤T결볋ꖻ볆ꅁr결닄j귓ꛛj=1T곛−쏶jꭙ볆ꅁQ(k)결꫱꧳ꛛꗑꯗ결ꛛj곛쏶뚥볆ꅁkꅁꪺc2꓀끴ꅆ꣤뗪때낲뮡꒣꙳Ꙣꛛ곛쏶ꅑꫭ1꒤ꅁꝙ꣏뢨뿰24듁ꅁꙢ5ꉈꪺ엣뗛ꓴ럇ꑕꅁꑔ귓볋ꖻꪺ늼돸륓곒꒣꙳Ꙣꛛ곛쏶ꅆ{R2}볆ꙃꪺ샋ꥷ닎군귈(L-B2 Q(K))뎣ꯜ낪ꕂ엣뗛ꅁ늼돸륓껉뚡볆ꙃꕩt꿠꙳Ꙣ늧뷨엜늧볆ꅁꯘ쒳꣏ꗎ(G)ARCH볒ꮬ녱꓀꩒ꅃꑀ귓쁈뻷륌땻(stochastic process)ꪺ껉뚡볆ꙃꅁ굙꣤ꖭꞡ귈ꅂ엜늧볆뭐Ꙁ엜볆(covariance)ꅁ꒣ꙝ껉뚡ꛓ엜ꅁ뭐껉뚡뽗ꗟ(independent of time)ꅁꭨꗴ꛳ꕾꗍ뷄삻뛈꣣땵볈ꪺ뱶암ꅁ롧륌ꑀ걱껉뚡ꯡꅁ라덶몥꫰Ꙟ귬꣓ꓴ럇ꅁꝥ뉻쎭ꥷꪬ멁ꅁ뫙꒧결ꥷ꧊(stationary)껉뚡볆ꙃꅆ꒧ꅁ굙땯ꗍꕾꗍ뷄삻ꅁꑀ엜볆Ꙣ껉뚡륌땻꒤ꅁ뮷싷꣤ꖭꞡ귈ꅁꭨ결ꭄꥷ꧊(nonstationary)껉뚡볆ꙃꅃ뛇닎군뙱ꓨꩫꯘꗟꙢ엜볆결ꥷ꧊꒧낲덝ꑗꅁ굙ꪽ놵맯ꭄꥷ꧊엜볆뙩ꛦ끪쉫꓀꩒ꅁꭨꕩ꿠늣ꗍ샋ꥷ낾뭾뭐낲꧊끪쉫(spuriousregression)(Granger and Newbold,1974)ꅑꙝꚹꅁ꣏ꗎ껉뚡볆ꙃ엜볆뙩ꛦ맪쏒곣ꡳꭥꅁ뚷ꗽ샋ꥷ엜볆ꪺꥷ꧊꽓뱸ꅃADF(augmented Dickey-Fuller)돦껚샋ꥷ(Dickey and Fuller 1981)결녠ꗎ꣓뵔ꥷ엜볆ꥷ꧊ꪺꓨꩫꅁ꣤샋ꥷ끪쉫ꚡ 9낾멁뭐깰멁ꭙ볆ꪺ볐럇깴꓀ꝏ결(T)ꥍ(24T)ꅁT결볋ꖻ볆ꅑꑀ녠멁꓀끴ꪺ 낾멁ꭙ볆결륳ꅁ깰멁ꭙ볆결3ꅃ10
결ꅇn∆X=a1X−1+∑b∆X1+ettit−t꣤꒤i=1∆결ꑀꚸ깴꓀륂뫢ꙝꑬ(first-order difference operator)ꅁe결ꗕ뺸궵뭾t깴ꅃADF돦껚샋ꥷꪺ뗪때낲뮡결엜볆ꅁ{X}ꅁ결ꭄꥷ꧊ꅁꝙat1=0ꅁ굙a1엣뗛늧꧳륳ꅁꭨ떴뗪때낲뮡ꅁ엜볆결ꥷ꧊ꅃꫭ1ꪺADF샋ꥷ떲ꩇ녯ꪾꅁꑔ귓볋ꖻꪺ늼돸륓볆ꙃꅁꙢ5ꉈꪺ엣뗛ꓴ럇ꑕꅁ곒떴꣤결돦껚ꪺ뗪때낲덝ꅁꑔ귓볋ꖻ돸륓볆ꙃ곒결ꥷ꧊ꅃꚹꑀꥷ꧊꽓뱸ꗧ맯삳꣬맏2ꅂ4뭐6ꪺ늼돸륓껉뚡ꢫ뛕ꅁꙢꑔ귓볋ꖻ듁뚡꒺ꅁ늼돸륓곒라꫰Ꙟ꣤ꖭꞡ귈ꅁꕩꕈꪽ놵뙩ꛦ끪쉫꓀꩒ꅃ맪믚뙓귈ꪺ껉뚡볆ꙃ룪껆ꅁ롧ADF돦껚샋ꥷꅁꗧ결I(0)엜볆ꅆ걏뮡맯삳꣬맏1ꅂ3ꅂ5ꪺ뛗뉶껉뚡볆ꙃ결I(1)ꅁ맯삳꣬맏2ꅂ4ꅂ6ꪺ뙓귈결뛗뉶ꪺꑀꚸ깴꓀ꅁ결I(0)ꅃꫭ1. ꕸ왗늼ꓩ돸륓냲ꖻ닎군뙱1995-981995-961997-98볋ꖻ볆1128573555ꖭꞡ귈볐럇깴랥ꑪ귈랥ꑰ귈낾멁()()()깰멁()()()J-B N 샋ꥷ***L-B Q(6)-B Q(12)-B Q(24)-B2 Q(6)***11
L-B2 Q(12)***L-B2 Q(24)***ADF(n)(3)*(1)*(3)*낾멁ꭙ볆뭐깰멁ꭙ볆ꑕ꒧걁뢹결볐럇깴ꅑJ-B N 샋ꥷ결Jarque-Bera녠멁꓀끴샋ꥷꅑL-BQ(k)ꥍL-B2 Q(k)꓀ꝏ결늼돸륓ꓴ럇뚵꣤ꖭꓨ뚵ꛛ곛쏶샋ꥷ,k결뢨뿰듁볆ꅑADF(n)결돦껚샋ꥷ,꣤꒤n결ꗎAIC뿯ꥷ꒧돌빁뢨뿰듁볆ꅃ*ꫭꗜꙢ5ꉍꪺꓴ럇ꑕ엣뗛ꅃ363432120003028100002680002460004000 95/09 96/05 97/02 97/10 98/07 TAIEX E맏1.ꕸ왗땯ꛦ뙱ꕛ앶믹볆(TAIEX)뭐뛗뉶(E), 1995-1998421005-20-412-5-10
95/09 96/05 97/02 97/10 98/07R e맏2.ꕸ왗늼ꓩ돸륓(R)뭐뙓귈(e), 1995-19982827800026700025600050004000 95/03 95/09 96/01 96/05 96/10 TAIEX E맏3.ꕸ왗땯ꛦ뙱ꕛ앶믹볆(TAIEX)뭐뛗뉶(E), 1995-1996211005-10-2-5-1013
95/03 95/09 96/01 96/05 96/10R e맏4.ꕸ왗늼ꓩ돸륓(R)뭐뙓귈(e), 1995-199636343230110002810000269000800070006000 97/05 97/10 98/01 98/06 98/10TAIEX E맏5.ꕸ왗땯ꛦ뙱ꕛ앶믹볆(TAIEX)뭐뛗뉶(E), 1997-199814
421005-20-4-5-10 97/05 97/10 98/01 98/06 98/10R e맏6.ꕸ왗늼ꓩ돸륓(R)뭐뙓귈(e), 1997-1998ꫭ1꒤ꪺ늼돸륓ꖭꓨ귈꙳Ꙣꛛ곛쏶ꅁ띴ꗜ늼돸륓볆ꙃꕩ꿠꙳Ꙣ늧뷨엜늧볆ꅁꖻꓥꙁꝑꗎꖿꚡꪺARCH샋ꥷ(Engle 1982)ꅁ왛맮늼돸륓ꪺ득깴뚵걏ꝟ꙳Ꙣ늧뷨엜늧ꪺARCH껄ꩇ(ARCH-effect)ꅃꫭ2ꝑꗎLM(Lagrange multiplier)닎군귈ꅁ샋ꥷꑔ귓볋ꖻ돸륓ꪺARCH껄ꩇꅃLM(k)샋ꥷꪺ닎군뙱결TR2ꅁꩁ녱ꑀꛛꗑꯗ결kꪺc2꓀끴ꅁ꣤꒤T결볋ꖻ귓볆ꅁR2결ꕈOLS꛴군ꪺ뮲ꝕ끪쉫ꚡ(auxiliary regression)ꪺꝐꥷꭙ볆귈ꅁk결뢨뿰듁볆ꅃꫭ2꒤ꪺTR2닎군귈엣뗛ꑪ꧳꣤5ꉈ셻곉귈ꅁꫭꗜARCH껄ꩇꪺ꙳Ꙣꅁ걏뮡늼돸륓ꪺꖭꞡ귈ꓨ땻ꚡꪺ득깴뚵꙳Ꙣ늧뷨엜늧볆ꅁꖲ뚷ꕈ(G)ARCH볒ꮬ뙩ꛦ늼돸륓뭐궷쁉ꪺ꓀꩒ꅃꫭ2. ARCH껄ꩇ샋ꥷ k1995-981995-961997-98 **15
*** *** *** *** *** *** *** *** *** *** ***LM(k)샋ꥷꪺ닎군뙱결TR2ꅁꩁ녱ꑀꛛꗑꯗ결kꪺc2꓀끴,k =1,…12ꅃ*ꫭꗜꙢ5ꉍꪺꓴ럇ꑕ엣뗛ꅃ5. 맪쏒꓀꩒ꖻꓥꕈꚡ(11)ꅂ(12)ꅂ(13)ꯘ멣ꪺGARCH-M볒ꮬꅁꛒ뱻걷뿄ꙍ뻷뷄삻ꅁ맪쏒놴끑궷쁉뙋ꓴ뭐ꕸ맴뙓귈Ꙣ늼돸륓륌땻꒤ꪺꢤꛢꅃ귌궺ꗽꝑꗎ돌ꑪ랧ꩫ꛴군ꗾ볋ꖻ듁뚡(1995-1998)Ꙩ뫘GARCH(p,q)-M볒ꮬꪺ덝ꥷꅁ뛇닎ꑗꅁ뇸ꗳ엜늧볆ꓨ땻ꚡ꒤ꪺ뢨뿰듁볆띕ꓖ띕ꙮꅃꙢARCH(q)-Mꪺ륌땻꒤ꅁꙝ결q=3껉ꅁ엜늧볆ꓨ땻ꚡ꒤ꪺ뢨뿰득깴ꖭꓨ귈꒴꣣ꚳ엣뗛ꪺ룑쓀꿠ꑏꅁꙐ껉ꅁARCH(2)-M ꪺLR샋ꥷ귈2(c=)ꅁꙢ5ꉈꪺꓴ럇ꑕ결엣뗛ꅁꗧꓤ꯹ARCH(3)-Mꪺ볒ꮬ덝ꥷꅁ귌뿯뻜ARCH(3)-M볒ꮬ꛴군늼돸륓ꪺ륌땻ꅃꛜ꧳GARCH(p,q)-M볒ꮬꅁ결ꡄ뫫슲ꅁ귌궭꣮p≤2ꅂq≤2꒧볒ꮬ닕Ꙙꅁꙝ결ht−2ꙢGARCH(2,1)-M꒤ꅁhꅁht−1t−2ꙢGARCH(2ꅁ2)-M꒤곒꒣엣뗛ꅑꕴꕾꅁGARCH(1,1)–M뭐16
GARCH(2,1)-M GARCH(1,2)–M 뭐GARCH(2,2)-M ꪺLR샋ꥷ귈ꗧ꒣엣뗛ꅁ꓀ꝏ낾Ꙗ꧳ꓤ꯹뫫슲ꪺGARCH(1,1)–M뭐GARCH (1,2)–M 볒ꮬꅃꫭ3ꙃꕘꗾ볋ꖻ듁뚡(1995-1998ꅞꪺARCH(3)-MꅁGARCH(1,1)-M뭐GARCH(1,2)-M볒ꮬ꛴군귈ꅁ꣤꒤뇸ꗳꖭꞡ돸륓결뭾깴뚵엜늧볆ꪺ꣧볆(s=19)ꅃ ꫭ3꒤ꑔ귓볒ꮬꪺ꧒ꚳ꛴군냑볆ꅁꙢ5ꉈꪺꓴ럇ꑕ곒결엣뗛ꅑ꣤꒤b0,bc 1, 1 ,c2뭐c3곒ꑪ꧳륳ꅑ(c1+c2+c3)=ꅁ(b1+c1)=ꅁ(b1+c1+c2)=곒ꑰ꧳1ꅁ몡ꢬ뇸ꗳ엜늧볆ꓨ땻ꚡ꒤ꪺ냑볆꛴군ꖲ뚷결ꖿꅂ엜늧볆결ꚬ샄뭐볒ꮬ결쎭ꥷꪺ궭꣮뇸ꗳꅆ볒ꮬ득깴ꖭꓨ뚵ꪺL-B Q닎군뙱샋ꥷ(ꝙL-B2 Q(k))ꅁꙢ5ꉍꪺꓴ럇ꑕꅁ뢨뿰ꛜ24듁ꅁ뎣꒣엣뗛ꅁ꒣꙳Ꙣ늧뷨엜늧볆ꅑ룻ꝃꪺꋚꋛ귈(ꝙ ARCH-LM(k))ꅁꗧ뵔ꥷ꒣꙳ꙢARCH껄ꩇꅁꑔ귓볒ꮬ덝ꥷ곒결빁럭ꅃHL결뿅뙱늼ꖫ돵ꩩ냊꯹쓲꧊ꪺꑀ귓볐ꅁꕎꫭꑀ귓뷄삻ꪺ12ꗍꥒꅁꚹꝙꑀ귓뷄삻Ꙣ롧륌Ꙩꓖ껉뚡ꯡ꒴꙳Ꙣꑀꕢꪺ껄ꩇꅁ꣤군뫢꒽ꚡ결ꅇHLꇗlog()log(∑b+)i∑cjꖻꓥ꣏ꗎꓩ룪껆ꅁHLꪺ돦ꛬ결ꓩꅁꙢꑔ귓볒ꮬ꒤ꅁARCH(3)-M볒ꮬ엣뉻룻결Ꟗ덴ꪺꩩ냊ꚬ샄꧊(꣤HL귈결ꅁꧺ엣ꑰ꧳GARCH(1,1)-M볒ꮬꪺ 뭐GARCH(1,2)-M 볒ꮬꪺꓩ)ꅃ ꫭ3꒤ꅁ귌땯뉻ꑔ귓볒ꮬꪺ늼돸륓륌땻곒꙳Ꙣ엣뗛ꪺ궷쁉뙋ꓴ(G)ARCH-M껄ꩇ(ꝙb>0)ꅁ늼결꣣ꚳ궷쁉ꪺ뿄냓ꭾꅁꝬꓞ궷쁉덗쇗ꪺ룪ꑈ쇊뙒늼ꖲ뚷뮡ꩁꣃ떹꒩ꕌ귌궷쁉 9ꖻꓥꗧꕈ뭾깴뚵ꪺ볐럇깴꛴군볒ꮬꅝꝙs=1ꅞꅁ꒣뷗걏뻚AICSC2럇?ꭨꅁ꣤떲ꩇ곒꒣쁵꧳s??껉ꪺ꛴군ꅁ꣤뚡ꪺ깴늧꧊꒣ꑪꅁ결론곙뵧둔ꅁ?ꖻꓥ뛈돸ꝩs??껉ꪺ(G)ARCH-M 볒ꮬ꛴군귈ꅃ17
뙋ꓴꅁ룉쁶꣤꯹ꚳ늼ꪺ궷쁉ꅆꙐ껉ꑔ귓뇸ꗳ엜늧볆륌땻곒꒣결ꥷꅝꝙb1≠0,c≠0ꅞꅁ결쁈껉뚡엜냊ꪺ궷쁉뙋ꓴ(time-varyingjrisk premiums)ꅃꑔ귓볋ꖻꪺ늼돸륓곒꙳Ꙣ엣뗛ꪺ뙓귈껄ꩇ(ꝙa<0)ꅁꚹꑀ떲ꩇ뭐Ajayi and Mougoue(1996)꣏ꗎꓩ룪껆ꅁ땯뉻ꕝ걁과냪ꅂꓩꖻ떥ꑋ귓ꑵ띾꓆냪깡꒤ꪺꑃ귓냪깡ꪺ믹볆뭐뛗뉶꙳Ꙣ듁Ꙁ뻣Ꙙ쏶ꭙꅁ땵듁덱덦뙓귈궰ꝃ늼돸륓ꪺ떲뷗ꑀ교ꅃ뙓귈뱗ꕛꕈꕾ맴ꫭꗜꪺ룪늣ꪺ돸륓ꅁꭐ꣏룪ꑈ엜룪늣닕Ꙙꅁ늾신늼룪룪ꛜꕈꕾ맴ꫭꗜꪺ뿄냓ꭾꑗꅁ궰ꝃ늼돸륓ꅃ엣뗛ꪺ뙓귈껄ꩇ꒣꙳Ꙣ늧뷨엜늧볆ꪺ뗽뻚(꒣엣뗛ꪺL-B2 Q뭐ARCH-ꋚM귈)ꅁꯘ쒳뙓귈ꕩꕈ룑쓀볋ꖻ듁뚡늼돸륓꣤ꩩ냊ꅁꓤ꯹Ꙣ늼돸륓륌땻꒤ꕛꑊ뙓귈엜볆ꕈ륷듺늼돸륓ꩩ냊ꅃ 늼돸륓꙳Ꙣ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴ(엣뗛ꪺb귈)뭐굴ꪺ뙓귈껄ꩇ(엣뗛ꪺa귈)ꅁꕌ귌Ꙣ걷뿄ꙍ뻷ꪺ껉뚡륌땻꒤ꅁ걏ꝟꕘ뉻뷕뻣ꅈꖻꓥ뙩ꑀꡂ맯ꫭ3볒ꮬ꛴군ꭙ볆Ꝁ쎭ꥷ꧊꓀꩒ꅝstability analysisꅞꅁ왛맮궷쁉뙋ꓴ뭐뙓귈껄ꩇꙢ껉뚡륌땻꒤ꪺ엜꓆ꅃ 샋듺냑볆ꪺ쎭ꥷ꧊ꅁꖻꓥꑷ녎볋ꖻ꓀돎ꚨ볋ꖻꑪꑰ곛꫱ꪺꑇ귓ꑬ뚰Ꙙ(냑빜ꫭ1)ꅁ닄ꑀ귓ꑬ볋ꖻ결ꖼ꣼걷뿄ꙍ뻷뱶암ꪺꖭ쁒껉듁(1995-1996)ꅁꕴꑀꭨ걏ꕝ걁걷뿄ꙍ뻷ꪺ냊샺껉듁(1997-1998ꅞꅁ귌ꝑꗎ뭐ꫭ3ꗾ볋ꖻ곛Ꙑꪺꑔ귓꛴군볒ꮬꅁ꓀꩒ꓱ룻걷뿄ꙍ뻷땯ꗍꭥꅂꯡ듁ꪺ늼돸륓ꛦ결ꅃ ꫭ4닄ꑀ귓ꑬ볋ꖻ냏뚡(1995-1996)ꪺ늼ꓩ돸륓볒ꮬ꛴군엣ꗜꅁ늧뷨엜늧볆샋ꥷꪺ닎군뙱L-B2 Q(24) 뭐ARCH껄ꩇ샋ꥷꪺLM귈(ARCH-LM(24))ꅁꛜ뢨뿰24듁뎣꒣엣뗛ꅁ꒣꙳Ꙣ늧뷨엜늧볆ꅑ18
ꑔ귓볒ꮬꪺ엜늧볆륌땻곒결쎭ꥷꅝꚹꝙ(c1+c2+c3)=ꅁ(b1+c1)=ꅁ(b1+c1+c2)=ꅞꅑꙢ5ꉈꪺ엣뗛ꓴ럇ꑕꅁ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴ(b)꛴군귈ꅁ낣ꑆꙢARCH(3)-M볒ꮬ꒤결엣뗛ꕾꅁꙢ꣢귓GARCH-M볒ꮬ꒤곒꒣엣뗛(GARCH(1,2)-M볒ꮬꙢ10ꉈꪺꓴ럇ꑕ결엣뗛ꅞꅑꛓ뙓귈껄ꩇ(a)Ꙣꑔ귓볒ꮬ꒤곒꒣엣뗛ꅃ ꫭ5ꪺ닄ꑇ귓ꑬ볋ꖻ냏뚡(1997-1998)ꪺARCH-M뭐GARCH-M볒ꮬ꛴군ꗧ곒닅Ꙙ때늧뷨엜늧볆볒ꮬ쎭ꥷꪺ궭꣮ꅃꙢꚹꑀ뿄ꙍ뻷듁뚡ꅁꑔ귓볒ꮬ곒ꕘ뉻엣뗛ꪺ(G)ARCH –M뭐뙓귈껄ꩇ(ꝙb뭐a곒엣뗛늧꧳륳)ꅁꚹꑀ떲ꩇ뭐귌ꭥꪺ륷듁곛ꑀ교ꅒ뿄ꙍ뻷샴맒ꑕꪺ늼ꖫ돵ꪺꖨ둔ꩩ냊ꅁ궰ꝃꑆ늼돸륓륷듺ꪺꖿ뵔꧊ꅁ뱗ꕛ늼꯹ꚳꪺ궷쁉ꅁ굙꒣떹꒩ꢬ냷ꪺ궷쁉뙋ꓴ룉쁶ꅁ룪ꑈ때띎꯹ꚳ늼ꅁ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴꅁꓗ꣤Ꙣ꒣쎭ꥷꪺ늼ꖫ돵꒤ꅁ걏뱶암늼돸륓ꪺ궫굮ꙝ꿀ꅑꙐ껉듁ꅁ뿄ꙍ뻷뷄삻ꑕꪺꕸ맴뙓귈꣤ꓞ땯ꪺ뙓귈륷듁ꅁ뮤꣏룪ꑈꕈ낪돸륓ꪺꕾ맴룪늣(꙰과꒸)듀ꕎꖻ냪룪늣(꙰늼)ꅁ뱗ꕛ늼ꖫ돵뷦삣ꅁ궰ꝃ늼믹껦뭐돸륓ꅁꑔ귓볒ꮬ꒤엣뗛ꪺ뙓귈껄ꩇꓤ꯹ꖻꓥ늼뭐ꕾ뛗결ꙮꪺ뿄듀ꕎ끝ꪺꕄ녩ꅁꖻ냪덦맴뙓귈궰ꝃ늼돸륓ꅃ 뭐1995-1996뿄ꙍ뻷땯ꗍꭥꪺꖭ쁒듁뚡ꪺ볒ꮬ꛴군(ꫭ4)ꓱ룻ꅁ1997-1998뿄ꙍ뻷듁뚡ꪺꑔ귓볒ꮬ늼돸륓륌땻(ꫭ5)ꅁ곒ꕘ뉻엣뗛ꪺ뙓귈껄ꩇ뭐룻녪ꪺ궷쁉뙋ꓴ뗽뻚ꅁꧺ엣ꪺꕘ걷뿄ꙍ뻷뷄삻ꕸ왗늼ꖫ돵ꅁꙢ꒣쎭ꥷꪺ뿄샴맒ꑕꅁ룪ꑈꑀꓨ궱ꟳ결뽮랥ꪺꙢꙕ귓쑶ꪧꪺ뿄냓ꭾ꒤둍ꡄ랥ꑪ돸륓ꪺ룪늣닕Ꙙꅑꕴꑀꓨ궱ꗧ라ꟳ싔띖뗻꛴궷쁉ꅁ군뫢뙋ꓴ룉쁶ꅃꚳ뷬ꪺ걏ꅁꑔ귓볒ꮬꪺ뇸ꗳ엜늧볆륌땻ꪺꖫ돵ꩩ냊꯹쓲꧊ꅁ꒣뷗걏19
Ꙣ∑b+걏ꙢHL뿅i∑cjꫭ3. 늼ꓩ돸륓볒ꮬ꛴군ꅁ 1995-1998R=a+++t0bhaeettteΩ−1~N(0,h)tttphb∑q=+bhce2t0i=1it−+i∑j=1jt−jARCH(3)-MGARCH(1,1)-MGARCH(1,2)***()()()ꍝ***()()()***()()()***()()()**()()***()()()**()()*()c1+c2+++c1+-B2 Q(6)-B2 Q(12)-B2 Q(24)-LM(6)-LM(12)
ARCH-LM(24)꛴군냑볆ꑕꪺ걁뢹꒺결볐럇깴ꅑHLꕎꫭꑀ귓뷄삻ꪺ12ꗍꥒ(ꓩ) ꅑL-B2 Q결맯볐럇꓆득깴ꖭꓨ뚵ꪺꛛ곛쏶샋ꥷ꒧Ljung-Box Q닎군뙱ꅁꫭ꒤ꙃꕘ뢨뿰6ꅂ12ꥍ24듁ꪺ샋ꥷ떲ꩇꅑ* ꫭꗜ꣤Ꙣ5ꉍꪺꓴ럇ꑕ엣뗛ꅃꫭ4. 늼ꓩ돸륓볒ꮬ꛴군,1995-1996R=a+h+e+t0baettteΩtt−1~N(0,h)th=b+∑p=bh20cti1it−+i∑qj=1ejt−jARCH(3)-MGARCH(1,1)-MGARCH(1,2)*()()()ꍝ***()()()()()()***()()()**()()*()()()**()()*()c1+c2+++c1+-B2 Q(6)-B2 Q(12)
L-B2 Q(24)-LM(6)-LM(12)-LM(24)꛴군냑볆ꑕꪺ걁뢹꒺결꣤볐럇깴ꅑHLꕎꫭꑀ귓뷄삻ꪺ12ꗍꥒ(ꓩ)ꅑL-B2 Q결볐럇꓆득깴ꖭꓨ뚵ꪺꛛ곛쏶L-B Q닎군뙱ꅁꫭ꒤ꙃꕘ뢨뿰6ꅂ12뭐24듁ꪺ샋ꥷ떲ꩇꅃARCH-LM결ARCH껄ꩇ샋ꥷꅃ* 뭐 ** ꓀ꝏꫭꗜ꣤Ꙣ5ꉍ뭐10ꉍꪺ엣뗛ꓴ럇ꑕ엣뗛ꅃꫭ5. 늼ꓩ돸륓볒ꮬ꛴군,1997-1998R=a+++t0bhaeettteΩtt−1~N(0,h)th=b+∑p=bhq2011cetiit−+i∑j=jt−jARCH(3)-MGARCH(1,1)-MGARCH(1,2)***()()()ꍝ***()()()***()()()***()()()***()()***()()()**()()***()()c1+c2+++c1+
-B2 Q(6)-B2 Q(12)-B2 Q(24)-LM(6)-LM(12)-LM(24)꛴군냑볆ꑕꪺ걁뢹꒺결꣤볐럇깴ꅑHLꕎꫭꑀ귓뷄삻ꪺ12ꗍꥒ(ꓩ)ꅑL-B2 Q결볐럇꓆득깴ꖭꓨ뚵ꪺꛛ곛쏶L-B Q닎군뙱ꅁꫭ꒤ꙃꕘ뢨뿰6ꅂ12뭐24듁ꪺ샋ꥷ떲ꩇꅃARCH-LM결ARCH껄ꩇ샋ꥷꅃ* 뭐 ** ꓀ꝏꫭꗜ꣤Ꙣ5ꉍ뭐10ꉍꪺ엣뗛ꓴ럇ꑕ엣뗛ꅃ뙱ꪺ왛쉉ꑗꅁ뿄ꙍ뻷듁뚡곒ꑰ꧳뿄ꙍ뻷땯ꗍꭥꅁSo ,Lam andLi(1997)땯뉻ꕸ왗늼룪ꑈꯜ깥꧶꣼꣬ꡃ귓ꗦ꧶ꓩ꒤꒣ꝑ꧳ꖫ돵ꪺ뿄끔꺧ꪺ뱶암ꅁꙢꚹꑀ왛쉉ꑗꅁ귌뭻결Ꙣ걷뿄ꙍ뻷꯹쓲듁뚡ꅁ럭룪ꑈꑶ덶몥보노뿄ꙍ뻷ꪺ궷쁉샴맒ꅁꕵ굮꒣걏ꟳ둣꓆ꪺ뿄끔꺧ꅁ룪ꑈ곒ꑶ닟멄ꣃ꿠ꢳ덴Ꝁꕘ빁럭ꪺ삳ꅁ듮깺꒣ꝑ뷄삻ꪺ꯹쓲껄ꩇꅑꕴꕾꅁ걆ꦲ럭ꞽꙢ뿄ꙍ뻷듁뚡ꪺꙕ뫘쎭ꥷꖫꪺ놹걉(ꚳꝑꪺ끔꺧)ꅁꧨ껸꒣ꝑ끔꺧ꪺ껄ꩇꅁꗧꕩ꿠셙듮꒣ꝑ뷄삻ꪺ꯹쓲꧊ꅃ 궷쁉뙋ꓴꙢꑔ귓볋ꖻꪺARCH(3)-M볒ꮬ꒤곒결엣뗛(냑빜ꫭ3ꅂ4ꅂ5)ꅁꛓꕂꕈHLꫭꗜꪺꖫ돵ꩩ냊엣ꗜARCH(3)-M륌땻돌결쎭ꥷꅁꖻꓥ뙩ꑀꡂꙢARCH(3)-M볒ꮬ냲슦ꑗꅁ왛맮ꕈ뇸ꗳ엜늧볆ꫭꗜꪺ꒣Ꙑ늼꯹ꚳ듁뚡ꪺ궷쁉ꅂ꣤맯삳ꪺ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴꅂ뭐뙓귈껄ꩇꪺ뷕뻣륌땻ꅃ ꫭ6ꙃꕘARCH(3)-M볒ꮬ꓀ꝏꙢꑔ귓볋ꖻ냏뚡ꪺ뇸ꗳ엜늧볆ꅂ궷쁉뙋ꓴ뭐뙓귈껄ꩇꪺ곛쏶닎군귈ꅃꑔ귓볋ꖻ냏뚡늼돸23
륓ꪺ엜늧볆뱵꧊뎣ꯜ낪11ꅁꙢ걷뿄ꙍ뻷뉛뭜ꪺ1997-1998꙾닄ꑇꑬ볋ꖻ냏뚡ꅁ꣤뱵꧊(=)ꧺ엣ꪺ낪꧳1995-1996꙾뿄ꙍ뻷땯ꗍꭥꪺ뱵꧊(=)ꅁ룪ꑈꙢ뿄뉖뛃ꪺ샴맒ꑕꅁꧺ엣ꪺ맯늼ꖫ돵ꩩ냊ꪺ삳ꟳꕛ뇓빕ꅃSo ,Lam and Li(1997)땯뉻ꕸ왗늼ꖫ돵Ꙣꩆꙡ냏꒤ꪺꩩ냊꧊돌낪ꅁ꣤ꕄ굮ꪺꑺ쉚꣓랽결ꖫ돵ꪺ끔꺧ꅁꖻꓥ뙩ꑀꡂ땯뉻ꅁꕸ왗늼꯹ꚳꑈ맯ꖫ놡뛕ꯜ걏뇓띐ꅁꑝ둎걏뮡ꅁꖫ돵ꩩ냊꧊ꪺ뱗ꕛꅁꖫ냑뭐녎ꟳꕛꭏꙵꅁ엜늧볆뱵꧊ꗧ쁈꒧뱗ꕛꅃꑔ귓볋ꖻ듁뚡ꪺ늼돸륓뙓귈뱵꧊곒ꑰ꧳112ꅁ룻꿊ꕆ뱵꧊ꅁ뿄ꙍ뻷듁뚡ꪺ뙓귈뱵꧊떴맯귈(=−)ꧺ엣ꑪ꧳ꙍ뻷ꭥꪺ뱵꧊떴맯귈(=−0053713.)ꅁ띴ꗜ뿄ꙍ뻷듁뚡꯹쓲꧊ꪺ뙓귈ꕛ궫늼돸륓ꪺ뙓귈껄ꩇꅃꙢ뱵꧊ꪺ왛쉉ꑗꅁ늼돸륓맯ꖫ돵ꖻꢭꩩ냊ꪺ뇓띐꧊뮷ꑪ꧳늼돸륓ꪺ뙓귈껄ꩇꅃ ARCH(3)-M볒ꮬ꒤ꪺ늼돸륓륌땻ꅁꙢꑔ귓볋ꖻ냏뚡ꅁ뎣꙳ 11 늼돸륓ꪺ엜늧볆뱵꧊결ꅒ†††dRheh=⋅dhR?꣤꒤dR결꛴군쏤믚엜늧볆껄ꩇꅁꝙ결b귈ꅑh뭐R꓀ꝏ결ARCH(3)-M볒dhꮬꪺ?엜늧볆뭐돸륓ꪺ륷듺ꖭꞡ귈ꅃ12늼돸륓ꪺ뙓귈뱵꧊결ꅒ†††dReee=⋅deR?꣤꒤dR결꛴군쏤믚뙓귈껄ꩇꅁꝙ결a귈ꅑh결ARCH(3)-M볒ꮬꪺ엜늧볆de륷듺?ꖭꞡ귈ꅑe결맪믚뙓귈ꪺꖭꞡ귈ꅃ13뿄ꙍ뻷땯ꗍꭥꪺꖭ쁒껉듁(1995-1996)ꅁ늼돸륓륌땻꒣꙳Ꙣ엣뗛ꪺ뙓귈껄ꩇ
냑빜ꫭ4?ꅃ24
Ꙣ엣뗛ꪺ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴꅁꫭ6엣ꗜ땯ꗍ뿄ꙍ뻷ꪺ닄ꑇꑬ볋ꖻ냏뚡ꪺ엜늧볆ꖭꞡ귈(Meanh=)꣤맯삳ꪺ궷쁉뙋ꓴꖭꞡ귈(MeanRP=)곒낪꧳뿄ꙍ뻷ꭥꪺ닄ꑀꑬ볋ꖻ냏뚡ꅑ귌뙩ꑀꡂꗎZ꒽ꚡ샋뗸덯ꑇ귓ꑬ뚰Ꙙ냏뚡ꪺ엜늧볆뭐궷쁉뙋ꓴꪺꖭꞡ볆걏ꝟ꙳Ꙣ깴늧ꅑ꣤꒤Z결ꖭꞡ볆걏륳ꅂ볐럇깴결ꊰꪺ녠멁꓀끴14ꅃ귌ꪺ뗪때낲뮡(H0)결꣢귓볋ꖻꪺꖭꞡ볆곛떥ꅁ맯ꗟ낲뮡(H1)결뿄ꙍ뻷ꪺ닄ꑇꑬ볋ꖻꪺꖭꞡ볆룻ꑪꅃꙢ5ꉈꪺ엣뗛ꓴ럇ꑕꅁ돦ꟀZ귈(=)떴ꑇ귓ꑬ볋ꖻ엜늧볆ꖭꞡ볆(Meanh)곛떥ꪺ뗪때낲덝(ꝙH0 ꅒ =)ꅁ뿄ꙍ뻷듁뚡ꅁꕎꫭ늼돸륓궷쁉ꪺ뇸ꗳ엜늧볆(=)엣뗛낪꧳뿄ꙍ뻷ꭥꖭ쁒듁뚡ꪺ돸륓엜늧볆(= )ꅁ걷뿄ꙍ뻷엣뗛뱗ꕛꖫ돵ꩩ냊뭐궷쁉ꅑ걏궷쁉뙋ꓴꪺ돦ꟀZ귈(=)꒣꿠떴ꑇ귓ꑬ볋ꖻ궷쁉뙋ꓴ곛Ꙑꪺ뗪때낲덝(ꝙH0 ꅒꇗ)ꅁ궷쁉뙋ꓴꙢ뿄ꙍ뻷ꭥꅂꯡ냏뚡ꣃ때엣뗛ꪺ깴늧ꅁ룪ꑈ궱맯뿄궷볉뱗ꕛꪺꖫ돵궷쁉ꅁ쇶땍굮ꡄꟳꙨꪺ궷쁉뙋ꓴ룉쁶ꅁꙢ닎군왛쉉ꑗꅁꣃ꒣엣뗛ꅃꫭ6 . ARCH(3)-M볒ꮬ꛴군닎군귈1995-981995-961997-98볋ꖻ볆 14꒤ꖡ랥궭ꥷ뉺(central limit theorem)ꕄ녩럭볋ꖻꢬ냷ꑪ( ≥30)ꅁꭨ꒣뷗ꗀ엩ꪬ?결꛳ꅁ꣢귓볋ꖻꖭꞡ귈ꪺ깴결녠멁꓀끴ꅃ25
()()()()()()eh ꥍee꓀ꝏ결늼돸륓엜늧볆뭐뙓귈뱵꧊ꅑMeanhꥍMean꓀ꝏ결 RP늼돸륓엜늧볆뭐궷쁉뙋ꓴꪺꖭꞡ볆ꅑ꛴군냑볆ꑕꪺ걁뢹꒺결볐럇깴ꅃ 걷뿄ꙍ뻷듁뚡ꅁꕎꫭ늼ꖫ돵ꩩ냊ꪺ늼돸륓뇸ꗳ엜늧볆ꧺ엣뱗ꕛꅁ뉺뷗ꑗꅁ궷쁉뙋ꓴ걏ꖫ돵ꩩ냊ꪺ뱗꣧볆ꅁ늼룪ꑈ럭굮ꡄ룻낪ꪺ궷쁉뙋ꓴꅁ궷쁉뙋ꓴꪺ뱗ꕛꙢARCH(3)-M볒ꮬ꒤ꣃ꒣엣뗛ꅁ덯ꕩ꿠걏ꙝ결ꕸ왗결ꑀꑰꮬ뙽꧱ꖫ돵ꅁꖨꑪꪺ걷뿄궷볉뷄삻ꕸ왗늼ꖫ돵ꅁ뱗ꕛꖫ돵궷쁉ꅁ궰ꝃ룪ꑈ꯹띎쑀ꅁ썥ꑪꪺ뷦삣뭐뙩ꑊꖫ돵띎쑀ꪺꝃ뢨ꅁ덹ꚨꖫ믹껦뭐돸륓ꪺꑕ럆ꅃꖫꓩꖭꞡ돸륓녱1995-1996꙾ꪺ- %뱀궰ꛜ1997-1998꙾ꪺ%ꅝ냑빜ꫭ1ꅞꅁ꙾ꖭꞡ돸륓녱1995-1996꙾ꪺꉈꑕ럆꣬1997-1998꙾ꪺ ꉈꅃChou(1988)ꕘꛛ1960꙾ꕎꕈ꣓ꅁ과냪ꖫ궷쁉ꪺ뱗ꕛ걏덹ꚨꖫ룪띎쑀궰ꝃꅂꖫꑕ껀ꪺ궫굮귬ꙝꅃꖫ돵궷쁉뱗ꕛꅁ굙굮궷쁉덗쇗ꪺ룪ꑈ뙩ꑊꖫ돵ꅁꖲ뚷떹꒩낪ꪺ궷쁉뙋ꓴ룉쁶ꅁ걷뿄ꙍ뻷뱳꩸ꓞ끟ꕝ걁궻들ꅂ띳ꕛꅂꩆꅂ곆ꛜ꿃곹ꅂ귛뒰떥늼ꖫ돵ꪺ꒣쎭ꥷꅁ궱맯ꚹꑀ랥꒣쎭ꥷꪺ뿄샴맒ꅁ룪ꑈ쏸꧳꛴군뭐굮ꡄ궷쁉룉쁶ꅁ맧쑀끨ꕘꖫ돵ꅁꕈ교꧳궷쁉뙋ꓴꣃꖼ쁈뗛궷쁉ꪺ뱗ꕛ엣뗛뱗ꕛꅃStenius(1991)놴끑ꫢ쓵(Finland)ꖫꩩ냊뭐궷쁉뙋ꓴꪺ곣ꡳꗧ녯ꕘ곛Ꙑꪺ떲뷗ꅁꙢ1980꙾ꕎꕀ곉뿄ꖫ돵꒣쎭ꥷꪺ26
샴맒ꑕ(꣒꙰1987꙾과냪ꖫꪺ녙뵌)ꅁ늼꯹ꚳꑈ꧓뻡뮼뱗ꪺ궷쁉ꅁꡓꚳ굮ꡄ룻낪ꪺ돸륓ꅃ6. 떲뷗뭐ꯘ쒳 ꖻꓥ쉘깩뛇닎ꪺGARCH(p,q)-M볒ꮬꅁꛒ뱻덱덦뙓귈결ꖫ돸륓ꪺꕴꑀ룑쓀엜볆ꅁ꣏ꗎ1995꙾1ꓫꫬꛜ1998꙾12ꓫ꦳ꅁ뉛뭜걷뿄ꙍ뻷ꪺꓩ룪껆ꅁ맪쏒놴끑궷쁉뙋ꓴ뭐덱덦뙓귈Ꙣꕸ왗ꖫ돸륓륌땻꒤ꪺꛦ결ꅃARCH(3)-MꅂGARCH(1,1)-M뭐GARCH(1,2)-Mꑔ귓볒ꮬ곒쏒맪Ꙣꕝ걁뿄ꙍ뻷ꪺꕼ꙾볋ꖻ듁뚡ꅁꕸ왗늼돸륓륌땻꙳Ꙣ쁈껉뚡엜냊ꪺ궷쁉뙋ꓴ뭐굴ꪺ뙓귈껄ꩇꅃ엣뗛ꪺ궷쁉뙋ꓴꕘ궱맯뿄ꙍ뻷ꓞ끟ꪺꖫ돵궷쁉ꅁ룪ꑈ궰ꝃ꯹띎쑀ꅁ굙굮궷쁉덗쇗ꪺ룪ꑈ뙩ꑊꖫ돵ꅁꖲ뚷떹꒩썂ꕾꪺ뙋ꓴ룉쁶ꅑ뙓귈껄ꩇꭨ걏ꕸ맴꯹쓲뙓귈꣤륷듁뮤꣏룪ꑈ궫뻣꣤룪늣닕Ꙙꅁꕈ룻낪돸륓ꪺ과꒸룪늣듀ꕎ늼ꅁ뱗ꕛ늼ꖫ돵뷦삣ꅁ궰ꝃ늼믹껦뭐돸륓ꅃ 귈녯ꩠ띎ꪺ걏Ꙣꚹꑀ뿄궷볉뷄삻ꕸꕟꅂ궻들ꅂ띳ꕛꅂꩆꅂ곆ꛜ꿃곹뭐귛뒰떥궫굮ꪺ걷볚과뿄ꖫ돵ꪺ샴맒ꑕꅁ늼ꖫ돵궷쁉뱗ꕛꅁ걏궷쁉뙋ꓴꣃꖼ엣뗛쁈꒧뱗ꕛꅁꚹꑀ맪뭐낪궷쁉ꅂ낪돸륓ꪺꑀ꿫뭻ꪾ꒣ꑀ교ꅁStenius(1991)ꗧ땯뉻럭Ꙩ볆뿄ꖫ돵꒣쎭ꥷ껉ꅁ궷쁉뙋ꓴ꒣라쁈궷쁉ꪺ뱗ꕛꛓ뱗ꕛꅃ ꖫ돸륓륌땻꙳Ꙣ굴ꪺ뙓귈껄ꩇ닅Ꙙꖻꓥ낲덝ꪺ륷듁ꅁ쁈뗛냪꒺뿄샴맒ꪺꛛꗑ꓆ꅂ냪믚꓆뭐냪믚뿄ꖫ돵띕쇍뻣Ꙙꅁ27
Ꙣ늳Ꙩꕈꖻ냪ꕾ냪덦맴ꫭꗜꪺ룪늣꒤ꅁ궷쁉덗쇗ꪺ룪ꑈ뻖ꚳꟳꙨꪺ뿯뻜ꅁ끬덶룻낪돸륓ꪺꚳ믹쏒꣩룪늣닕Ꙙꅁ늼ꖫ돵ꪺꫭ뉻뭐ꕾ뛗ꖫ돵ꧺ엣꙳Ꙣ곛꒬쑶ꪧ뭐듀ꕎꪺ쏶셰꧊ꅃꖻ냪덱덦뙓귈륷듁ꅁ뱗ꕛꕈꕾ냪덦맴ꫭꗜꪺꕾ뛗룪늣돸륓ꅁ룪ꑈ녎뱗ꕛ꣤꯹ꚳꓱ꣒ꅁ듮ꓖꕈ냪꒺덦맴ꫭꗜꪺ늼룪늣룪ꅁꓗ꣤걏ꕘ뉻릳걷뿄ꙍ뻷꒤냪ꑪ뎰걆ꩶꅂ굸ꅂ궸뱵떥ꕾꗍ뷄삻껉ꅁꓞ땯룪ꑈꪺꕸ맴뙓귈륷듁ꅁ늼뭐ꕾ뛗꣢뿄늣ꭾꪺ듀ꕎ쏶ꭙꟳꕛꧺ엣ꅃ ꫱꙾꣓덜Ꙩ냪믚냲롧뉺ꑈ걏결꓀뒲궷쁉ꅁ걏곝ꙮꕸ왗늼ꖫ돵ꭥ뒺ꅁ꿉꿉ꕛꑊ뒣낪맯ꕸ왗늼ꪺ룪ꓱ궫ꅁꖻꓥ뗽뻚엣ꗜ꒣쎭ꥷꪺꕾ뛗ꖫ돵뱶암늼돸륓뭐ꩩ냊ꅁꙝꚹꅁ덱덦뙓귈ꓞ땯ꪺ늼ꖫ돵룪궷쁉ꅁ삳걏냪꒺늼룪ꑈ군릺룪ꕸ왗ꖫꪺ냪믚냲롧뉺ꑈꡍ떦ꪺꑀ귓궫굮뗻꛴굮ꗳꅁ룪ꡍ떦뛈ꛒ뱻늼ꖫ돵ꛛꢭꪺ볐ꅁꦿ늤ꕾ뛗ꖫ돵뇸ꗳꅁꕩ꿠뻉교낾뭾ꪺꝐ쉟ꅃ28
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