냪ꗟꩆ뗘ꑪ뻇냪믚ꗸ띾곣ꡳ꧒ 뫓ꑨ뷗ꓥ 뻉뇐뇂ꅇ뎯뇒? 돕ꑨ 륂ꗎ륷듺덎뭐꣢뚵ꚡꭄꗟꝙ룉덦롧샙굱쇊뙱볒ꮬ꧳놱꣮ꕾ맴꙳뙱뭐셠ꚨꖻ꒧곣ꡳ Applying Forecasting Techniques and Two-item NIR-EOQ Model of Foreign Currency for Controlling Inventory and Total Cost 곣 ꡳ ꗍꅇ뎯ꕱ뺧 벶 ꒤뗘ꗁ냪ꑅꑑꑇ꙾ꑃꓫ
냪ꗟꩆ뗘ꑪ뻇뻇ꛬ뷗ꓥ뇂앶껑 ꖻ뇂앶껑꧒뇂앶꒧뷗ꓥ결ꖻꑈꙢ냪ꗟꩆ뗘ꑪ뻇 ꡴꧒________닕 뻇꙾ꯗ닄 뻇듁꣺녯 ꑨ뻇ꛬ꒧뷗ꓥꅃ 뷗 ꓥ ꙗ 뫙ꅇ 뻉뇐뇂ꥭꙗꅇ 뻇 ꗍ ꥭ ꙗꅇ 뻇 뢹 ꅇ ꖻꑈ꣣ꚳ뗛Ꝁ끝늣앶꒧ꑗꙃ뷗ꓥꗾꓥ룪껆ꅁ냲꧳룪랽Ꙁ뉺꧀ꅂꙞꫀ라뭐뻇덎곣ꡳ꒧ꗘꪺꅁꭄ녍쓝ꅂ때쁶뇂앶냪ꗟꩆ뗘ꑪ뻇ꅂ냪깡맏껑쁝ꛦ걆끼냪깡곬뻇ꥥ귻라곬뻇덎룪껆꒤ꓟꅁ녯꒣궭ꙡ냬ꅂ껉뚡뭐ꚸ볆ꅁꕈ띌셙ꅂꗺ뫐볆ꛬ꓆떥ꙕ뫘ꓨꚡ궫뭳뒲ꖬꅂ땯ꛦꑗ룼뫴룴ꅁ뒣꣑얪ꭄ샧ꝑ꧊뷨꒧뵵ꑗ샋꿁ꅂ빜쓽ꅂꑕ룼ꙃꙌꅃ ꑗ굺볆ꛬ꓆꒽뙽ꓨꚡ궭ꅇ ꆼ껕꒺ꅂ껕ꕾ꒽뙽ꅃ?ꆼ껕꒺꒽뙽ꅁ껕ꕾꙝꑗꙃ뷗ꓥꗓ뷐녍ꝑꅝ껗뢹ꅇ†††††?ꅞꅁ뷐꧳?꙾ꯡ꒽뙽ꅃ?ꆼ껕꒺꒽뙽ꅁ껕ꕾ†††††††††††††††††?ꅁ뷐꧳?꙾ꯡ꒽뙽ꅃ?뇂앶꒺깥ꞡ때뚷굱ꗟ엽뭐뇂앶ꮴ곹껑ꅁ뇂앶꒧땯ꛦ앶결ꭄ녍쓝꧊땯ꛦ앶ꝑꅃꖻ뇂앶꧒결꒧ꚬ뿽ꅂ궫뭳ꅂ땯ꛦ뻇덎곣땯ꝑꗎꞡ결때쁶ꅃ볆ꛬ꓆꒽뙽ꓨꚡ굙ꖼ꓄뿯ꅁꖻꑈꙐ띎뗸Ꙑ뇂앶껕꒺ꅂ껕ꕾ꒽뙽ꅃ 곣ꡳꗍ쎱ꙗ (뿋떧ꖿ랢) ꓩ듁ꅇ꒤뗘ꗁ냪 ꙾ ꓫ ꓩ 뮡ꧺꅇꖻ뇂앶껑뷐ꕈ뛂떧벶뱧ꣃ룋굱꧳꿈ꖻ뷗ꓥ껑ꙗ궶꒧ꚸ궶ꅃ
뭸쇂쏣 ꑀ껌늴ꅁ꣢꙾곣ꡳ꧒ꪺꓩꑬ닗꧳굮Ꙣ꒵ꓩ릺ꑕꕹ쉉ꅃꙞ띑덯꣢꙾곣ꡳ꧒ꪺꗍ겡ꅁ녱ꛒꑗ곣ꡳ꧒껉ꪺ뎶아ꑀꪽꛜ꒵ꓩꝙ녎싷껕ꪺ놨놣ꅃꙢ덯녎꫱ꑃꛊꓑꪺꓩꑬ꒤ꅁ껉녠냝ꛛꑶ결꒰믲굮꣓꧀곣ꡳ꧒ꅈꛓ덯꣢꙾ꪺꡄ뻇ꗍ뉐ꕉꕘꑆ꒰믲ꅈꛓꑓ녯꣬ꑆ꒰믲ꅈꓗ꣤Ꙣ뉠ꑈ쁒껉ꅁ럭ꧬ뗛꽨닖ꪺꢭ싟궱맯뗛낵꒣ꞹꪺ뷗ꓥ껉ꅁꓟ꒤ꢺꑀ결꒰믲ꪺ셮궵ꭋꟳꕛ녪꽐룟냝뗛ꅈꛓ덯뫃냝Ꙣ꒵ꓩ닗꧳ꚳꑆ룑떪ꅃꙢ덯ꑀ걱셽ꢯꪺ뷗ꓥ뱧Ꝁ륌땻꒤ꅁꙢ꒣뚡쉟ꪺ귗꒤ꕘꑀ귓ꖿ뵔ꪺꓨꙖꅁꛓ덯꣤꒤덜ꚳ뗛덜Ꙩ꒣ꢬ결ꕾꑈ륄ꪺꢯ굗ꅃ덯걏곣ꡳ꧒ꗍ뉐꒤돌곃뙑ꪺꑀ걱륌땻ꅁꑝ걏뻇닟ꚨ돌궫굮ꪺꑀ귓엩뭻ꅃꙝꚹꅁꙢ뷗ꓥꝙ녎ꞹꚨ꒧믚ꅁ띑ꕈ돌룛벰ꪺꓟ띐쇂ꢺꑀ룴뎭꛱뗛ꑈꅃ ꖻ뷗ꓥꪺꞹꚨ궺ꗽ굮띐쇂꺦깶 뎯뇒?ꛑ깶ꅁ걏ꛑ깶굀ꓟꅂ닓ꓟꅂ꒣립꣤럐ꪺ뻉ꑕꅁꖻ뷗ꓥꑾ녯ꕈ뚶ꝑꞹꚨꅃꛑ깶Ꙣ뻇덎놴꿁ꑗ쑙싔뭐뭻꽵ꪺ뫫꾫ꅁꟳ걏냶빩ꑆ뻇ꗍꓩꯡ때뷗쑾쓲뉠덹둎띾ꑗꪺ굴덤멁ꯗꅃ쇂쇂녺ꅁꛑ깶ꅃ꽵ꪺ쇂쇂녺ꅃꙐ껉ꅁ띐쇂꧒꒺ꪺ 녩냪ꦾꛑ깶ꅂ ꓽꟊꛑ깶ꅂ둞ꗉ뻰ꛑ깶ꅁꕾ꧒ꪺ 뭵ꟓ쑐ꛑ깶ꅂ 덜믊ꛑ깶ꅂ 몵꩙뗘ꛑ깶ꅂDr. Crawfordꅁ걏뷑ꛬꛑ깶Ꙣꙕ곛쏶뷒땻믢냬ꑗꪺ끖뵭ꅁ뻇ꗍꑾ꿠Ꙣ땵땵꣢꙾ꪺ곣ꡳ꧒뻇닟륌땻꒤몡룼ꛓ쉫ꅃꚹꕾꅁꑦ룕ꥥ귻꒸냶곬ꑪ뻇껕 ꩌ뙩끝ꛑ깶뭐ꩆ뗘ꑪ뻇냪믚롧샙뻇꡴ ꓽꝑꛑ깶ꅁ꣢ꛬꛑ깶Ꙣꑦ룕륌땻꒤뿋꓁ꥍ쒧ꪺ멁ꯗꕈꑪ깶꿅ꪺ궷뵤ꅁ맯꧳곣ꡳ꓀꩒뽗꽓ꪺꢣ룑뭐엞뿨ꯤꛒ왛꧀ꪺꓞ뻉ꅁ뻇ꗍ뗛맪샲꽱Ꙩꅃ띐쇂꣢ꛬꛑ깶떹꒩ꖻ뷗ꓥ뷑Ꙩ쑟뙑ꪺꯘ쒳ꅁ꣏녯ꖻ뷗ꓥ꿠냷ꟳ뾲ꞹ뻣뭐ꕒ맪ꅃ ꣤ꚸꅁ띐쇂꧒ꑗꪺꝕ뉺ꑰꛋꅁꡃꚸ뎣돂럐꙯산ꑪ깡덂뉺ꯜꙨ몾롈ꪺꛦ걆ꥹꅃ띐쇂Ꙑ꧸뮷ꅂꑪ귴ꅁꙢ뷗ꓥ벶뱧륌땻꒤ꪺꦼꚹꖴ껰ꅂ곛꒬꓁뵒ꅂ꾡쑲ꅃ띐쇂뎭ꖴ뉹룑삣ꑏꪺ뉹꧓륆ꅂ뒼ꦾꅂ곬ꗺꕈ꽚ꑗꙐ뻇ꯛꥧꅂ꣘
뱠ꅂ맅뚲ꅂ땮ꯊꅂ꒤쎢ꅂ깒둀ꅂ뉑ꪳꅂꗉꅂ곕륆ꅂ놩돇ꅂꑈ뮨ꅁ녎ꗃ뮷끏녯ꥍꝁ귌ꑀ끟ꯗ륌ꪺ곣ꡳ꧒껉ꗺꅃ쇙ꚳꕩ띒ꪺ뻇ꥦꖿ돇ꅂ뒭돇ꅂ걆뫺ꅂꩆ궧ꅂ솨둀ꅂꧺ껼ꅂꥻꮺꅂ뉢걉ꅁ쇂쇂ꝁ귌Ꙣ곣ꡳ꧒떹ꪺꓤ꯹ꅃꚳꑆꝁ귌ꅁ냪ꗸ꧒녎ꕒ몡ꟳꙨꪺ겡ꑏ뭐앷꾺ꅃꛓ돌ꢯ굗ꪺꥳ볤ꅁ셠걏Ꙣꝃ볩껉떹돌Ꙩꪺꓤ꯹ꅁꙝ결ꚳꝁꪺ뎭꛱ꅁ엽곣ꡳ꧒ꪺꗍ겡엜ꪺꟳꕛꪺꕒ맪ꅂ싗둉ꅁ꣢꙾꣓ꑀ끟ꝖꑏꅂꙀꙐꚨꪺꙞ뻐ꅁ꛱쁈뗛ꩆ뗘돌과ꪺ궷뒺뉠듓꧳ꓟꅃ 돌ꯡꅁ굮쇂쇂돌뿋띒ꪺ깡ꑈꅃ쇂쇂ꪨꪨꅂ뛽뛽ꢯ굗ꪺꑵꝀꅁ떹꒩20둘꙾꣓때뱾때뱻ꪺꡄ뻇ꗍ뉐ꅁ뉀때롧샙굴뻡ꪺ삣ꑏꅃꚹꕾꅁꪨꪨꅂ뛽뛽맯ꗍ겡쉉멷ꪺ쏶럓뭐띒앀걏ꞹꚨ곣ꡳ꧒뻇띾돌ꑪꪺꓤ걗ꅃ쇂쇂돌뿋띒ꪺꥦꥦ뚮땘뭐?롡ꅁꝁ귌셠걏꒣립꣤럐ꪺ얥뙄굗ꅂꧪꯨꅁꙁꙨꪺ꒣둲Ꟗꑝꙝ결ꝁ귌ꛓ껸ꖢꅁꝁ귌걏ꗍꥒ꒤돌궫굮ꪺꑀ뎡ꗷꅁꑝ걏돌궫굮ꪺ깡ꑈꅁ쇂쇂ꝁ귌뎭꛱ꯗ륌셽ꢯꪺ곣ꡳ꧒ꗍ뉐ꅃ 뛈녎ꚹ뵧뷗ꓥ쑭떹돌벰띒ꪺ깡ꑈꅃꙝ결ꚳꝁ귌ꑀꪽ꒣쉟ꪺꓤ꯹ꅁꑾꕩꕈ냭꯹꣬돌ꯡꑀ꣨ꅁ녎뷗ꓥ낵돌ꙮꪺꝥ뉻ꅃ쇂쇂ꝁ귌ꅃ ꕱ뺧 ꑟꫡ붬 뉍뇡 7/25/2003
륂ꗎ륷듺덎뭐꣢뚵ꚡꭄꗟꝙ룉덦롧샙굱쇊뙱볒ꮬ꧳놱꣮ ꕾ맴꙳뙱뭐셠ꚨꖻ꒧곣ꡳ 곣 ꡳ ꗍꅇ뎯ꕱ뺧 뻉뇐뇂ꅇ뎯뇒? 돕ꑨ 냪ꗟꩆ뗘ꑪ뻇냪믚ꗸ띾곣ꡳ꧒ 뷗ꓥ멋굮 ꕾ뛗믈ꛦ꒧ꕾ맴꧟룉걆떦껚뻚믈ꛦ놵꣼ꕾ맴뙒ꅂ뷦뛗돦Ꙩ맨ꛓꚨꅂ땵뎡ꛬ뭐돌꣎꯹ꚳ뎡ꛬ꣓ꡍꥷ꧟룉냊Ꝁꅃ럭ꕾ맴꙳뙱결땵뎡ꛬꛓ낾싷돌꣎꯹ꚳ뎡ꛬ껉ꅁꕾ뛗믈ꛦꑝ라ꙝꕾ맴뙒ꅂ뷦뛗돦Ꙣ꽓ꥷ듁뚡ꙀꙐ땯ꗍꛓꚨꑀꭄꗟꝙ꧊꒧룉덦ꅝNon-instantaneous Receipt ꅆNIRꅞꓨꚡꙞ쉫돌꣎꯹ꚳ뎡ꛬꅃꖻ곣ꡳ꒧궫쉉녎Ꙑ껉ꛒ뙱꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꣓룑ꡍ믈ꛦ꒧싹ꕾ맴돌꣎꯹ꚳ뎡ꛬ냝썄ꅃꖻ곣ꡳꣃ링룕ꕈAR-GARCH뭐AR-TGARCH볒ꮬ꣓뙩ꛦꕾ맴믝ꡄ뙱꒧륷듺ꅃꙝ뛇닎꒧돦뚵ꚡ늣ꭾEOQ볒ꮬNIR-EOQ꙳뙱볒ꮬ꒤꒧믝ꡄ뙱엜볆곒ꕈꅵꖭꞡ믝ꡄ뙱ꅶ꣓군뫢돌꣎꯹ꚳ뎡ꛬꅃ땍ꛓꕾ뛗믈ꛦ꒧귓ꝏꕾ맴믝ꡄ뙱Ꙣꙕ뙧듁뚡덱녠ꕩ꿠ꝥ뉻ꙖꑗꙖꑕ쇍뛕꒧꽓꧊ꅃꙝꚹꅁ굙뇄ꗎꖭꞡ믝ꡄ뙱럭낵돦뚵ꚡNIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆녎뻉교볒ꮬ삳ꗎꑗ꒧낾깴ꅃꖻ곣ꡳꕴꕾꙁ삳ꗎ꧔껦쓵ꩶ궼볆ꅝLagrange Multiplierꅞ꣓ꯘ멣ꕘꭄ뵵꧊꣢뚵ꚡꕾ맴꒧NIR-EOQ꙳뙱볒ꮬꅃꗸ뇦뒣꣑ꕾ뛗믈ꛦꡍ떦뙩ꛦꕾ맴꙳뙱놱꣮ꡍ떦꒧냑ꛒꅃ 쏶쇤꙲ꅇꕾ맴꙳뙱ꅂ롧샙굱쇊뙱ꅂꑀ꿫꓆ꛛ끪쉫뇸ꗳ늧뷨엜늧볆ꅂ꧔껦쓵ꩶ궼볆 i
Applying Forecasting Techniques and Two-item NIR-EOQ model of Foreign Currency for Controlling Inventory and Total Cost Graduate StudentꅇSsu-Ju Chen AdvisorꅇDr. Chie-Bein Chen Graduate Institute of International Business, National Dong Hwa University Abstract Dump or replenishment policy of foreign exchange bank is depended on the difference in amount of purchasing and selling orders. This leads to the long or short position and the optimal holding position of foreign currency inventory in the bank and the execution of dump and replenishment is decided by those situations. When the short position occurs and deviates to the optimal holding position, the bank will take a non-instantaneous receipt (NIR) to regress the foreign currency inventory to the optimal holding position during a specific period that the purchasing and selling orders commonly happened. The focus of this research is to consider a two-item NIR-EOQ model to simultaneously solve two foreign currency optimal holding position problem. This research attempts to use AR-GARCH and AR-TGARCH models to forecast the demand of foreign currency, since both the typical single-item EOQ model and the NIR-EOQ model have been using the average demand as a variable to calculate the optimal reorder quantity. However, there may be a characteristic of upward or downward trend demand of foreign currency in each period of time. If using the average demand of foreign currency as variable and inputting them into the NIR-EOQ model may generate a bias in applications. Furthermore, the Lagrange multiplier will be used to construct a non-linear two-item foreign currency NIR-EOQ model. The results of this research can provide the decision makers of the foreign exchange bank as a reference for two-item foreign ii
currency inventory control. Key words: Foreign currency inventory, economic order quantity, GARCH, Lagrange multiplier iii
ꗘ뿽 궶ꚸ ꒤ꓥ멋굮 …………………………………………………………………….. i 굞ꓥ멋굮 ………………..………..…………………………………….……. ii ꗘ뿽 ……………………..………..……………………………………….…. vi 맏ꗘ뿽 ……………….…..…………………………………………….…….. vii ꫭꗘ뿽 …………………….………………………..………………….…….. ix 닄ꑀ뎹 뫼뷗 ………………..…………………..…………………….……. 1 곣ꡳ굉뒺뭐냊뻷 ………………………..…………………….…... 1 곣ꡳ냝썄뭐ꗘꪺ ...………………..………………………….…... 4 곣ꡳ걛멣 ..…………………………………………………….…... 5 곣ꡳ걹땻뭐뫵굮 .…………………………………………………. 7 닄ꑇ뎹 ꓥ쑭놴끑 ……………………….……………..…………….…….. 9 ꕾ맴ꖫ돵뭐꙳뙱놱꣮ ..…..……………………..………….……... 9 Ꙩ뚵늣ꭾ꒧EOQ꙳덦볒ꮬNIR-EOQ꙳덦볒ꮬ ..……………. 11 GARCH뭐TGARCH볒ꮬ꒧삳ꗎ ..…………..……….….……... 12 닄ꑔ뎹 ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧ꯘ멣 .......……………………... 16 ꕾ맴꙳뙱볒ꮬ꒧ꯘ멣 ..………..……………..…………………… 16 돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ ..…………………………… 16 ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ ……………………………. 17 ꡴닎꽓꧊뭐Lagrange궼볆꒧쏶ꭙ ..…………………….. 19 ꡴닎엜볆꽓꧊뭐Lagrange궼볆꒧뵵꧊쏶ꭙ .…………... 20 돌꣎Lagrange궼볆꒧ꡄ룑 ..…………………………….. 22 ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧귗ꖿ .…………………… 25 iv
궶ꚸ AR-GARCH믝ꡄ뙱륷듺볒ꮬ꒧ꯘ멣 ..…….……………………….. 26 돦껚샋ꥷ ……………………………..……………….……... 29 ADF샋ꥷꩫ ..……………………………………………... 30 PP샋ꥷꩫ ..……………………………………………….. 31 AR-GARCH볒ꮬ ...……………………..…………….……... 32 AR-GARCH 볒ꮬ꒧덝ꥷ ..………………………………….. 33 AR-GARCH볒ꮬ꒧꽓꧊ ..…………………………………… 34 ARCH LM 샋ꥷ뭐 Ljung-Box샋ꥷ ..………………………. 35 AR-GARCH 볒ꮬ꒧꛴군 ..………………………………….. 36 AR-GARCH 볒ꮬ꒧륷듺 ..………………………………….. 36 AR-TGARCH볒ꮬ ..………………………………………….. 37 ꓱ룻륷듺셚껄꒧ꓨꩫ ..………………………………………. 38 닄ꕼ뎹 맪쏒떲ꩇ꓀꩒ …………………….……….……………………… 41 볋ꖻ룪껆냲ꖻ꓀꩒ ....…………………………………..………… 41 볋ꖻ룪껆ꢫ뛕맏 ..…………………………………………… 42 볋ꖻ룪껆냲ꖻ닎군뙱꓀꩒ ..…………………………………. 44 AR륷듺볒ꮬ꒧ꯘ멣 ..…………….……….……………………… 46 볋ꖻ곛쏶꧊꒧샋ꥷ ..…………………………………………. 46 볋ꖻꥷ멁꧊꒧샋ꥷ ..…………………………………………. 49 AR-GARCH뭐AR-TGARCH볒ꮬ꒧ꯘ멣 ...…………………… 50 ARCH껄ꩇ꒧샋ꥷ .……….………………….……………… 51 GARCH볒ꮬ냑볆꛴군뭐빁Ꙙ꧊샋ꥷ ...…………………….. 54 AR-GARCH볒ꮬ냑볆꛴군 .……………….…………… 55 AR-GARCH볒ꮬ꒧빁Ꙙ꧊뙅쉟 ....…….………….………… 58 v
궶ꚸ AR-TGARCH볒ꮬ냑볆꛴군뭐빁Ꙙ꧊샋ꥷ ...….…….…….. 58 AR-TGARCH볒ꮬ꒧냑볆꛴군 ...…….………….…….. 59 AR-TGARCH볒ꮬ꒧빁Ꙙ꧊샋ꥷ ..….……….………… 59 AR-GARCH뭐AR-TGARCH볒ꮬ륷듺떲ꩇ꒧ꓱ룻 ..………….. 61 ꣢뚵ꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧볆뻚꓀꩒ ……………………… 64 닄꒭뎹 떲뷗뭐ꯘ쒳 …………………….……….………………………… 67 떲뷗 …………………….……….………………………………… 67 곣ꡳ궭꣮ ..…..……………………..………………………….…... 69 ꯡ쓲곣ꡳꯘ쒳 …………………….……….……………………… 70 냑ꛒꓥ쑭 …………………..…………….…………………………….…….. 71 뿽A 볚꒸ꗦ꧶뙱꒧땻ꚡ냵ꛦ떲ꩇ ...……………………………..……. 75 vi
맏ꗘ뿽 맏 궶ꚸ 냪ꕾ뛗ꖫ돵닕슴맏 ..…...…………………….……………………… 2 곣ꡳ걛멣 ..….…………………………………...………….………….. 6 곣ꡳ걹땻 …………………………………...…………………….……. 8 ꯹ꚳꚨꖻ꣧볆꒧ꚱ뵵 ..…………….…………………………….…….. 24 2000-2001꙾뚡뙧ꑀꛜ뙧꒭꒧ꕾ뛗ꚨꗦ뙱꒧ꖭꞡ볆 ..….…………….. 27 2000-2001꙾뚡뙧ꑀꛜ뙧꒭꒧ꕾ뛗ꚨꗦ뙱엜늧볆 ...…….……………. 27 2000-2001꙾뚡뙧꒻꒧ꕾ뛗ꚨꗦ뙱ꖭꞡ볆 ..…….……….…………… 28 2000-2001꙾뚡뙧꒻ꕾ뛗ꚨꗦ뙱꒧엜늧볆 ..…………….……………. 28 과꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ .…..………………….………… 43 과꒸ꗦ꧶뙱ꢫ뛕맏ꅝ2002. 7ꅞ ..……………………………………… 43 과꒸ꗦ꧶뙱꒧ꚸ볆꓀끴맏 ..………….………………………………... 45 볚꒸ꗦ꧶뙱꒧ꚸ볆꓀끴맏 ..…………….……………………….…….. 45 과꒸ꗦ꧶뙱꒧곛쏶ꭙ볆(ACF) .………………….…………………… 47 과꒸ꗦ꧶뙱뉢곛쏶ꭙ볆(PACF) ……………………………………… 47 볚꒸ꗦ꧶뙱곛쏶ꭙ볆(ACF) ………………….………………………. 48 볚꒸ꗦ꧶뙱뉢곛쏶ꭙ볆(PACF) .……………………………….…….. 48 과꒸ꗦ꧶뙱득깴곛쏶ꭙ볆ꅝACFꅞ …………………………………… 52 과꒸ꗦ꧶뙱득깴낾곛쏶ꭙ볆ꅝPACFꅞ ..…..…………………………. 52 볚꒸ꗦ꧶뙱득깴곛쏶ꭙ볆ꅝACFꅞ ..…………………….…………… 53 볚꒸ꗦ꧶뙱득깴낾곛쏶ꭙ볆ꅝPACFꅞ ………………………………. 53 과꒸AR-GARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ ..……………… ….. 63 과꒸AR-TGARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ………………… 63 vii
맏 궶ꚸ 볚꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ ….…………………………….. 75 볚꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ …..…………………………………….. 75 볚꒸AR-GARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ …..……………. 77 볚꒸AR-TGARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ ….…………… 77 viii
ꫭꗘ뿽 ꫭ 궶ꚸ ꕾ뛗ꗦ꧶뙱꒧냲ꖻ닎군뙱 .…….……………………………….……... 44 ꣢뚵ꗦ꧶뙱꒧볋ꖻ곛쏶ꭙ볆뭐낾곛쏶ꭙ볆귈 ..……………………… 49 볋ꖻꥷ멁꧊샋ꥷ ..……………..……………..………………………… 50 ꕾ맴ꗦ꧶뙱득깴ꖭꓨ꒧곛쏶ꭙ볆뭐뉢곛쏶ꭙ볆귈 ….………….……. 54 과꒸AR-GARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 ..………..….………… 56 볚꒸AR-GARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 ..……………………... 57 ꕾ맴AR-TGARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 ..…………………… 60 과꒸믝ꡄ뙱볒ꮬ륷듺떲ꩇ셚껄ꓱ룻 ..………………………………. 62 NIR-EOQ꙳뙱볒ꮬ꒧냲ꖻ엜볆룪껆 ………………………………….. 64 돦뚵ꚡNIR-EOQ꙳뙱볒ꮬ꒧돌꣎꯹ꚳ뎡ꛬ뭐꙳뙱셠ꚨꖻ .….……... 65 ꣢뚵ꚡNIR-EOQ꙳뙱볒ꮬ꒧돌꣎꯹ꚳ뎡ꛬ뭐꙳뙱셠ꚨꖻ ….……… 65 볚꒸믝ꡄ뙱볒ꮬ륷듺떲ꩇ셚껄ꓱ룻 ..………………………………. 76 ix
닄ꑀ뎹?뫼뷗? 곣ꡳ굉뒺뭐냊뻷 냪ꕾ뛗ꖫ돵ꕩꕈ릺꓀결압ꯈꖫ돵믈ꛦ뚡ꖫ돵꣢귓뱨ꚸꅃ귓ꑈ뱴냓걏믈ꛦ꒧압ꯈꅁꛓ뙩ꅂꕘꑦ뱴냓ꭨ걏믈ꛦ돌ꕄ굮꒧ꕾ뛗믝ꡄꥍ꣑떹ꅃꕘꑦ뱴냓녎ꕾ뛗냢꒩ꕾ뛗ꥷ믈ꛦꅁ뙩ꑦ뱴냓Ꙗꕾ뛗ꥷ믈ꛦ쇊뙒ꕾ뛗ꅁꚨꑆ압ꯈ뭐믈ꛦ뚡ꗦ꧶꒧ꖫ돵ꅁ슲뫙압ꯈꖫ돵(Customer Market)ꅃ꧒뿗ꪺꅵꕾ뛗ꥷ믈ꛦꅶ걏롧꒤ꖡ믈ꛦ뇂앶ꥷꕩꕈ뿬뉺ꕾ뛗띾냈꒧믈ꛦꅃꚹꕾꅁ꒤ꖡ믈ꛦꗧ라뻚걆떦꒧꧒믝ꅁ꣓뙩ꛦꖫ돵꒧ꑺ륷뭐뷕론냊Ꝁꅃꑀ꿫ꛓꢥꅁꑀ깡믈ꛦ럭ꓩ꒧뙒뛗뭐뷦뛗썂꒣라곛떥ꅃ굙ꕾ뛗믈ꛦꙝꛓ늣ꗍ뛗ꝉ궷쁉ꕾ뛗룪꒣ꢬ돑빬ꪺ냝썄ꅁꛓ꒣쑀꯹ꚳ덯뫘Ꙩ뙒Ꙩ뷦꒧뎡ꛬꅁ둎믝꣬ꖫ돵ꑗ냢ꕘ룉ꑊꅁꕈꖭ뿅뙒ꅂ뷦뙗뎡ꛬꅝSquare Positionꅞꅁ륆꣬꣤꧒Ᶎ뇦꒧뎡ꛬꓴ럇ꅃ냓띾믈ꛦꑝꕩ꿠결ꑆ돐덹ꝑ볭ꅝ륷듁뛗뉶엜냊ꅞꅁꛓꛜꖫ돵ꑗ륷ꗽ뙒ꑊ냢ꕘꕾ뛗ꅃ덯뫘믈ꛦ뚡ꪺ뙒뷦ꖫ돵ꅁ슲뫙결믈ꛦ뚡ꖫ돵(Inter-bank Market)ꅁꭙ돌궫굮꒧ꕾ뛗ꖫ돵ꅁ띎ꝙꑀ꿫꧒뫙꒧ꅵꕾ뛗ꖫ돵ꅶꅝ냑빜맏1ꅞꅝꓽ쒣뾳ꅁ1999ꅞꅃ ꗘꭥ냪ꥷꕾ뛗믈ꛦ뭐압ꯈ뚡꒧ꕾ뛗ꗦ꧶ꅁ뛗뉶ꓨ궱ꭙꗑ꣑믝싹ꓨꛛꗑ쒳굱ꅁꡓꚳꩫ덗ꑗ꒧궭꣮ꅃ믈ꛦ뚡ꗦ꧶ꓨ궱ꅁꙢ꒻ꑑꑋ꙾ꕾ뛗ꖫ돵ꯘꗟ꒧ꫬꭙ덺륌ꗾ엩ꕾ뛗ꥷ믈ꛦ닕ꚨ꒧ꅵꕾ뛗ꗦ꧶꒤ꓟꅶ뚰꒤ꗦ꧶ꅃ꣤ꗲ꒶ꓨꚡ뇄싹Ꙗ돸믹ꅆꛜꗁ냪ꑃꑑꑋ꙾ꗦ꧶꒤ꓟ닕결ꕾ뛗롧곶냓쑷돆ꑰ닕ꅃꑃꑑꑅ꙾ꚨꗟꕸꕟꕾ뛗ꖫ돵땯깩냲라ꅝꑷꟳꙗ결ꕸꕟꕾ뛗롧곶꒽ꕱꅞꅁꗦ꧶꣮ꯗꗧ쁈꒧엜ꅃ꣤ꓨꚡ걏ꗑꗦ꧶싹ꓨꛛꛦ뙒뷦롧ꗑꕸꕟꕾ뛗롧곶꒽ꕱꕎ결벼Ꙙꞡꕩꅁ뙒뷦뛗뉶ꗑ꣑믝싹ꓨꛛꗑ쒳굱ꅁ놩ꙕ믈ꛦ꯹ꚳꕾ뛗뙒뙗ꅝ뷦뙗ꅞ 1
꒧빬썂꒣녯뙗륌ꖡꛦ덗ꥷ궭썂1ꅃꑋꑑꑃ꙾꒭ꓫ닄ꑇ깡ꕾ뛗롧곶꒽ꕱꅝ꒸ꓓꅞ ꒤ꖡ믈ꛦ 믈ꛦ뭐믈 ꖫꛦ뚡꒧ꕾ뛗ꖫ돵ꕾ뛗롧샙냓 ꖫ돵돵 뷕뷕론ꅝ1ꅞ?뻡ꗴ믈ꛦ뙒뷦ꕾ뛗 론뭐ꕾ맴ꧮ듚꒧꒤꒶ 뭐 ꑺꅝ2ꅞ?뭠뚰ꣃ닎군ꕾ뛗ꗦꑺ륷꧶룪껆 륷 ꅝ3ꅞ?뒣꣑냪꒺ꅂꕾꕾ뛗놡 돸뒣꣑ꙕꥷ믈ꛦ ꕾ뛗ꥷ믈ꛦA ꕾ뛗ꥷ믈ꛦB ꖫ돵뛗뉶떲믈냢ꛦꕾ뚡뛗꒧ꗦ꧶ꖫ돵뛗뉶떲냢ꕾ뛗 믈ꛦ뭐압ꯈ뚡꒧ꕾ뛗ꖫ돵 ꖫ돵뛗뉶떲쇊ꕾ뛗ꖫ돵뛗뉶떲쇊ꕾ뛗 ꕘꑦ냓꣤ꕌꕾ뛗꧒녯 뙩ꑦ냓꣤ꕌꕾ뛗믝ꡄ 맏 뗹ꅇꑗ맏꒧맪뵵ꫭꕾ뛗ꖫ돵꒤꒧ꕾ맴떲쇊꒧냊Ꝁꅁꛓ뗪뵵ꫭꕾ맴떲냢꒧냊Ꝁꅃ? 1귓ꑈ뛗ꑊ듚뛗ꕘ듚럭꙾닖뽮뙗륌꒭ꛊ롕떥귈과꒸껉ꅝꗸ띾ꭨ결꒭ꑤ롕과꒸ꅞꅃ 2
ꚨꗟꅁꖴ꽽Ꙩ꙾꣓ꗑꕸꕟꕾ뛗롧곶꒽ꕱ뽗ꞽ궱ꅁ꣏녯ꕾ뛗ꖫ돵뙩ꑊ꧊쑶ꪧ꒧껉ꕎꅃꙝꚹꅁ믈ꛦ걏덺륌ꕾ뛗롧곶냓꒧벼Ꙙ돸믹뭐ꕴꑀꗦ꧶맯ꓨ륆ꚨꗦ꧶ꅁꕾ뛗롧곶냓ꕵ걏녱꒤쇈꣺ꅁꖻꢭꣃ꒣꯹ꚳ뎡ꛬꅝꓽ쒣뾳ꅁ1999ꅞꅃ ꑀ꿫ꛓꢥꅁ믈ꛦ꒧ꕾ뛗ꗦ꧶띾냈둎꙰Ꙑꗸ띾꒧ꗦ꧶ꮬ멁ꅁ꣤ꕩ꿠ꙝ뛗뉶꒧셻껉ꩩ냊ꛓ뻉교ꕾ뛗믝ꡄ뙱꒧엜ꅃꙝꛓꅁ럭믈ꛦ궱맯믝ꡄ뙱꒧곰땍뱗ꕛ껉ꅁ꣤ꕩ꿠ꙝꕾ뛗꒧꙳뙱꒣ꢬꛓ뻉교ꗦ꧶ꖢ뇑ꅆꛓ꣤ꚨꖻ녎꒣뛈ꓮ꧳돠ꖢꚹꚸꗦ꧶뻷라ꅁꗧ쇴ꝴ믈ꛦꭈꗎ꒧돠ꖢꕈꯈꓡ꒧걹ꖢꅃꙝꚹꅁ믈ꛦ꒧ꕾ뛗ꗦ꧶쇶뭐맪믚꒧냓ꭾꗦ꧶꒧ꮬ멁ꚳ꧒꒣Ꙑꅁꕾ뛗꒧ꗦ꧶ꮬ멁ꅁꙢ냓ꭾ꙳Ꙣ꿊덦놡껉ꅁꗧ라늣ꗍ꿊덦ꚨꖻꅃ굙결궰ꝃ꿊덦ꚨꖻꛓꑪ뙱꯹ꚳꕾ맴ꅁ믈ꛦꗧ녎ꕘ뉻꯹ꚳ륌Ꙩꕾ맴ꛓ뻉교믈ꛦ꒺뎡룪땵꿊꒧뉻뙈ꅁꛓ덯볋ꪺ놡녎ꑪꑪꙡ뱗ꕛ믈ꛦ샧륂꒧ꝸ쏸꧊ꅃ Ꙣꑪ뎡꓀ꪺ믈ꛦꕾ맴꙳뙱볒ꮬ꒤ꅁꞡꛒ뱻ꕈ돦뚵덦맴ꮬ멁꣓뙩ꛦꅝꩌ뙩끝ꥍ뎯쑒둦ꅁ1997ꅆHamidi and Bell, 1982ꅞꅃ땍ꛓ믈ꛦ둎꙰Ꙑꑀ꿫ꗸ띾ꅁ꣤꧒뻖ꚳ꒧룪ꚳꑀꥷ뎡ꛬ(볆귈)ꅁ럭믈ꛦꙐ껉꯹ꚳ꣢뚵ꕾ맴껉ꅁ뱗ꕛ돦ꑀꕾ맴꙳뙱뛕ꖲ듮ꓖꕴꑀꕾ맴꒧꯹ꚳ뙱ꅃꙝꚹꅁ굙ꕈ돦ꑀꕾ맴꒧꙳뙱볒ꚡ꣓뙩ꛦ꣢뚵ꕾ맴뉖ꙘꙀ꙳꒧꙳뙱ꅁꭨ쏸ꕈ륆꣬꽵ꖿ꣢뚵ꚡꕾ맴꒧돌꣎꯹ꚳ뎡ꛬ꒧놱꣮ꅃꙢ덜Ꙩ끷맯돦뫘늣ꭾ꙳덦볒ꮬ꒧곣ꡳ꒤ꅁ롧샙굱쇊뙱볒ꮬꅝEconomic Order Quantity ModelꅆEOQꅞ꣣돆Ꙣ꒣Ꙑ룉덦ꮬ멁ꑕꅁ꣓귗꙳뙱볒ꮬ꒧꽓꧊ꅁꚹ결EOQ꙳뙱볒ꮬ삳ꗎꑗ꒧쁵뛕ꅝKlein et al., 1990ꅆChen and Wong, 2003ꅆGuder and Zydiak, 1999ꅆ뎢쳉솾ꅁ2002ꅞꅃ꣤ꚸꅁ돦뚵ꚡEOQ꙳뙱볒ꮬ낲ꥷ냓ꭾ룉덦껉꒣꣼ꭥ롭껉뚡꒧뱶암ꅁꛓꚹꑀ꽓꧊뭐ꕾ맴룉덦꒧놡곛럭쏾ꅃꚹꕾꅁ믈ꛦꕾ맴꒧룉덦뇄ꭄꗟꝙ꧊룉덦ꅝNon-instantaneous ReceiptꅆNIRꅞꅁꗧꝙ럭걙ꑀ믈ꛦꙢ껸꿓ꕾ맴꙳뙱ꅝꝙ놵꣼뙒뛗돦ꅞ껉ꅁꙐ껉Ꙣꖫ돵ꑗ룓믈ꛦꗧ라뙒뛗ꅝꝙ놵꣼뷦뛗돦ꅞꅁꛓꭄ뇄꣺ꑀ꿫냓ꭾ꒧뻣뙱룉덦ꮬ멁ꅃꙝꛓꅁ껚뻚ꭥ궱꒧뇔굺ꅁꖻ곣ꡳ녎ꕈNIR-EOQ꙳뙱볒ꮬ결냲슦꣓ꯘ멣꣢뚵ꚡꕾ맴꙳뙱볒ꮬꅃꙢ뎡꓀꒧꙳덦놱꣮곣ꡳ꒤ꞡ덝ꥷNIR-EOQ꙳뙱볒ꮬ꒧믝 3
ꡄ뙱결ꖭꞡ믝ꡄ뙱ꅁ땍냪꒺꒧ꕾ맴믝ꡄ뙱Ꙣꙕ뙧듁뚡ꕩ꿠ꝥ뉻ꙖꑗꙖꑕ꒧쇍뛕ꩩ냊뉻뙈ꅃ굙ꕈꖭꞡ믝ꡄ뙱꒧ꓨꚡ꣓뙩ꛦ볒ꮬ군뫢ꅁꭨ때ꩫ꺷꺻꣬뫫뵔꒧엜냊놡ꅃꙝꚹꅁꙢ꣢뚵ꚡꕾ맴꙳뙱볒ꮬ꒧삳ꗎꑗ녎늣ꗍ룻ꑪ꒧꙳뙱놱꣮낾깴ꅃ걇ꖻ곣ꡳ꒤녎끷맯꣢뫘ꕾ맴꒧믝ꡄ뙱ꅁ륂ꗎARꅝAutogressiveꅞ-GARCH ꅝGeneralized Autoregressive Conditional HeteroscedasticꅞꕈAR-TGARCHꅝThreshold-GARCHꅞ륷듺볒ꮬ꣓맯귓ꝏ믈ꛦ뙩ꛦ귓ꝏꕾ맴믝ꡄ뙱볒ꮬ꒧륷듺ꅁꣃ녡ꑊ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒤ꕈ뙩ꛦꚹ꣢뫘ꕾ맴꒧돌꣎꯹ꚳ뎡ꛬ꒧군뫢ꅃ 곣ꡳ냝썄뭐ꗘꪺ ꙝꚹꅁ껚뻚ꑗ굺놡ꅁꖻ곣ꡳꚳ꣢귓ꕄ굮곣ꡳ냝썄ꚨ꙰ꑕꅇ ꅝ1ꅞ?꙰꛳ꯘꗟꑀ귓꣢뚵ꚡꕾ맴꒧NIR-EOQ꙳뙱볒ꮬꅁꣃꙢ돌ꑰꚨꖻꗘ볐ꑕ꣓뙩ꛦꡄ룑ꕾ맴돌꣎꯹ꚳ뎡ꛬꅃ ꅝ2ꅞ?굙ꕾ맴믝ꡄ뙱ꝥ뉻U2ꅝ뙧듁꧊꒧ꙖꑗꙖꑕ쇍뛕ꅞꩩ냊꽓꧊ꅁ뻉교꒣빁Ꙙꕈꖭꞡ믝ꡄ뙱녡ꑊ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒤ꅃꙝꛓꅁꖻ곣ꡳ껚뻚ꙕ믈ꛦ륌ꕨ꒧ꕾ맴믝ꡄ뙱룪껆ꅁꛒ뱻꙰꛳륂ꗎAR-GARCHAR-TGARCH볒ꮬ꣓ꯘꗟ귓ꝏꕾ뛗믈ꛦ꒧돦ꑀꕾ맴믝ꡄ뙱륷듺볒ꮬꅃ 냲꧳ꑗ굺곣ꡳ냝썄꒧둹굺ꅁꖻ곣ꡳ꒧곣ꡳꗘꪺ결ꅇ ꅝ1ꅞ?륂ꗎLagrange궼볆뭐AR-GARCHꅂAR-TGARCH볒ꮬꅃ귗ꖿ뛇닎NIR-EOQ꙳뙱볒ꮬꙢ믝ꡄ뙱엜볆낲덝ꑗ꒣Ꙙꥹ꒧덂ꅃꣃꯘꗟꑀ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅃ 2 Leng(1996)땯뉻남Ꝋꓩ뛪듁덦5 ꓀쓁냏뚡ꗦ꧶룪껆군뫢뛗뉶엜냊꒧ꑀ뚥ꛛ곛쏶ꭙ볆ꅁ떴맯귈믹껦엜냊ꖭꞡ귈ꅁ돌ꑪ뭐돌ꑰ믹껦뵤돲떥ꑔ뫘볐꣣ꚳ귋U ꮬ멁ꅁ믹껦엜냊ꚸ볆ꭨ결U ꮬ멁ꅃChan(2000)샋엧궻들꒧늼ꖫ돵ꅁ땯뉻믹껦엜냊ꗧꝥ뉻U ꮬ멁ꅃChakrabarti(2000)ꗧ땯뉻뱷냪남Ꝋꝉ과꒸꒧ꝙ듁ꖫ돵꒧ꓩ꒺뙒뷦믹깴돸륓뉶꣣ꚳU ꮬ멁ꅃꓽꓥꅝ2000ꅞ땯뉻냪꒧ꕾ맴믝ꡄ뙱ꗧꝥ뉻Uꩩ냊꒧꽓꧊ꅃ 4
ꅝ2ꅞ?ꕈ믈ꛦ꒧ꙕ뫘ꕾ맴륷듺믝ꡄ뙱룪껆ꖻ곣ꡳ꧒뒣ꕘ꒧꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅁ꣓ꡄ룑ꕘꕾ맴돌꣎꯹ꚳ뎡ꛬꅁꕈ룑ꡍ믈ꛦꕾ맴뙗뙒ꛓ뻉교꙳뙱륌Ꙩ꒧놡ꅃꚹꝙꕩ궰ꝃ믈ꛦ꒧ꕾ맴꯹ꚳꚨꖻꅁ녱ꛓ뱗ꕛ믈ꛦ꒧쑶ꪧ쁵뛕ꅃ 뷗ꓥ걛멣 ꖻ곣ꡳ꒧곣ꡳ걛멣ꅁ꙰맏꧒ꗜꅃꙢ맏꒤녎ꖻ곣ꡳ꒧곣ꡳ냝썄꓀결ꅇꅝ1ꅞ꙰꛳ꯘꗟ꣢뚵ꚡꕾ맴꒧NIR-EOQ꙳뙱볒ꮬꅁꣃꙢ돌ꑰꚨꖻꗘ볐ꑕ꣓뙩ꛦꡄ룑ꕾ맴돌꣎굱쇊뙱ꅆꅝ2ꅞ륂ꗎAR-GARCHAR-TGARCH볒ꮬ꣓ꯘꗟ귓ꝏꕾ뛗믈ꛦ꒧돦ꑀꕾ맴믝ꡄ뙱륷듺볒ꮬꅃꙝꚹꅁꖻ곣ꡳ굮룑ꡍꑗ굺냝썄꒧ꡂ왊결ꅇ궺ꗽꅁꙢ돌ꑰ셠ꚨꖻꗘ볐ꑕꡄ룑꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅃꖻ곣ꡳ덺륌Lagrange궼볆꒧륂ꗎꕈꡄ룑꣢뚵ꚡꕾ맴NIR-EOQ볒ꮬ꒧돌꣎룑ꅁꣃ끴Ꙙ돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧ꓱ룻ꅁ뮡ꧺꚹ꣢볒ꮬ꒧깴늧ꅃ땍ꛓꅁ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒤꙳Ꙣ믝ꡄ뙱ꩩ냊뉻뙈꒧냝썄ꅃꙝꚹꅁ때ꩫꕈꖭꞡ믝ꡄ뙱녡ꑊ볒ꮬ뙩ꛦ볒ꮬ꒧덗릺ꡄ룑ꅃ꧒ꕈꖻ곣ꡳ륂ꗎAR-GARCH뭐AR-TGARCH꣢뫘믝ꡄ뙱륷듺볒ꮬꅁꣃ끴Ꙙ돦껚샋ꥷ꙰ADF샋ꥷPP샋ꥷ꒧ꓨꩫꕈ쇗ꝋ룪껆Ꟈꙃꝥ뉻ꭄꥷ멁꒧냝썄ꅃ돌ꯡꅁꖻꓥꟆ뇦싇ꗑꑗ굺꒧ꡂ왊뮡ꧺꕾ맴믝ꡄ뙱륷듺볒ꮬ맯NIR-EOQ꙳뙱볒ꮬ꒧뱶암뭐돦뚵ꚡ뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧깴늧ꅃ 5
ꕾ맴ꚨꗦ뙱꒧귬ꥬ룪껆? ꥷ멁꧊샋ꥷꅇ ADF샋ꥷ PP샋ꥷ 곣ꡳ냝썄 2ꅇ 륂ꗎAR -GARCHAR-TGARCH볒ꮬ꣓ꯘꗟ귓 ꝏꕾ뛗믈ꕾ맴믝ꡄ뙱륷듺볒ꛦ꒧돦ꑀꕾ맴믝ꡄꮬꅇ 뙱륷듺볒ꮬꅃ AR-GARCH볒ꮬ AR-TGARCH볒ꮬ 곣ꡳ냝썄1ꅇ ꕾ맴륷듺믝ꡄ뙱 ꕾ맴ꖭꞡ믝ꡄ뙱 ꙰꛳ꯘꗟ꣢뚵ꚡꕾ맴꒧NIR -EOQ꙳뙱볒ꮬꅁꣃꙢ돌ꑰꚨꖻ ꗘ볐ꑕ꣓뙩ꛦꡄ룑ꕾ맴돌꣎ ꯹ꚳ뎡ꛬꅃ ꣢뚵ꚡꕾ맴돦뚵ꚡꕾ맴 NIR-EOQNIR-EOQ꙳뙱볒ꮬ ꙳뙱볒ꮬ 1. ꓱ룻ꕾ맴믝ꡄ뙱륷듺볒ꮬ맯 NIR-EOQ꙳뙱볒ꮬ꒧뱶암ꅃ 2. 돦뚵ꚡ뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳ 뙱볒ꮬ꒧깴늧ꅃ 맏 곣ꡳ걛멣 6
곣ꡳ걹땻뭐뫵굮 ꖻ곣ꡳ꒧걹땻꙰맏꧒ꗜꅃ닄ꑀ뎹ꯘꗟ곣ꡳ냊뻷ꅂ굉뒺ꅂ냝썄뭐ꗘꪺꅁꣃ뮡ꧺ냪ꕾ뛗ꖫ돵꒧륂Ꝁꪬꩰꣃ뵔ꗟ믈ꛦꕾ꙳뙱냝썄꒧꧒Ꙣꅃ닄ꑇ뎹녎Ꙟ압ꖻ곣ꡳ꒧곛쏶ꓥ쑭ꅁꝴꅝ1ꅞꕾ맴ꖫ돵뭐꙳뙱놱꣮ꅁꅝ2ꅞꙨ뚵늣ꭾ꒧EOQ꙳덦볒ꮬNIR-EOQ꙳덦볒ꮬꅝ3ꅞAR-GARCH뭐AR-TGARCH륷듺볒ꮬ떥ꅃ닄ꑔ뎹ꭨꕝꝴꑆ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뇀뻉맯AR-GARCH뭐AR-TGARCH륷듺볒ꮬ꒧ꯘ멣뭐셚껄뗻꛴ꓨꩫꝀꑀ놴끑ꅃ닄ꕼ뎹녎뙩ꛦ맪쏒룪껆꒧꓀꩒뭐덂뉺ꅁꣃ뮲ꕈꙕ뫘맏ꅂꫭ꣓꒩ꕈꝥ뉻ꅃ닄꒭뎹맯ꖻ곣ꡳ꧒뒣ꕘ꒧ꕾ맴륷듺볒ꮬ뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅁ꧳꙳뙱셠ꚨꖻ돌ꑰ꓆ꑕ꒧꙳뙱놱꣮셚껄ꅁꣃꕈꚹ뒣ꕘꖻ곣ꡳ꒧곣ꡳ떲뷗뭐ꯡ쓲곣ꡳ꒧ꯘ쒳ꅃ 7
닄ꑀ뎹ꅇ 곣ꡳ냊뻷ꅂ굉뒺ꅂ냝썄뭐ꗘꪺ 닄ꑇ뎹ꅇ ꓥ쑭놴끑 닄ꑔ뎹ꅇ 륂ꗎAR-GARCH뭐AR-TGARCHꯘꗟꕾ 맴믝ꗦ뙱꒧륷듺볒ꮬ 닄ꑔ뎹ꅇ?닄ꑔ뎹ꅇ?돦뚵ꚡꕾ맴꣢뚵ꚡꕾ맴 NIR-EOQ꙳뙱NIR-EOQ꙳뙱 볒ꮬ뇀뻉?볒ꮬ뇀뻉? 닄ꕼ뎹ꅇ 맪쏒꓀꩒ 닄꒭뎹ꅇ 떲뷗뭐ꯘ쒳 맏 곣ꡳ걹땻 8
닄ꑇ뎹 ꓥ쑭놴끑 ꖻ론Ꙟ압ꣃ뻣뉺ꚳ쏶ꅇ(1)ꕾ맴ꖫ돵뭐꙳뙱놱꣮ꅂ(2)Ꙩ뚵늣ꭾ꒧EOQ꙳덦볒ꮬNIR-EOQ꙳덦볒ꮬ(3)GARCHTGARCH볒ꮬ꒧삳ꗎ떥곛쏶ꓥ쑭ꅃ ꕾ맴ꖫ돵뭐꙳뙱놱꣮ ꑀ꿫ꛓꢥꅁꕾ뛗믈ꛦ놵꣼압ꯈ뙒뷦ꕾ뛗ꯡꅁ굙뙒ꑊ썂Ꙩ꧳뷦ꕘ썂ꅁ둎늣ꗍ뙒뙗ꅝ뫙Ꙩ쁙ꅆOverboughtꅞꅁ꒧ꅁꭨ늣ꗍ뷦뙗ꅝ뫙쁙ꅆ Oversoldꅞꅃꕾ뛗믈ꛦꕩ꿠쑀띎ꭏ꯹덯ꑀ뙒뙗뷦뙗ꪬꩰꅁꛓꚨ뎡ꛬꅝLong Positionꅞꅁ땵뎡ꛬꅝShort Positionꅞꅃꛓꚹꅂ땵뎡ꛬꝙ결ꕾ뛗믈ꛦ꧒꯹ꚳ꒧ꕾ맴꙳뙱뎡ꛬꅃ Chakrabarti(2000)ꕾ뛗믈ꛦ꯹ꚳꕾ맴꙳뙱꒧돌ꕄ굮ꗘꪺ걏결ꕌ압ꯈ뒣꣑ꗟꝙ꧊꒧ꗦ꧶ꅁ꒣뷗꣤걏ꝟ놵꣬띳굱돦ꅁꕾ뛗믈ꛦ녎싇ꗑ쓀꧱ꕘꓢ꒤꒧꙳덦꣓ꞹꚨꗦ꧶ꅃChakrabartiꗧꕘꙢꑀ귓ꭄ뚰앶ꚡ꒧믈ꛦ뚡ꪺꕾ뛗ꖫ돵꒤ꅁ낲덝ꕾ뛗ꗦ꧶냓결궷쁉끫쇗ꅁ럭ꗦ꧶냓놵꣬압ꯈ꒧뷦ꕘ뎡ꛬꅁꕂ꒣쑀꯹ꚳ덯믲Ꙩ꒧뎡ꛬ껉ꅁꗦ꧶냓라녎꧒꒣쑀꯹ꚳ꒧뎡ꛬ신뷦떹꣤ꕌꗦ꧶냓ꅃꙐ볋ꪺ꣤ꕌꗦ꧶냓ꗧ녎꧒꒣쑀꯹ꚳ꒧뎡ꛬ신뷦ꕘꕨꅁ둎릳ꗡ뽓뾻솦ꑀ꿫ꅁꛓꚹ뫘ꛦ결녎라덹ꚨꗦ꧶냓볈껉꧊꙳덦꒧ꑗꅃ ꙢBessembinder(1994)꒧곣ꡳ꒤ꕘ꯹ꚳꕾ맴꙳뙱녎라꣏녯ꕾ뛗믈ꛦ꒧뻷라ꚨꖻꑗꅃꙝ결꯹ꚳ낪걹냊꧊꙳뙱뎡ꛬ꧒녯꒧ꝑ꺧룻ꝃ걹냊꧊꙳듚꧒녯꒧ꝑ꺧결ꝃꅃꙝꚹꅁꕾ뛗믈ꛦ덱녠라껚뻚굱돦걹뙱녎꧒꯹ꚳ꒧꙳뙱굱Ꙣꑀ돌꣎꯹ꚳ뎡ꛬꅃ굙ꕾ뛗믈ꛦ꧒놵꣼꒧뷦돦ꑪ꧳뙒돦ꛓ꯹ꚳ뎡ꛬꅁ뙒돦ꑪ꧳뷦돦꧒꯹ꚳꪺ땵뎡ꛬ낾싷ꑆ꣤꧒굱ꥷꪺ돌꣎꯹ꚳ뎡ꛬꅃꕾ뛗믈ꛦ녎라Ꙣ믈ꛦ뚡ꖫ돵낵ꑀ꧟룉ꪺ냊Ꝁꅁ맯꣤꧒꯹ꚳꪺ꙳뙱낵ꑀ뎡ꛬ뷕뻣ꅃꛓ껚뻚꙳뙱놱꣮ 9
볒ꮬꅁꕾ뛗믈ꛦ녎라맯꣤돸믹낵뷕뻣ꅁꕈꝬꓞꟳꙨꪺ뙒돦뷦돦꣓ꖭ뿅꣤꙳덦뎡ꛬꅃꑀ꿫ꛓꢥꅁꕾ뛗믈ꛦꕩ껚뻚꣤ꕌꗦ꧶냓ꗲ꒶냓ꪺ룟믹놡ꅁ냑ꛒ꣤ꕌ압ꯈꪺꥥ끕믹껚뻚ꖼ꣓ꖫ돵ꪺꓨꙖ늣ꗍ륷듁꣓굱ꥷ뷕뻣믹껦ꅃ 껚뻚 Madhavan et al. (1993)꙳덦놱꣮볒ꮬꅁ럭꙳뙱ꓱꗘ볐ꓴ럇결낪껉ꅁ롧곶냓녎라궰ꝃ쏒꣩믹껦ꅁꕈꝬꓞꗦ꧶쇊뙒ꟳꙨꪺ쏒꣩ꅁ싇ꕈ궰ꝃꖼ꣓ꪺ꙳덦꯹ꚳꚨꖻꅆ굙륷듁꧒꯹ꚳꪺ꙳덦맯꧳ꖼ꣓ꪺ샲ꝑꚳꖿꙖ쏶ꭙꅁꭨ라뱗ꕛ돸믹ꓴ럇ꅃ곛Ꙑꪺ뉺뷗삳ꗎꙢꕾ뛗ꖫ돵ꗧ걏꙰ꚹꅃ꙳덦ꪺ뱗ꕛ맯뙒ꓨꕎꫭ뗛뎡ꛬꪺ뱗ꕛ땵뎡ꛬꪺ듮ꓖꅁ맯뷦ꓨꛓꢥꭨ결뎡ꛬꪺ듮ꓖ땵뎡ꛬꪺ뱗ꕛꅃꙝꚹ럭ꕾ뛗믈ꛦ궱맯뱗ꕛꪺ뎡ꛬ땵뎡ꛬꪺ듮ꓖ껉ꅁ녎라Ꙣꑀ룻ꝃ믹껦ꗦ꧶ꅃ꒧ꅁ굙ꕾ뛗믈ꛦ덂꧳ꑀ듮ꓖꪺ뎡ꛬ뱗ꕛꪺ땵뎡ꛬꅁꭨ녎라Ꙣꑀ룻낪믹껦ꗦ꧶ꅃ슲ꛓꢥ꒧ꅁ굙ꕾ뛗믈ꛦ꯹ꚳꖿ(Positive)ꪺ꙳덦뎡ꛬꅁꭨꚹꕾ뛗믈ꛦ녎라걏ꑀ뉢뷦ꓨꅁ꒧ꅁ굙꯹ꚳ굴(Negative)ꪺ꙳덦뎡ꛬꅁꭨ녎라걏ꑀ뉢ꪺ뙒ꓨꅝFrimo et al., 1999ꅞꅃ ꩌ뙩끝ꥍ뎯쑒둦ꅝ1997ꅞꕘꕾ뛗믈ꛦ꒧ꕾ맴꙳뙱껉녠굮궱맯꙳뙱륌Ꙩ륌ꓖꪺ냝썄ꅃ믈ꛦ꒧과꙳뙱ꓴ럇꒧ꡍ떦냝썄ꅁ걏ꡍꥷ믈ꛦ꒧과꙳뙱ꓴ럇ꅁꕈ삳ꕉꖼ꣓과꒧ꝙ껉믝ꡄꅃ꣤곣ꡳ꒤ꕘ믈ꛦ꒧과꙳뙱볒ꮬ꫱꧳끥돸떣꙳덦볒ꚡꅁ땍꣤ꡍ떦꒤꒧깴늧덂Ꙣ꧳ꅇ (1) 뛇닎끥돸떣꒧꙳덦ꡍ떦볒ꚡ꧒끑뷗ꪺ덦ꭾ꣣껉껄꧊ꅁ듁뚡닗ꑆ꣤믹귈ꕩ꿠ꑕ궰꒣꣣믹귈ꅁ둎과ꛓꢥꅁ럭듁뚡떲ꟴ꣤꒴걏믈ꛦ꒧룪늣ꅃ (2) 뛇닎꒧끥돸떣꙳덦ꡍ떦볒ꚡꅁꙢ믝ꡄ듁뚡때뫲ꯦ굱쇊놹걉ꅁ땍믈ꛦ꒧과ꕩꙝ꿊덦ꚨꖻ꒧ꙝ꿀ꅁꙢ믝ꡄ듁뚡뙩ꛦ뫲ꯦ굱쇊놹걉ꅃ (3) 뛇닎꒧끥돸떣ꡍ떦냝썄ꅁ끬ꡄꝑ볭랥ꑪ꓆결귬ꭨꅁꛓ믈ꛦ꒧과꙳뙱ꓴ럇ꡍ떦냝썄Ꙣ꧳끬ꡄꚨꖻ랥ꑰ꓆결꣤ꗘ볐ꅃ 룓곣ꡳ륂ꗎHamidi and Bellꅝ1982ꅞ꧒ꯘ멣꒧꙳뙱볒ꮬꅁꣃ뿯꣺냪꒺걙ꑀ냓띾믈ꛦ꒧룪껆꣓뙩ꛦ꓀꩒ꅁꛓ꣤맪쏒떲ꩇ땯뉻믈ꛦ꒧과믝ꡄ뙱ꝥ뉻녠멁꓀끴꒧ꮬ멁ꅁꕂ믈ꛦꡍ떦뛉Ꙗ꧳꯹ꚳ륌Ꙩꪺ과꙳뙱ꅁꙝꛓ뻉교룪꒧ 10
뚢롭ꕈ륤썂꯹ꚳꚨꖻ꒧굴뻡ꅃ Lengꅝ1996ꅞ땯뉻남Ꝋꓩ뛪듁덦5 ꓀쓁냏뚡ꗦ꧶룪껆군뫢뛗뉶엜냊꒧ꑀ뚥ꛛ곛쏶ꭙ볆ꅁ떴맯믹껦엜냊꒧ꖭꞡ귈돌ꑪ뭐돌ꑰ믹껦뵤돲떥ꑔ뫘볐꣣ꚳ귋U ꮬ멁ꅁ믹껦엜냊ꚸ볆ꭨ결U ꮬ멁ꅝChan, 2000ꅞꅁꕂꚹ뫘Uꮬꩩ냊뉻뙈꒣뛈걍꧳ꕾ뛗꒧믹껦ꩩ냊ꑗꅁꗧꕘ뉻Ꙣꕾ뛗ꚨꗦ뙱꒧ꩩ냊뉻뙈꒧꒤ꅝꓽꓥꅁ2000ꅞꅃ Ꙩ뚵늣ꭾ꒧EOQ꙳덦볒ꮬꭄꗟꝙ룉덦EOQ꙳덦볒ꮬ 돦뚵늣ꭾ꒧EOQ볒ꮬ쇶뱳결덜Ꙩꗸ띾륂ꗎ꧳꙳덦뫞뉺ꅁ땍ꛓ꣤ꥼ꙳Ꙣ덜Ꙩ꒣Ꙙꥹ꒧낲덝ꕩ뙩꒧덂ꅃꙝꛓꚳ덜Ꙩ뻇끷맯EOQ볒ꮬ뒣ꕘ뙩꒧ꓨꩫꅃ꣤꒤ Klein et al.ꅝ1990ꅞꕈMaloneyꅝ1987ꅞ꧒뒣ꕘ꒧Ꙩ뚵ꚡEOQ꙳덦볒ꚡ결냲슦귗ꖿEOQ볒ꮬ돦뚵꙳덦꒧볒ꮬꅃꣃ륂ꗎ Lagrange 궼볆꣓떲Ꙙ궭꣮ꚡ뭐ꗘ볐ꚡꅁꕈ몡ꢬKarush-Kuhn-Tucker ꅝKKTꅞ뇸ꗳꅝLuenberger, 1984.ꅞꅁꣃ덺륌 Lewisꅝ1981ꅞ꙾뒣ꕘ꒧뵵꧊띪둍ꅝLine-searchꅞꓨꩫꯘꗟ돌빁 Lagrange 궼볆꒧ꑗꅂꑕ곉ꅁꡄ룑ꕘꑀ돌꣎Lagrange 궼볆ꅁꣃꯘꗟ꣢뚵꙳덦꒧ EOQ볒ꮬꅃ꣤ꯡꅁChen et al.ꅝ2003ꅞ꓀ꝏ륂ꗎ Lewisꅝ1981ꅞꕈ Ziegler (1982)ꪺꓨꩫꡄ룑돌꣎ Lagrange 궼볆ꑗꅂꑕ꒧쏤곉귈ꅃZiegler ꕈꑇ꓀ꩫ결냲슦꧒땯깩ꕘ꒧ꅵ돌ꫬ-맯낸냝썄ꅝPrimal-dual Schemeꅞꅶꓨꩫ꣓귗ꖿ뵵꧊띪둍ꩫꅁꕈꡄ룑ꕘꟳ결륇꫱돌꣎ Lagrange 궼볆꒧ꑗꅂꑕ곉ꅁꣃꚹ꣓ꯘꗟꑀ귓Ꙩ뚵꙳덦꒧EOQ볒ꮬꅃWalshꅝ1975ꅞEdwin and Stanislawꅝ1996ꅞ맯꧳돌꣎Lagrange 궼볆꒧ꡍꥷꭄ뵵꧊볒ꚡ꒧덗릺ꡄ룑ꚳ룔닓꒧꒶닐ꅝLin, 1994ꅞꅃ Guder and Zydiakꅝ1999ꅞꅁꗧ끷맯EOQ볒ꮬ꒧궭꣮ꚡ낵ꑀ귗ꖿꅃꙢ뉻맪놡맒ꑕꅁꗸ띾Ꙣ뙩ꛦꗍ늣껉ꅁꕩ꿠Ꙑ껉ꝑꗎꙨ뫘귬껆꣓뙩ꛦ꣤ꗍ늣겡냊ꅃꙝꛓꙢ궭꣮ꚡ꒧낲ꥷꑗꅁ뚷ꛒ뱻꣢귓꣢귓ꕈꑗꪺ귬ꪫ껆꒧띦끴ꅃꙝꚹꅁꙢ 11
귬ꪫ껆ꪺ깷꙳ꑗꅁ믝Ꙑ껉끷맯Ꙩ뫘ꪫ껆ꪺ껸꿓뉶ꅁ꣓뙩ꛦ귬ꪫ껆꒧꯹ꚳ뭐ꙁ굱쇊ꪺꛦ결ꅃ꧒ꕈꙁ굱쇊쉉ꕈ굱쇊뉶ꞡ결꣤ꛒ뙱ꪺ궫쉉꒧ꑀꅃꙢꚹ곣ꡳ꒤꣤ꝑꗎEOQ꒧볒ꮬꅁ낲덝Ꙣ돦뚵늣ꭾꙨ궫귬껆꣓랽꒧볒ꮬ궭꣮ꑕꅃꣃꕈ셠꙳덦ꚨꖻ돌ꑰꪺꗘ볐ꑕꅁꡄ룑ꕘꙕ뫘귬껆돌꣎꙳뙱ꙁ굱쇊쉉ꅃ Ꙣ뎢쳉솾ꅝ2002ꅞ끷맯ꕢ뻉엩늣띾꒤Ꟗ덴걹냊꙳덦꒧꯹ꚳ냝썄ꅃꛒ뱻ꕈꩁ냈ꓴ럇결궭꣮뇸ꗳꅁ돌ꝃ셠ꚨꖻ결ꗘ볐ꅁꯘꗟ꣢EOQ꙳덦볒ꮬꅃ꣤ꑀꭙ뇄ꖭꞡ믝ꡄ뙱Ꝁ결룓볒ꮬ믝ꡄ뿩ꑊ엜볆ꅁ꣤ꑇꝑꗎARꅝ1ꅞꅝFirst-order Auto Regressionꅞ볒ꮬꝀ결믝ꡄ륷듺꒧ꑵ꣣ꅃꛓꯘꗟ덯꣢뫘꒣ꙐEOQ꙳덦볒ꮬ꒧ꗘꪺꅁꙢ꧳귗ꖿEOQ볒ꮬ꒤냑볆덝ꥷ꒧냝썄ꅃꟆ뇦덺륌ꑀ귓룻럇뵔꒧뿩ꑊ엜볆귈ꅁ꣓뱗ꕛ볒ꮬ꒧빁ꗎ꧊ꅃ꣤곣ꡳ떲ꩇ땯뉻ꅁ륂ꗎ믝ꡄ륷듺꒧EOQ볒ꮬꅁꙢ곛Ꙑꩁ냈ꚨꖻꪺ덝ꥷꑕꅃ녎ꕩꟳ럇뵔ꙡ군뫢ꕘ꙳덦꒧돌꣎꯹ꚳꓴ럇꙳덦꒧ꙁ굱쇊쉉ꅃ ꓽꓬ땞 (1995) 녩늱쉅떥(1998)맯꧳돦뚵늣ꭾNIR-EOQ꙳덦볒ꮬ삳ꗎ꧳롧샙ꗍ늣뙱꒧ꡍꥷꚳ룔닓꒧꒶닐ꅃ GARCH뭐TGARCH볒ꮬ꒧삳ꗎ GARCH볒ꮬ결Bollerslevꅝ1986ꅞ꧒뒣ꕘ꒧ARCH볒ꮬ꒧귗ꖿꅁꕂꛛ1980꙾ꕎ꒧ꯡ뎰쓲ꚳ뻇ꅝBollerslev, 1992; Bollerslev, 1994ꅆꩌ랡뚯ꅁ1997ꅞ귗ꖿARCH볒ꮬꅁꕈ륂ꗎ꧳ꟳꙨ꒣Ꙑ믢냬꒧륷듺ꅁꕈꑕ녎Ꟈ뮡ꧺGARCH볒ꮬꕈTGARCH볒ꮬ꒧곛쏶ꓥ쑭ꅃ Baillie and Bollerslevꅝ1989ꅞꕈꩫ궦ꅂꢽ꧔ꅂꓩ뛪ꅂ럧ꑨꩫ궦ꅂ굞싩남Ꝋ뙩ꛦ삳ꗎ맪쏒꓀꩒ꅁ떲ꩇ땯뉻ꙕ냪뛗뉶ꪺ엜냊뉶때ꛛ곛쏶ꅆꙢGARCH 볒ꮬꑕꅁ땯뉻뛗뉶꣣ꚳ낪깬깰쁈껉뚡엜ꪺ뇸ꗳ엜늧볆꒧꽓꧊ꅁꚹꑇ귓꽓꧊라쁈볋ꖻ듁뚡ꪺꕛꛓ엜ꪺ꒣엣뗛ꅃꛓꙢ West and Choꅝ1995ꅞꪺ곣ꡳ꒤ꕘꅁ꣤뇄ꗎ GARCHꅝ1, 1ꅞ볒ꮬꅂIGARCHꅝ1, 1ꅞꅂ꣢귓AR 12
볒ꮬꕈ때ꗀ볆볒ꮬ꣓뙩ꛦ륷듺ꅁ꓀ꝏꕈ남Ꝋꅂꓩ뛪ꅂꩫ궦ꅂꕛ맴ꕈ굞싩ꝉ과꒸꒧뛗뉶룪껆ꅁ꣓뙩ꛦ꓀꩒ꅃ꣤곣ꡳ떲ꩇ땯뉻Ꙣ땵듁ꅝꑀ뙧ꅞ륷듺ꑕꅁꕈ GARCH 볒ꮬ꒧륷듺셚껄룻꣎ꅁꛓꙢ륷듺ꝕ볆꧔껉ꅝ12뙧ꅂ24뙧ꅞꅁꭨ때ꩫ냏꓀꛳룻꣎ꅃ Ꙣ뎯ꓟꑀꅝ1996ꅞ꒧곣ꡳꅁ꣤ꕈ띳ꕸ맴ꝉ뒫과꒸꒧뛗뉶룪껆Ꝁ결볐ꪺꅁꣃ륂ꗎDickey and Fuller (1981)꧒뒣ꕘ꒧쉘뱗ꮬ돦껚샋ꥷꅝAugmented Dickey-Fuller TestꅆADFꅞꅝNelson and Plosser, 1982ꅞPhillips and Perron ꅝ1988ꅞ ꒧때ꗀ볆샋ꥷꩫꅝPPꅞ꣓샋ꥷ룪ꙃꟇꙃ꒧ꥷ멁꧊ꅝPindyck, 1991ꅞꕈ쇗ꝋGranger and Newbold (1974)꧒뒣ꕘ꒧뗪낲끪쉫ꅝSpurious Regressionꅞ꒧ꙍ쁉ꅃꣃ륂ꗎ덶ꓩ륷듺ꩫꯘ멣 GARCHꅝ1, 2ꅞ뭐 ARIMAꅝ0, 1, 1ꅞ꒧뛗뉶륷듺볒ꮬꅁꙢ95ꉍꪺꭈ뿠ꓴ럇ꑕꓱ룻볒ꮬ륷듺냏뚡ꅃ맪쏒떲ꩇ땯뉻 GARCH ꒧륷듺셚껄룻 ARIMA ꒧셚껄결꣎ꅃ ꛓꓽꓥꅝ2000ꅞꪺ곣ꡳ꒤뒣ꕘꕈGARCHꅝ1, 1ꅞ볒ꮬꕈNewey-West샋ꥷ꣓엧쏒ꕾ뛗ꖫ돵뚡꒧꙳덦껄ꩇꅁ꣤땯뉻ꙢGARCHꅝ1, 1ꅞ 볒ꮬꪺ엜볆엣뗛꧊떲ꩇꧺ엣Ꙩ꧳Newey-west ꪺ꛴군떲ꩇꅃ꙳덦놱꣮껄ꩇꙢGARCHꅝ1, 1ꅞ 볒ꮬ껉ꅁ엣뗛ꕩ뱶암ꚬ뵌뙽뵌ꪺ믝ꡄ뙱뛗뉶엜냊뉶ꅁꕈNewey-west ꛴군껉ꅁꕵ꿠녯꣬꙳덦놱꣮껄ꩇ맯ꚬ뵌뙽뵌ꪺ믝ꡄ뙱ꚳ엣뗛뱶암ꅃꙝꛓ볒ꮬꪺ엣뗛꧊ꑗGARCHꅝ1, 1ꅞ볒ꮬ꒧엣뗛꧊낪꧳Newey-West샋ꥷꅃ ꓗꑬ랽ꅝ2002ꅞ꣤덺륌 ARIMAGARCH 볒ꮬꪺ끴빁ꅁꙁ꣏ꗎ덶ꓩ륷듺ꩫꅁ꣓ꯘꗟ륪ꧮ듚ꝑ뉶륷듺꒧볒ꮬꅃꙢ볒ꮬ끴빁꒧ꯡ땯뉻ꕈGARCHꅝ1, 2ꅞꕈARIMAꅝ2, 0, 2ꅞ결ꑇ룻꣎꒧볒ꮬꅃꣃꕈ덯꣢뫘볒ꮬ꣓뙩ꛦ륷듺ꅃꛓ꣤맪쏒떲ꩇ엣ꗜꅁꙢ95ꉍꪺ륷듺냏뚡ꑕ GARCH ꒧륷듺셚껄룻 ARIMA 볒ꮬ결꣎ꅁꕂꙢ뭾깴ꪺ뿅뙱뚵ꗘꑗ GARCH 볒ꮬ꒧륷듺낾뭾ꗧ룻 ARIMA볒ꮬ결ꑰꅃ Ꙣꮸꓥ꧉ꅝ1999ꅞ꒧곣ꡳꅁ꣤ꕄ굮덺륌 GARCH 볒ꮬꪺ귗ꖿ꣓놴끑 13
늼ꖫ돵ꪺ엜냊맯꧳ꑵ띾ꗍ늣볆ꪺ륷듺ꅁꣃꕂꝑꗎ꣤ꩩ냊ꪺꓨꙖ꒣Ꙑ꣓덝ꗟ쉥귈ꅝThresholdꅆꕈꑺ쉚뚵결ꅵ0ꅶꅞꅃ꣤곣ꡳ떲ꩇ땯뉻럭믹돸륓뉶결ꖿꅂ결굴낪꧳ꅂꝃ꧳쉥귈맯꧳ꑵ띾ꗍ늣엜냊곒꙳Ꙣ꒣맯뫙ꪺ껄ꩇꅁ떲ꩇ엣ꗜ럭ꖿꪺꕈ낪꧳쉥귈ꪺ믹돸륓엜꓆곛맯꧳굴ꪺꥍꝃ꧳쉥귈ꪺ믹돸륓엜꓆꣏맯ꑵ띾ꗍ늣볆ꚳ룻ꑪꪺ뱶암ꅃ 빇ꓑ뱷ꅝ2002ꅞꪺ곣ꡳ꒤ꅁ껚뻚Bollerslevꅝ1986ꅞ꧒뒣ꕘ꒧ARCH볒ꮬ결냲슦ꯘ멣ꕘGARCH 볒ꮬꕈ ARMA-TGARCH볒ꮬꅁꣃ끷맯ꕸ왗ꅂꓩꖻꕈ과냪ꖫ돸륓뉶꒧ꩩ냊꧊꣓뙩ꛦ곣ꡳꅃꙢꚹ곣ꡳ꒤ꕘꅁꙢ덜Ꙩꪺ뿄룪껆꒤ꅁꞡ꣣ꚳꑀ뫘ꩩ냊롳뭅꧊ꅝVolatility Clustersꅞꪺ껄삳ꅃꚹꑀ껄삳ꭙꭥ듁꒧ꑪ둔ꩩ냊ꅁ녎꛱쁈ꑕ듁ꚨꙐꙖꙖ꒧ꑪ둔ꩩ냊ꅆꙐ뉺ꅁꭥ듁ꑰ둔꒧ꩩ냊ꅁꗧ꛱쁈ꑕ듁ꑰ둔꒧ꩩ냊엜꓆ꅃꙝꚹꅁ꣤ꛒ뱻ꙢGARCH볒ꮬ꒤ꕛꑊꑀ쉥귈ꅁꕈ귗ꖿGARCH볒ꮬꅃ돌ꯡꅁꣃ륂ꗎEagleꅝ1982ꅞꕈ Ljung and Boxꅝ1978ꅞ꧒뒣ꕘ꒧ARCH LM샋ꥷ뭐Ljung Box샋ꥷ꣓샋ꥷGARCH볒ꮬ뭐TGARCH볒ꮬ꒧빁Ꙙ꧊ꅃ맪쏒ꪺ떲ꩇ땯뉻ꅁꗑ꧳ Threshold GARCHꅝTGARCHꅞ ꕛꑊꑀ쉥귈ꅝThresholdꅆꕈꑺ쉚뚵결ꅵ0ꅶꅞ낵결볒ꮬ꒧꓀곉쉉ꅁꕈꛒ뱻꣤돸륓뉶ꪺꓨꙖ꧊냝썄ꅁꙝꛓ꣤Ꙣ덂뉺ꭄ맯뫙꧊ꪺ룪껆ꑗꅁ TGARCH 볒ꮬ룻 GARCH 볒ꮬ맯ꩩ냊꧊꒧륷듺ꚳ룻꣎ꪺ떲ꩇꅃ ꩌ랡뚯(1997)끷맯ꕸ왗늼ꖫ돵꒧ꩩ냊ꛦ결ꅁꣃ귗ꖿGARCH볒ꮬꯘꗟ꒣맯뫙GARCH볒ꮬꕈ쉥신뒫GARCHꅝꝙTGARCHꅞ볒ꮬꅃꙝꚹꅁ룓곣ꡳ꒧꒣맯뫙GARCH볒ꮬꙢ삳ꩩ냊꒣맯뫙껄ꩇꪺꓨꩫꑗꅁ걏꒹덜끔꺧뱶암ꚱ뵵ꓨ땻ꚡꪺ뇗뉶뭐멉뙚뚵ꅁꕩ뻚ꖼ륷듁엜냊ꪺꖿꅂ굴뢹ꛓ엜ꅃ덺륌꓀꩒끔꺧뱶암ꚱ뵵ꓨ땻ꚡꪺ냑볆ꅁꕩꕈ엣ꗜꕘ꒣맯뫙GARCH볒ꮬꅁ낣ꑆꕩ삳ꖿꅂ굴Ꙗꪺꖼ륷듁엜냊맯ꩩ냊ꚳ꒣맯뫙꧊ꪺ뱶암꒧ꕾꅁ쇙ꕩ낻듺꣬ꩩ냊꒣맯뫙꧊ꪺ신뭐룪끔땻ꯗ낾뭾껄ꩇ떥ꛦ결ꅃ결ꑆ셁룑TGARCH볒ꮬ맯꧳ꩩ냊ꛦ결ꪺ룑쓀꿠ꑏꅁ룓곣ꡳ띪뚰ꕈꕸ왗늼ꖫ돵ꪺ믹돸륓룪껆뙩ꛦ맪쏒곣ꡳꅃ껚뻚룓곣ꡳꯘꗟꪺ꒣맯뫙GARCH볒ꮬTGARCH볒ꮬ맯ꕸ왗 14
늼ꖫ돵ꪺ믹돸륓룪껆뙩ꛦꩩ냊ꛦ결ꪺ맪쏒곣ꡳ떲ꩇꅁ엣ꗜ룓곣ꡳ꧒ꯘꗟ꒧TGARCH볒ꮬꙢ룑쓀ꕸ왗늼ꖫ돵ꩩ냊ꪺꛦ결꿠ꑏꅁ룻뛇닎ꪺꑀ꒣맯뫙GARCH볒ꮬ결ꙮꅃꚹꕾꅁ껚뻚꒣맯뫙GARCH볒ꮬ맯ꕸ왗늼ꖫ돵믹엜냊ꩩ냊ꛦ결ꪺ맪쏒떲ꩇꅁ엣ꗜꕸ왗믹ꩩ냊ꪺꛦ결꣣ꚳARCH껄ꩇꅂ꒣맯뫙꧊ꕈ룪끔땻ꯗ낾뭾떥꽓꧊ꅃꙢꑬ볋ꖻ듁뚡볒ꚡ쎭낷꧊ꪺ샋엧ꑗꅁ맪쏒떲ꩇ엣ꗜ룓곣ꡳ꧒ꯘꗟꪺTGARCH볒ꮬꪺ끴빁꧊ꅁ꒴땍룻뛇닎꒣맯뫙GARCH 볒ꮬ룑쓀ꩩ냊꿠ꑏ결ꙮꅃ 15
닄ꑔ뎹?꣢뚵ꚡꕾ맴义??䕏?꙳뙱볒ꮬ꒧ꯘ멣? ꖻ곣ꡳ녎ꯘ멣ꚨ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅁꣃꙢ돌ꑰꚨꖻꗘ볐ꑕꡄ룑믈ꛦ꒧ꕾ맴돌꣎꯹ꚳ뎡ꛬꅃ땍ꛓꙢ뙩ꛦ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뇀뻉륌땻껉ꅁ믝ꗽꛒ뱻볒ꮬ꒤믝ꡄ뙱엜볆꒧륷듺ꅃꙢ뛇닎꒧EOQ꙳뙱볒ꮬNIR-EOQ꙳뙱볒ꮬ꒤ꞡ낲ꥷ뙧듁믝ꡄ뙱결ꖭꞡ믝ꡄ뙱ꅃꑀ꿫ꛓꢥꅁꕝꝴꕾ뛗ꖫ돵Ꙣ꒺꒧냪믚뿄ꖫ돵ꪺ믹껦ꩩ냊ꅂꗦ꧶뙱뙒뷦믹깴ꞡ꣣ꚳ뙧듁꧊ꙖꑗꙖꑕ쇍뛕꒧꽓꧊ꅝLeng, 1996ꅆChan, 2000ꅆChakrabarti, 2000ꅆꓽꓥꅁ2000ꅞꅃꙝꚹꅁꖻ곣ꡳ꒧곣ꡳ궫쉉ꕩ꓀결ꅇꅝ1ꅞꕾ맴꙳뙱볒ꮬ꒧ꯘ멣ꅝ2ꅞAR-GARCH믝ꡄ뙱륷듺볒ꮬ꒧ꯘ멣ꅃ ꕾ맴꙳뙱볒ꮬ꒧ꯘ멣 때뷗꙳뙱꒧뉺ꗑ결꛳ꅁ꯹ꚳ꙳뙱돌ꕄ굮ꪺ꣢귓뉺ꗑꝙ결ꅇ(1)꛳껉삳뙩ꛦ룉덦ꕈ(2)삳꯹ꚳꙨꓖ꒧꙳뙱ꅝꝙ꙳뙱놱꣮ꅞꅃ땍ꛓꙢꕾ맴뭐ꑀ꿫냓ꭾ꒧룉덦ꮬ멁꒣Ꙑꅃꚹꑀ깴늧ꕄ굮꣓ꛛ꧳ꕾ맴꒧뒫뛗ꅁꙝ뛗뉶ꩩ냊Ꟗ덴ꅁꛓ뻉교ꕾ맴꙳뙱믹귈엜냊ꅃ Ꙣ뛇닎꒧EOQ꙳뙱볒ꮬ꒤ꅁꕩ뻚꒣Ꙑ꒧룉덦ꓨꚡ꣓귗ꖿ볒ꮬꅁꛓ꣏녯볒ꮬꙢ륂ꗎꑗ룻ꑀ꿫꒧꙳뙱볒ꮬ꣓ꪺꟳꚳ뱵꧊ꕾꅃ뛇닎꒧EOQ꙳뙱볒ꮬ때ꭥ롭껉뚡ꪺ낲ꥷꑗ곛럭닅Ꙙꕾ맴꒧룉덦ꮬ멁ꅃ결궰ꝃ꯹ꚳꕾ맴꒧궷쁉믈ꛦ맯꧳ꕾ맴꒧꙳뙱놱꣮뇄ꭄꗟꝙ꧊룉덦ꅝNon-instantaneous Receipt ꅆNIRꅞꓨꚡ꣓뷕뻣꙳뙱ꕈ륆돌꣎꯹ꚳ뎡ꛬꅃ 돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ 돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧륂ꗎ믝ꛒ뱻ꑔ귓볒ꮬ꒧냲ꖻ낲덝ꅃ 16
1. 돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧셠ꚨꖻ곛럭꧳꣤꙳뙱꯹ꚳꚨꖻꕈ룉덦ꚨꖻ꒧ꕛ셠ꅃꛓꚹ룉덦ꚨꖻ걏낲덝뽗ꗟ꧳굱돦꒧ꑪꑰꅁꗧꝙ룉덦ꚨꖻ결ꑀ녠볆ꅃ 2. ꙢNIR-EOQ꙳뙱볒ꮬ꒤ꅁ뙧듁믝ꡄ쁈껉뚡꒧엜꓆덑뗸결걏ꑀ귓ꥷ꒧꓀끴ꮬ멁ꅁ꙰녠멁꓀끴ꅃ 3. 룉덦결ꭄꗟꝙ꧊ꅁꝙ럭ꕾ뛗믈ꛦ꯹ꚳꕾ맴낾싷꣤꧒굱ꥷ꒧돌꣎뎡ꛬꅁ럭ꕾ맴꙳뙱결땵뎡ꛬꛓ낾싷돌꣎꯹ꚳ뎡ꛬ껉ꅁꕾ뛗믈ꛦꑝ라ꙝꕾ맴뙒ꅂ뷦뛗돦Ꙣ꽓ꥷ듁뚡ꙀꙐ땯ꗍꛓꚨꑀꭄꗟꝙ꧊꒧룉덦ꓨꚡꙞ쉫돌꣎꯹ꚳ뎡ꛬꅃ 냲꧳ꑗ굺꒧ꑔ귓낲덝ꅁ돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ결 1*rq=kdc−2*[2/(1)]ꅁ꣤꒤ q ꕎꫭꕾ맴꒧돌꣎뷕뻣뙱(롧샙굱쇊뙱)ꅁkꕎpꫭꕾ맴꒧ꡃꚸ룉덦ꚨꖻꅁdꕎꫭꕾ맴ꡃꑀ뙧듁껉뚡꒧믝ꡄ뙱ꅁꛓcꕎꫭꡃꑀ돦ꛬꕾ맴Ꙣꡃꑀ뙧듁껉뚡꒺꒧꯹ꚳꚨꖻꅁr ꕎꫭꕾ맴꒧믝ꡄ뉶(ꝙꡃꑀ뙧듁껉뚡ꪺꕾ맴뷦ꕘ뙱뷦ꕘ뉶)ꅁpꕎꫭꕾ맴꒧뙒ꑊ뉶(ꝙꡃꑀ뙧듁껉뚡ꪺꕾ맴뙒ꕘ뙱)ꅝꓽꓬ땞ꅁ1995ꅞꅃ ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ 껚뻚돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧낲덝ꅁ꣓뙩ꛦ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뇀뻉ꅃ낲ꥷꙢ볒ꮬ꒤꙳Ꙣ꣢뚵ꕾ맴(i=1, 2)껉ꅁꭨ뻚돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꪺ낲덝ꅃꕩ덝ꥷ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ결ꕈꑕ꒧ꮬ멁ꅇ 1rq2 ′=2kd/c(1−i[)], i = 1, 2. ꅝꅞ iiiipi꣤꒤ q′ ꕎꫭ닄i뚵ꕾ맴꒧돌꣎꯹ꚳ뎡ꛬꅝ뙒ꑊ뷕뻣뙱ꅞꅆkꕎꫭ닄iii뚵ꕾ맴꒧ꡃꚸ룉덦ꚨꖻꅆdꕎꫭ닄i뚵ꕾ맴ꡃꑀ뙧듁껉뚡꒧믝ꡄ뙱ꅆcꕎꫭii 17
닄i뚵ꕾ맴ꡃꑀ돦ꛬꙢꡃꑀ뙧듁껉뚡꒺꒧꯹ꚳꚨꖻꅁr ꕎꫭ닄i뚵ꕾ맴뷦ꕘi뉶ꅁpꕎꫭ닄i뚵ꕾ맴꒧뙒ꑊ뉶ꅃꚹ덂rp결ꑀ왛듺귈ꅝꝙ결ꑀ뵔ꥷ귈ꅞꅁiiiꕩꕏrci(1−)=wꅁꭨc뭐w결ꑀ뵵꧊쏶ꭙꅁꭨ꒽ꚡ()ꕩ결ꑕꚡ꣓ꫭiiiipiꗜ꒧ꅇ 1q′=(2kdw)2 , i = 1, 2. iiii ꅝꅞ Ꙣ뛇닎NIR-EOQ볒ꮬ꒤ꅁ뻣귓볒ꮬ꒤ꖼ꙳Ꙣꗴ꛳궭꣮ꚡꅃ땍ꛓꅁꙢ걙놡ꩰꑕꅁꚹ볒ꮬꕩ꿠ꕘ뉻ꗴ꛳ꮬ멁꒧궭꣮ꅁ꙰ꕾ맴꙳뙱셠썂꣤ꕌꗴ꛳뫞뉺ꑗ꒧ꕩ꿠궭꣮ꅃ결ꑆ샋뗸꣢뚵ꕾ맴꙳뙱꡴닎ꅁꣃ끴Ꙙ셠덦맴꙳뙱셠썂ꅁQꅁ꒧궭꣮ꚡꅁꭨ궭꣮ꚡꕩꫭꗜ꙰ꑕꅇ vq′11+v2q′2≤Q, ꅝꅞ ꣤꒤v1 v2결q′1 q′2꒧앶궫ꙝꑬꅃ굙ꕏq1=v′1q1q2=vq′22ꅃꭨ궭꣮ꚡꅝꅞꕩꫭꗜ꙰ꑕꅇ q+q2≤Q 1. ꅝꅞ 냲꧳ꡃꑀ돦ꛬ껉뚡꒧셠ꚨꖻ돌ꑰ꓆꒧낲덝ꅁꚹꗘ볐ꚡ꒧볆뻇볒ꮬꭨꕩꫭꗜ꙰ꑕꅇ rci(1−)q2ii minpkdf()=∑i+ii q[] i=12qi2wqkd =∑iiii[+], ꅝꅞ =12qii s. t. q1+q2≤Q, ꅝꅞ q1,q2≥0. ꚹ볒ꮬꕝꝴꑆꑀ귓ꕙ꧊ꗘ볐꣧볆ꑀ귓ꭄ뵵꧊궭꣮ꚡꅃꙝꚹꅁꙢ뙩ꛦ덗릺ꡄ룑꒧ꭥꅁ믝덺륌Lagrange궼볆ꅁꕈ룑ꡍꭄ뵵꧊궭꣮ꚡꪺ냝썄ꅃꙝꚹꅁꙢ녎Lagrange궼볆ꅁlꅁ녡ꑊ궭꣮ꚡ꒧ꭥꅁKKT뇸ꗳꅝKarush-Kuhn-Tucker 18
conditionsꅞ결ꑀꖲ굮ꕂꕒ꓀ꅝLuenberger, 1984ꅞ꒧뇸ꗳꅃꕏl결꒽ꚡ()ꑀ귓ꭄ굴꒧Lagrange궼볆ꅁ럭lꇖ0ꅁꑗ굺꒧궭꣮ꚡꅝꅞ녎ꟳ꣣뱵꧊ꅁꙝꛓꚹ덂꒧KKT뇸ꗳꝙ결ꅇ q=(2kdw+2l), i=1, 2, ꅝꅞ iiii q1(l)+q2(l)=Q. ꅝꅞ ꑀ꿫꣓뮡ꅁꗘ볐ꚡꅝPꅞꡄ룑꒧볐럇꓆땻Ꟈ걏녎꒽ꚡꅝꅞ꒧ q1(l) 뭐q2(λ)녡ꑊ꒽ꚡꅝꅞ꒧꒤ꅁꛓLagrange궼볆꒧ꡄ룑ꓨꚡꅁꕩ덺륌뵵꧊띪둍ꅝLine-searchꅞ꒧ꓨꩫ꣓뙩ꛦꡄ룑ꅝWalsh, 1975ꅞꅃꝙ싇ꗑLagrange궼볆뭐꽓ꥷ꡴닎뚡쏶덳꧊꒧ꯘꗟꅁ꣓ꕘ돌꣎꒧Lagrange궼볆ꅃꚹꝙꗑLagrange궼볆ꑗꅂꑕ곉꒧띪둍ꓨꚡ꣓ꡄ룑돌꣎Lagrange궼볆ꅝKlein, et al., 1990ꅆLin et al., 1994ꅆEdwin and Stanislaw, 1996ꅞꅃ ꡴닎꽓꧊뭐Lagrange궼볆꒧쏶ꭙ ꖻ곣ꡳ꒧ꕄ굮ꗘꪺꙢ꧳뵔뭻꙳Ꙣ꧳꒽ꚡꅝꅞ꒤꒧Lagrange궼볆뭐꒣Ꙑ꡴닎꽓꧊뚡꒧ꑀ교꧊쏶ꭙꅃꙢ덯귓꓀꩒꒤ꕩꥷ롱ꑀ귓ꑀ꿫꓆꒧꣢뚵ꕾ맴꒧꙳뙱꡴닎결SpꅝPrimary Systemꅞꅁꚹ꡴닎ꗑꑃ귓냑볆꧒멣ꚨꅇ Sp=S(w1,k1,d1;w2,k2,d2;Q), ꚹ덂꒧ w,k,d 뭐 Q Ꙣ꙰ꭥ꧒ꥷ롱ꅃꙢꚹ꓀꩒꒤낲덝wU, kUꕈdUꕎꫭiii꣤냑볆꒧돌ꑪ귈ꅁꛓ wL, kL ꕈ dLꭨꕎꫭ꣤냑볆꒧돌ꑰ귈ꅃ결ꑆ꓀꩒꡴닎엜볆꽓꧊뭐궭꣮ꚡ꒤Lagrange궼볆꒧쏶ꭙꅁꖲ뚷끷맯ꡃ귓엜볆꽓꧊떹꒩귓ꝏ끑뷗ꅃ럭꣤ꕌ꒧엜볆꽓꧊귈ꥷ껉ꅁ돑빬꒧엜볆꽓꧊Ꙣ덯귓볒ꮬ꒤걏꒹덜엜냊ꅃꙝꚹꅁꙢ꣤ꕌ뇸ꗳ꒣엜ꑕꅁ럭걙ꑀ엜볆꽓꧊땯ꗍ엜냊껉ꅁLagrange궼볆뭐ꚹ엜볆꽓꧊꒧쏶ꭙꭋ녯ꕈꯘꗟ끟꣓ꅃ셼꣒꣓뮡ꅁꕩ녎꯹ꚳꚨꖻꅝwꅞ뭐Lagrange궼볆뚡꒧쏶덳꧊뙩ꛦ꓀꩒ꅃ결ꡄ뙩ꛦ슲꓆꓀꩒ꅁꕩꙁꯘꗟꕈꑕ 19
꣢귓ꚸ꡴닎ꅝSPL,SPUꅞ꣓뙩ꛦ꓀꩒ꅇ SPL=S(wL,k1,d1;wL,k2,d2;Q), SPU=S(wU,k1,d1;wU,k2,d2;Q). ꑗ굺꒧꓀꩒ꕩ꓀결ꕈꑕ꣢귓ꡂ왊ꅇ 1. 닄ꑀꡂ왊걏싇ꗑ몥뱗뙱꒧ꓨꚡꕈ륆ꚨ녎SPLSPU신ꚨSp꒧륌땻ꅃ 2. 닄ꑇꡂ왊걏녎ꚸ꡴닎SPL신뒫ꚨSPUꅁꙁ녎SPU신뒫ꚨSPLꅁ꣤결녱Ꙑꑀ귓꡴닎꽓꧊뿯ꕘ꒧냑볆ꣃ낵떥뙱꒧ꖭ늾ꅃ ꕈꑕ녎끷맯Lagrange궼볆뭐뿯ꥷ꡴닎꒤꒧엜볆꽓꧊꒧뵵꧊쏶ꭙ뙩ꛦ끑뷗ꅃ ꡴닎엜볆꽓꧊뭐Lagrange궼볆꒧뵵꧊쏶ꭙ Lagrange궼볆뭐꽓ꥷ꡴닎꒧엜볆꽓꧊뚡꒧뵵꧊쏶ꭙꪺꯘꗟ걏낲덝Ꙣ꣤ꕌ꡴닎꒧엜볆꽓꧊꒣엜ꑕ꣓뙩ꛦꅃꙝꚹꅁ굙낲ꥷ볒ꮬ엜볆꒤꒧꯹ꚳꚨꖻ늣ꗍ엜냊껉ꅁꭨLagrange궼볆뭐꯹ꚳꚨꖻ뵵꧊쏶ꭙ꒧ꯘꗟꅁ걏낲ꥷꙢ룉뙱ꚨꖻ믝ꡄ뙱꣢엜볆꒣엜ꑕ꣓뙩ꛦꡄ룑ꅃ뒫ꢥ꒧ꅁLagrange궼볆뭐룉뙱ꚨꖻ믝ꡄ뙱꒧뚡ꪺ뵵꧊쏶ꭙꅁꗧ꙳Ꙣ꧳덯꽓ꥷ꒧놡ꩰ꒤ꅃꙝꚹꅁꙢꖻ론꒤녎ꕈꕎ볆꒧ꓨꚡ꣓쏒ꧺ덯꡴닎꒧엜볆꽓꧊뭐Lagrange궼볆뚡꒧뵵꧊쏶ꭙꅃ ꥷ뉺ꑀꅇꕏSAꕈSB결꣢꙳뙱꡴닎꣤꡴닎꙰ꑕꅇ SA=S(w,k1,d1;w,k2,d2;Q) , S B=S(w+dw,k1,d1;w+dw,k2,d2;Q). ꧳ꚹ꡴닎꒤ꅁ낲ꥷꙢ꣤ꕌ엜볆꒣엜ꑕꅁ뛈ꚳ꯹ꚳꚨꖻ늣ꗍ엜냊ꅃꕏλAlB결꣢귓Lagrange궼볆ꅁꣃ녎λA뭐λB꓀ꝏ녡ꑊSA뭐SB꒧꒤ꅃꙢSA뭐SB꣧볆꒤ꅁdwꅂλA뭐lB녎꙳Ꙣꑀ뵵꧊쏶ꭙꅃ 쏒ꧺꅇꕏqA뭐q꡴닎SiB꓀ꝏꕎꫭiA뭐SB꒤ꅁꕾ맴 i ( i ꇗ1, 2)꒧NIR-EOQ꙳ 20
뙱볒ꮬꅁ땍ꯡ녱녎SA뭐SB꒧엜볆녡ꑊ꒽ꚡꅝꅞ꒤ꅇ 1qA=[2kd(w+2l)],iꇗ1, 2; iiiA2 ꅝꅞ 1 qB=[2kd(w+dw+2lB)]2, iꇗ1, 2 . ꅝꅞ iiiꕴꕾꅁꙢ꒽ꚡꅝꅞ떹ꥷꅁ qA1+qA2=qB1+qB2=Q ,ꚹꚡ띎꣧ꅁ굙qA1,qB1,qA2qB2꒧꓀ꗀꞡ곛Ꙑꅁꭨ w+2l=w+w+ Ad2lB, ꅝꅞ ꣤ꚨ꒧뵵꧊쏶ꭙ꙰ꑕꅇ 1 lB=lA-dw. ꅝꅞ 2 ꥷ뉺ꑇꅇꕏSAꕈSB결꣢뚵ꚡꕾ맴꙳뙱꡴닎꣤꡴닎꙰ꑕꅇ SA=S(w,k,d;w,k,d;Q) , SS(kkdkk,d;Q) B=w,+d,;w,+d .꧳ꚹ꣢꡴닎꒤ꅁ낲ꥷ꣤ꕌ엜볆꒣엜ꑕꅁ뛈ꚳꕾ맴룉뙱ꚨꖻ늣ꗍ엜냊ꅃꕏλAꕈλB결ꑀLagrange궼볆ꅁꣃ녎λA뭐lB꓀ꝏ녡ꑊSA뭐SB꒧꒤ꅃꙢSA뭐SB꣧볆꒤ꅁdkꅂlA뭐lB녎꙳Ꙣꑀ뵵꧊쏶ꭙꅃ 쏒ꧺꅇ쏒ꧺ륌땻둎꙰Ꙑꥷ뉺ꑀꅁ땍ꛓ꣤뵵꧊쏶ꭙ꙰ꑕꅇ (k+dk)1k B=A++wdll, ꅝꅞ k2k ꥷ뉺ꑔꅇꕏSAꕈSB결꣢뚵ꚡꕾ맴꙳뙱꡴닎꣤꡴닎꙰ꑕꅇ SA=S(w,k,d;w,k,d;Q) , SB=S(w,k,d+dd;w,k,d+dd;Q) . 21
꧳ꚹ꣢꡴닎꒤ꅁ낲ꥷ꣤ꕌ엜볆꒣엜ꑕꅁ뛈ꚳ믝ꡄ뙱늣ꗍ엜냊ꅃꕏλAꕈλB결ꑀLagrange궼볆ꅁꣃ녎λA뭐λB꓀ꝏ녡ꑊSA뭐SB꒧꒤ꅃꙢSA뭐SB꣧볆꒤ꅁδdꅂλA뭐λB녎꙳Ꙣꑀ뵵꧊쏶ꭙꅃ 쏒ꧺꅇ쏒ꧺ륌땻둎꙰Ꙑꥷ뉺ꑀꅁ땍ꛓ꣤뵵꧊쏶ꭙ꙰ꑕꅇ (d+dd)1ddlB=lA+w d2d, ꅝꅞ ꑗ굺뵵꧊쏶ꭙ꒧ꯘꗟꅁ꒣뛈뒣꣑꡴닎꒧엜볆꽓꧊뭐Lagrange궼볆쏶ꭙꯘꗟ꒧ꓨꩫꅁꗧ뒣꣑Lagrange궼볆Ꙣ꽓ꥷ놡맒ꑕ꒧군뫢ꓨꚡꅃ놵ꑕ꣓녎꒶닐꙰꛳군뫢돌꣎꒧Lagrange궼볆ꕈ꙰꛳ꡍꥷ꣓ꡍꥷLagrange궼볆쏤곉귈ꅃ 돌꣎Lagrange궼볆꒧ꡄ룑 ꖻ론꒤ꅁ녎뒣꣑ꑀ귓슲꧶군뫢Lagrange궼볆끟ꥬ귈꒧ꓨꩫꅃꚹꕾꅁꖻ론꒤ꗧ녎뒣꣑ꑀ귓Lagrange궼볆꒧ꑗꅂꑕ곉궭귈ꪺ군뫢ꓨꩫꅃꣃꕂ녎끑뷗ꚹ궼볆꒧ꑗꅂꑕ곉궭뭐ꗘ볐꣧볆뚡꒧쏶ꭙꅝKlein et al., 1990ꅞꅃ ꅝ1ꅞ?Lagrange궼볆끟ꥬ귈꒧ꡍꥷ 낲ꥷ볒ꮬ꒤ꅁw=w1=w2ꅁLewis(1981)뒣ꕘꑀꪽ놵군뫢ꗘ볐ꚡꅝPꅞ꒧Lagrange궼볆ꪺꓨꩫꅃ꣤룑ꩫ걏녎꒽ꚡꅝꅞ꒤꒧q(l)녡ꑊ꒽ꚡꅝꅞ꒤iꕈꡄ룑ꕘLagrange궼볆귈ꅁ꣤군뫢ꚡꭨ꓀굺꙰ꑕꅇ 1*12(2kd)21ii l=[∑2]−w. ꅝꅞ 2Q2i=1땍ꛓꅁ둎ꑀ꿫꓆꒧볒ꮬꛓꢥꅁw1≠w2ꅃꙝꚹꅁ때ꩫ덺륌ꪽ놵군뫢꒧ꓨꚡ꣓ꡄ룑돌꣎꒧Lagrange궼볆ꅃ꒴ꕩ륂ꗎꑗ굺꒧ꓨꩫꡄ룑Lagrange궼볆ꑗꅂꑕ궭꒧귈ꅃ ꅝ2ꅞ?Lagrange궼볆꒧ꑗꅂꑕ곉귈꒧ꡄ꣺ 낲덝볒ꮬ꒧꯹ꚳꚨꖻ결w1≤w2꒧ꮬ멁ꅁꭨ뻚꒽ꚡꅝꅞꥷ롱ꥷ롱궼볆꒧ꑗꅂꑕ곉궭꒧귈λL뭐λU결ꅇ 22
112(2kd)2ii21 lL=[∑]−w2, ꅝꅞ 2i=1Q2112(2kd)2l=∑ii21 U[]−w1. ꅝꅞ 2i=1Q2Ꙣꡄ룑ꕘꑀ닕끟ꥬ꒧Lagrange궼볆꒧ꑗꅂꑕ곉귈꒧ꯡꅁꕩ륂ꗎ궼볆ꑗꅂꑕ곉궭귈띪둍ꓨꚡꅁ꣓셙ꑰ궼볆귈ꑗꅂꑕ곉궭ꅁꕈ륇꫱ꕘꑀ돌꣎Lagrange궼볆꒧귈ꅃꙝꚹꅁ껚뻚꒽ꚡꅝꅞꅂꅝꅞ뭐ꅝꅞꅁꕩꕈ땯뉻꣬Lagrange궼볆뭐꯹ꚳꚨꖻ꣧볆꒧뚡ꪺ쏶ꭙꅃ꧒ꕈꅁꚹ덂ꗽꥷ롱l=h(w)ꅁꗧꝙLagrangei궼볆결꯹ꚳꚨꖻ꒧꣧볆ꅃ꧶ꢥ꒧ꅁ굙ꚹ덂ꕏ꯹ꚳꚨꖻ(w)결Lagrange궼볆꣧볆ꅁꝙw=g(l)ꅁꛓg(l)ꕩꥷ롱꙰ꑕꅇ ii2kd(w+2l) w=g(l)=iij−2l, j=3-i. ꅝꅞ i11[Q(w+2l)2−(2kd)22]jjjꙢ꒽ꚡꅝꅞ볆꒤ꅁ낲ꥷl>−wꅁ덺륌꣧볆gꅁ녯ꕈꯘꗟji2h(i=1, 2)ꅁꕂh결ꑀ쑙껦뮼듮ꅂꖿ맪볆꒧ꕙ꣧볆ꅃLagrange궼볆?결꯹ꚳꚨiiꖻw꒧꣧볆ꅁꭨ돌꣎꒧Lagrange궼볆녎ꕘ뉻Ꙣh(i=1, 2)곛떥꒧껉ꅁꝙ결il*=h1(w1)=h2(w2)ꅃ껚뻚ꚹ꒽ꚡꅁꕩꕈ싇ꗑ꯹ꚳꚨꖻ꒧엜냊꣓ꯘꗟh1(w1)뭐h2(w2)꒧뚡ꪺ쏶ꭙꅃ맏ꕩ둹굺ꕘ덯쏶ꭙꅁꛓh1(w1)뭐h2(w2)쏶ꭙ꒧늣ꗍꅁ걏덺륌h1(w1)꣧볆꒤ꗑw2엜냊꣬w1ꕈh2(w2)꣧볆꒤ꗑw1엜냊꣬w2꒧륌땻꣓샲녯ꅃꙢ맏꒤ꓴꖭ뙢결ꚨꖻ꣧볆ꛓꮫꪽ뙢결맯삳꒧Lagrange궼볆ꅆꛓ셡깹볐lL결l=h1(w)ꚱ뵵Ꙣ[w2,h1(w2)]꒧꓁쉉ꛜꮫꪽ뵵결w=w1꒧ꗦ쉉ꅃꛓ셡깹볐lUꭨ걏꣺[w′′,h1(w′′)]뭐[w′,h(w′1)]꒧뵵걱뭐ꮫꪽ뵵결w=w1 ꒧ꗦ쉉ꅃꛓw′뭐w′′꒧귈걏ꗑw′=g1(lU)뭐w′′=g1(lL)ꛓ녯ꅁꙝꛓlL뭐lU걏결떽ꑗꅂꑕ곉꒧륌땻ꅁꕂ 23
lL=lL+∇h1(w2)(w1−w2), ꅝꅞ lU=lL+(lU−lL)[(w′′−w)w′′1−w′]. ꅝꅞ ꛓ∇h1(w2)걏ꗑh1(w)Ꙣw2껉꒧뇗뉶ꅃ lU h l2(w) U l* h1(w) lL lL w′′w ′ ww1 2 맏 ꯹ꚳꚨꖻ꣧볆꒧ꚱ뵵ꅝKlein et al., 1990ꅞ ꥷ뉺ꕼꅇ럭ꗘ볐ꚡ꒧돌꣎Lagrange궼볆꒧l∗>0껉ꅁꭨl∗꒧ꑗꅂꑕ곉걏ꗑlL 뭐lU꣓ꡍꥷ꒧ꅃ 쏒ꧺꅇMaloneyꅝ1987ꅞ뒣ꕘh(i=1, 2)ꅁꕂ꣤결ꑀ쑙껦뮼듮ꅂꖿꕙ맪볆꣧볆ꅃi냲꧳ꕙ맪볆꣧볆꒧꽓꧊ꅁ꣤ꩁ녱 * l=h1(w1)≥h1(w2)+∇h1(w2)(w1−w2) 24
=lL+∇h1(w2)(w1−w2), =λL, ꅝꅞ ꣤ꕩꗑꚹꯘꗟꑕ궭귈ꅁꛓꑗ궭귈꒧ꯘꗟꗧꗑꕙ꣧볆꒧꽓꧊ꡄ녯ꅇ h1[a(w′−w′′)+w′′]≤a[h(w′)−h(w′′11)]+hc′′1()=a(lU−lL)+lL. 맯꧳ꗴꑀa∈(0,1)ꅁꕂa=(w′′−w1)(w1−w′),ꭨ *(′′−) =h(wwwl)≤111(lU−lL)+lwL (1−w′)=lU. ꅝꅞ ꙝꛓꯘꗟ꣤ꑗ궭귈ꅃꗧ떽ꑆꑗꅂꑕ곉궭귈ꪺꡄꩫꅃꚹꗧ뒣꣑ꑆ맯돌꣎Lagrange궼볆ꡄ룑꒧뙩ꅃꙝꚹꅁ꒽ꚡꅝꅞ뭐ꅝꅞꕩ삳ꗎ꧳Ꙩ닕볆뻚ꅁꪽ꣬ꑗꅂꑕ곉꒧귈륇꫱꧳ꑀ쉉ꅁꭨ덯ꑀ쉉ꝙ결돌꣎꒧Lagrange궼볆ꅃ ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧귗ꖿ ꑗ굺꒧꓀꩒낲ꥷ볒ꮬ엜볆dꅝ믝ꡄ뙱ꅞ결ꑀꖭꞡ(ꥷ)꒧믝ꡄ뙱ꅃ땍ꛓ맪믚ꑗꙢ과ꗦ꧶ꖫ돵ꚨꗦ뙱걏ꝥ뉻ꑀ뫘Uꩩ냊꒧꽓꧊ꅁ꙰맏꧒ꗜꅃꗑ맏ꅁꕩꕈ땯뉻뙧ꑀꛜ뙧꒭Ꙣꕸꕟ과ꖭꞡꚨꗦ뙱꒧엜꓆ꅃꙢ맏꒤엣ꗜ뙽뵌꣬9ꅇ15꓀껉꣤ꖭꞡꚨꗦ뙱곹결과ꑔꑤ롕ꖪꕫꅁ꣤ꯡꖭꞡꚨꗦ뙱ꝥ뉻ꑀ뗤셙꒧ꪬ멁ꅁꪽ꣬11ꅇ00ꖪꕫꖭꞡꚨꗦ뙱ꥬꚳꑗ뒭ꪺ쇍뛕ꅃꛓꯡꑀꪽ꣬12ꅇ00낱ꓮꗦ꧶꒧ꭥ과꒧ꖭꞡꚨꗦ뙱ꞡ결꯹쓲뗤셙꒧놡ꅃꛓꑕ14ꅇ00ꗦ꧶궫띳뙽ꥬꛜꚬ뵌ꭥ듁ꅁꖭꞡꚨꗦ뙱ꗧ결ꑀ꯹쓲뗤셙꒧ꪬ멁ꅁꑀꪽ꣬ꚬ뵌껉ꚨꗦꑾꑓꑪ둔ꑗ뒭ꅃꙝꚹꅁꙢ과ꗦ꧶ꖫ돵ꗾꓩ꒧ꗦ꧶뙱ꝥ뉻ꋣꩩ냊꒧꽓꧊ꅃꛓꚹꑀ꽓꧊ꗧꕘ뉻Ꙣ뙧꒻꒧ꗦ꧶ꓩ꒧꒤ꅁ꙰맏꧒ꗜꅃ 뙧ꑀꛜ뙧꒭ꕸꕟ믈ꛦ뚡과ꗦ꧶ꖫ돵ꡃ15 ꓀쓁ꖭꞡꚨꗦ뙱ꪺ엜늧볆ꅁ꙰맏꧒ꗜꅁ엣ꗜ뙽뵌ꛜ9ꅇ15 ꪺꖭꞡꚨꗦ뙱꒧엜늧볆결돌ꑪꅁ꣤ꯡ덶몥 25
뗤셙ꅃꑕ14ꅇ00 ꯬둟ꗦ꧶ꯡꛜ14ꅇ15 ꪺꖭꞡꚨꗦ뙱꒧엜늧볆ꑝꚳꑗ꒧쇍뛕ꅁ꣤ꯡꛜꑕꚬ뵌ꭥꑝ뎣뗤셙ꪺ놡ꅃ땍ꛓꚬ뵌ꪺꖭꞡꚨꗦ뙱꒧엜늧볆ꅁ걏ꗾꓑ돌ꑪꅃꗾꓩ쏾U ꮬꅃꙐ볋ꪺꅁ뙧꒻ꕾ맴ꖭꞡꚨꗦ뙱꒧엜늧볆ꪺ꓀ꝇ놡ꅁ꙰맏꧒ꗜꅃꗧ쏾꧳뙧ꑀꛜ뙧꒭꒧꓀ꝇꮬ멁ꅁꚨꑀUꩩ냊꒧ꮬ멁ꅃ ꑀ꿫놡ꩰꅁ냪ꕾ뛗ꖫ돵꒣뷗걏돦ꑀꕾ맴ꚨꗦ뙱뛗뉶엜냊뉶떴맯귈ꪺꖭꞡ볆엜늧볆ꅃꙢ뙽뵌ꚬ뵌꙳Ꙣꚳ룻ꑪ둔ꯗꪺꩩ냊ꅁ뭐ꑀ꿫냪믚뿄ꖫ돵ꪺꩩ냊꽓꧊곛닅ꅝChan, 2000ꅆChakrabarti, 2000ꅞꅃꙝꚹꅁꖻꓥ링룕신뒫ꙕꕾ맴ꚨꗦ꧶뙱결ꙕꕾ뛗ꥷ믈ꛦ꒧믝ꡄ뙱ꅁꕂꕛꕈ귗NIR-EOQ꙳뙱볒ꮬꅃꣃꝑꗎAR-GARCH ꕈAR-TGARCH볒ꮬꅝBaillie and Bollerslev, 1989ꅆWest and Cho,1995ꅆꓗꑬ랽ꅁ2002ꅆ빇ꓑ뱷ꅁ2002ꅞꅁ륷듺ꙕꕾ뛗ꥷ믈ꛦ꒧믝ꡄ뙱ꅁꕈ귗NIR-EOQ꙳뙱볒ꮬ꒤꒧믝ꡄ뙱엜볆ꅃꑕ론녎둎AR-GARCHꕈAR-TGARCH볒ꮬ꒧꽓꧊ꕈ볒ꮬ꒧ꯘ멣ꓨꚡ낵ꑀ뮡ꧺꅃ AR-GARCH믝ꡄ뙱륷듺볒ꮬ꒧ꯘ멣 ꗑ꧳ꙕꕾ뛗ꥷ믈ꛦꕾ맴꒧믝ꡄ뙱샀ꕾ맴ꗦ꧶뙱ꝥꑀꟀ뫝ꭰ(꙰ꕢ쏤Uꮬ)꒧꽓뱸ꅁꙝꛓꕩꕈ륂ꗎAR-GARCHꕈAR-TGARCH볒ꮬ꣓뙩ꛦ믝ꡄ뙱륷듺ꅃ럭닎군룪껆ꕩ꿠ꙝ껉뚡엜냊ꛓ늣ꗍ엜꓆ꅁꛓ뻉교볒ꮬꙢ냑볆뇀꛴껉늣ꗍꑀ뗪낲끪쉫꒧뉻뙈ꅝSpurious RegressionꅞꅝGranger and Newbold, 1974ꅞꅃꙝꚹꅁꙢ뙩ꛦ볒ꮬꯘ멣꒧ꭥꅁꖲ뚷ꗽ뙩ꛦ돦껚샋ꥷꅁꕈ뵔뭻꧒뇽뙩ꛦ꓀꩒꒧엜볆걏ꝟ결ꑀꥷ멁꒧Ꟈꙃꅃꗑ꧳돦껚샋ꥷ걏끷맯껉뚡Ꟈꙃ쁈뻷륌땻꒧ꥷ멁꧊뙩ꛦ샋엧ꪺꓨꩫꅃ꣤ꚸꅁꖲ뚷끷맯AR-GARCH볒ꮬ꣓뙩ꛦARCH LM 샋ꥷꕈ뵔뭻룓볒ꮬ걏ꝟ꣣ꚳ껄뉶꧊ꅃꙝꚹꅁꕈꑕ녎끷맯돦껚샋ꥷꅂAR-GARCH뭐AR-TGARCH볒ꮬARCH LM볒ꮬ꒧륷듺ꓨꩫꓱ룻뙩ꛦ끑뷗ꅃ 26
5045403530252015105009:0009:30010:0010:3011:0011:3012:0012:3013:013:3014:0014:3015:0015:3016:00 맏 2000-2001꙾뚡뙧ꑀꛜ뙧꒭꒧ꕾ뛗ꚨꗦ뙱꒧ꖭꞡ볆ꅝꕸꕟꕾ뛗롧샙꒽ꕱꅞ 181614121086420009:0009:1509:3009:4511:4512:0012:1512:3010:0010:1510:3010:4511:0011:1511:3 맏 2000-2001꙾뚡뙧꒻꒧ꕾ뛗ꚨꗦ뙱ꖭꞡ볆ꅝꕸꕟꕾ뛗롧샙꒽ꕱꅞ 27
900800700600500400300200100009:0009:3010:0010:3011:0011:3012:0012:3013:0013:3014:0014:3015:0015:3016:00 맏 2000-2001꙾뚡뙧ꑀꛜ뙧꒭꒧ꕾ뛗ꚨꗦ뙱꒧ꖭꞡ볆ꅝꕸꕟꕾ뛗롧샙꒽ꕱꅞ 900800700600500400300200100009:0009:1509:3009:4510:0010:1510:3010:4511:0011:1511:3011:4512:0012:1512:30 맏 2000-2001꙾뚡뙧꒻ꕾ뛗ꚨꗦ뙱꒧엜늧볆ꅝꕸꕟꕾ뛗롧샙꒽ꕱꅞ 28
돦껚샋ꥷ ꖻ곣ꡳ녎뇄ꗎAR-GARCH볒ꮬ뭐AR-TGARCH볒ꮬ꣢뚵ꕾ맴믝ꡄ뙱륷듺볒ꮬꅁꣃ끴ꙘRATS륱뢣땻ꚡ꣓뙩ꛦ볒ꮬ냑볆꒧꛴군ꅃꙢ뛇닎군뙱롧샙끪쉫볒ꮬ꒤ꅁꑪ뎣낲덝껉뚡Ꟈꙃ룪껆결ꑀꥷ멁(Stationary)Ꟈꙃꅁꝙ꣤닎군꽓꧊꒣라쁈뗛껉뚡꒧엜냊ꛓ늣ꗍ엜ꅃ땍ꛓ뉻맪ꪬꩰ꒤덜Ꙩ롧샙엜볆ꞡ라쁈뗛껉뚡꒧엜ꅃꙝꚹ라ꥍ껉뚡쇍뛕늣ꗍ녋꓁꒧쏶덳ꅁꗧꝙ덯엜볆꒣걏ꥷ멁Ꟈꙃꅃ굙꣏ꗎꭄꥷ멁꒧Ꟈꙃ꣓뙩ꛦ뛇닎꒧껉뚡Ꟈꙃ끪쉫꓀꩒ꅝ꙰OLS 껉ꅞꅁꭨ륷듺꒧떲ꩇꕩ꿠늣ꗍ Granger and Newbold (1974)꧒뒣ꕘ꒧뗪낲끪쉫ꅝSpurious Regressionꅞ꒧ꙍ쁉ꅁꙝꛓ덹ꚨ꛴군샋ꥷꑗ꒧뭾깴ꅃ Pindyck (1991) 맯ꥷ멁꒧룑쓀결ꅇꅵ볐ꪺ엜볆꒧쁈뻷땻Ꟈꪺ꽓꧊(characteristics)꒣라쁈뗛껉뚡ꛓ엜ꝙ결ꥷ멁ꅃꅶ뒫ꢥ꒧ꅁ꙰ꩇ껉뚡Ꟈꙃ결ꥷ멁ꅁꭨꚹꟇꙃ껉녠라ꚳꙞ꣬꣤ꖭꞡ귈꒧뛉Ꙗꅁꛓ뛈슶뗛ꖭꞡ귈낵엜냊ꅁ걇꣤엜늧볆ꚳꑀ궭ꥷ귈ꅃꛓ럭뢨깴듁뚡뱗ꕛ껉ꅁꛛ곛쏶ꭙ볆라ꑕ궰ꙡꭄ녠Ꟗ덴ꅁ뙚싷뉻Ꙣ뙖뮷꒧륌ꕨ맯뉻Ꙣ꒧뱶암뙖ꑰꅁꖦ꒧끏뻐곛럭ꙡ땵볈ꅁꙝꚹꟇꙃꥷ멁믝닅Ꙙꕈꑕꑔ귓뇸ꗳꅇ ꅝ1ꅞE(x) =E(xm , s≠0, ꅝꅞtt−) =sꅝ2ꅞVar(x)=Var(x)tt−=s2=g, ꅝꅞ sx ꅝ3ꅞCov (x,x−)=Cov (x−,x) . ꅝꅞ ttstjt−j− =gssꛛ녱Granger and Newbold(1974)뒣ꕘ낲꧊끪쉫꒧냝썄ꯡꅁ덂뉺ꭄꥷ멁엜볆뚡쏶ꭙ꒧곣ꡳꓨꩫ둎ꑀꪽꝸ쉚뗛롧샙뻇ꅁꙝꛓ끪쉫꓀꩒륹껉ꖢꕨ빡ꅃNelson and Plosser(1982)맯과냪룪껆뙩ꛦ돦껚샋ꥷꅁ땯뉻셠엩롧샙엜볆뒶륍꙳Ꙣ돦껚꒧뉻뙈ꅁꚹꯡ뵔뭻엜볆걏ꝟ꙳Ꙣ돦껚ꅁꭋꚨ결ꑪ뎡꓀롧샙꓀꩒ꭥ꒣ꕩ꿊꒧땻Ꟈꅃ굙ꑀ엜볆믝롧륌dꚸ깴꓀ꥬ륆ꥷ멁ꅁꭨ뫙ꚹ엜볆결ꑀ뻣Ꙙ꿅ꚸ결d꒧Ꟈꙃꅁꫭꗜ결I(d)ꅃ굙ꑀ엜볆롧륌ꑀꚸ깴꓀ꝙ륆ꥷ멁ꅁꭨꚹ엜볆결 29
I(1)Ꟈꙃꅁ닅Ꙙꑀ귓돦껚륌땻(Unit-root Process)3ꅃ돦껚샋ꥷꑄ걏끷맯Ꟈꙃ쁈뻷륌땻꒧ꥷ멁꧊뙩ꛦ샋엧꒧ꓨꩫꅁ걇뙩ꛦ덜Ꙩ군뙱볒ꮬꭥꅁ삳ꗽ맯돦ꑀ엜볆뙩ꛦ돦껚샋ꥷꅃꖻꓥ꒤녎ꕈDickey and Fuller (1981) 뒣ꕘ꒧쉘뱗ꮬ돦껚샋ꥷ(Augmented Dickey-FullerTestꅆADF) Phillips and Perron (1988) ꒧때ꗀ볆샋ꥷꩫꅝPPꅞꑇ뫘샋ꥷꓨꩫ맯엜볆뙩ꛦ돦껚샋ꥷꅁꕈꑕ꓀ꝏ꒶닐덯ꑇ뫘ꓨꩫꅃ ADF샋ꥷꩫ Dickey and Fuller(1981)돌ꚭ뒣ꕘ샋ꥷ돦껚꒧ꓨꩫꅁꑀ꿫뫙결DF 샋ꥷꩫꅁꗑ꧳DF 샋ꥷꩫꖼꕛꑊ삳엜볆꒧뢨깴뚵ꅁ꙰ꚹ녎라꣏끪쉫득깴뚵꙳Ꙣꛛ곛쏶꒧뉻뙈ꅁ끪쉫뭾깴뚵녎때ꩫ결ꑀꗕ뺸궵(white noise)ꅃ끪쉫ꚡ꒤ꕛꑊ삳엜볆꒧뢨깴뚵ꅁꝙ결ADF 샋ꥷꩫꅃꙢADF ꩫ꒤ꅁꕩꝑꗎ꒣ꝴ쇍뛕뚵뭐ꝴ쇍뛕뚵ꅝyꅞ꣢끪쉫ꚡ꣓샋ꥷꅃꭨ샋ꥷ걙ꑀ엜볆x걏ꝟ결I(0)껉ꅁ끪쉫ꚡt덝ꥷ결ꅇ p ∆x=a0+a1x−1+∑b∆xe, ꅝꅞttit−+ iti=1p ∆x=a0+a1x−+ay+∑b∆xe, ꅝꅞ tt12it−+iti=1꣤꒤ p 결뢨ꯡ듁볆ꅃ 굙a1엣뗛ꙡ늧꧳륳ꅁꭨꕩ떴돦껚ꭄꥷ멁꒧뗪때낲덝ꅆꝟꭨx녎꒣t걏ꑀ귓 I(0)Ꟈꙃꅃ결샋엧엜볆꒧뻣Ꙙ꿅ꚸ걏ꝟ결 I(1)Ꟈꙃꅁꭨ녎엜볆ꙁ꣺ꑀꚸ깴꓀ꯡ녯꣬ꅇ p2 ∆=a∆x−+∑b∆2x11xe, ꅝꅞ ttit−+iti=1p ∆2x=a+a∆xb201−1+∑∆xe. ꅝꅞ ttit−+iti=1 3 굙ꑀ엜볆믝롧륌dꚸ깴꓀ꥬ륆ꥷ멁ꅁꭨ뫙ꚹ엜볆결ꑀ뻣Ꙙ꿅ꚸ결d꒧Ꟈꙃꅁꫭꗜ결I(d)ꅃ굙ꑀ엜볆롧륌ꑀꚸ깴꓀ꝙ륆ꥷ멁ꅁꭨꚹ엜볆결I(1)Ꟈꙃꅁ닅Ꙙꑀ귓돦껚륌땻(Unit-root Process)ꅃ 30
굙a1 엣뗛ꙡ늧꧳륳ꅁꭨx결I(1)Ꟈꙃꅃꙝꚹ샋ꥷ닎군귈곛Ꙑ꧳ꑀ꿫꒧tt샋ꥷ닎군뙱ꅁ꣤꓀끴늧꧳t꓀끴ꅁ걇셻곉귈꒣Ꙑ꧳ꑀ꿫꒧t샋ꥷ닎군뙱ꅃ PP샋ꥷꩫ ADF 샋ꥷꩫꅁ쇶ꑷꛒ뱻ꑆꟇꙃ곛쏶ꪺꕩ꿠꧊ꅁ꒴낲덝득깴뚵결곛Ꙑ뽗ꗟ꓀끴(Identically Independent Distributionꅆiid)ꅁꝙ낲덝ꙕ듁엜늧볆꣣믴ꑀ꧊ꅃPP샋ꥷꩫ끷맯ADF 샋ꥷ뙩ꛦ귗ꖿꅁ꒹덜끪쉫득깴뚵꣣Ꟈꙃ곛쏶쁈껉뚡엜늧꒧뇸ꗳ엜늧꧊ꅃPP 샋ꥷ뇄ꗎ꒤ꖡ랥궭ꥷ뉺ꪺ뉺뷗꣓꓀꩒ꅁ득깴뚵ꛒ뱻ꛛ곛쏶ꅂ늧뷨꧊ꅁ꣏꣤결ꑀꗕ뺸궵ꅁ떲ꩇ쏒ꧺ꣤샋ꥷ닎군뙱ꪺ랥궭꓀끴ꥍDickey and Fuller (1981)ꪺ랥궭꓀끴곛Ꙑꅃ ꛒ뱻엜볆꒧ꛛ끪쉫볒ꮬ꙰ꑕꅇ **x* x=m+att−1+e, ꅝꅞ t x~~y=m+b(t−+a~)x−1+e, ꅝꅞ ttt2꒽ꚡꅝꅞꕵꕝꝴ녠볆뚵ꅝm*ꅞꅁꛓ꒽ꚡ()ꕝꝴ녠볆뚵ꅝm~ꅞ뭐쇍뛕뚵ꅝyꅞꅃꭥꚡ꒤꣣돦껚ꪺ뗪때낲덝결ꅇH1*0:a=1, H2*0:a=1m*,=0ꅁꯡꚡ결H1~0:a=1, H2~~0:a=1,b=0ꕈH3a~~0:=1,b=0m~,=0ꅃꚹ껉샋ꥷ닎군뙱결Z(ta~),Z(Φ, Z(Φ3)ꅃ t2)1 Z322(ta~)=(susy) ta~ [ 43D21−yxsy1 ] ( sy1−s ), ꅝꅞ tuZ(Φ)=22222~62( susy1 ) Φ2−( 12sy1 ) ( sy1−su ) [ y (a−1)−( y48Dx ) ] ꅝꅞ 22 ( sy1−su ), Φ=2~2−12~21( s ) [ys0−ys] , Φ=3~2−12~2 2( s ) [ ys0−ys ], Φ=~2−1~ 3( 222s ) { y [ s0−( x−x−1 ) ] −ys}, t 31
y2 s0=y−1∑2(y−y, tt−1)t=1ZΦ=22()2222~63 ( susy1 ) Φ3− ( 1sy1 ) ( sy1−su ) [ y ( a−1 )-( y48Dx ) ] ꅝꅞ 22 ( sy1−su ).꣤꒤ꅁta~결뛇닎꒧t샋ꥷ닎군뙱ꅁΦ1ꅂΦ2ꅂΦ3결 F 샋ꥷꅁ2s0결꒽ꚡꅝꅞ뭐ꅝꅞꙢ꒣Ꙑ뗪때낲덝ꑕ꒧득깴엜늧볆결ꑀ교꛴군ꚡꅁ~2s결꒽ꚡꅝꅞ뭐ꅝꅞ꒧돌ꑰꖭꓨ득깴엜늧볆ꅁDx결꽸(X′X)꒧ꛦꙃ귈ꅁꛓ yX 결ꑀy*3꒧꽸끽ꅃꚹꕾꅁ2sy1결s2=12li→my−E(u)꒧ꑀ교꧊꛴군ꚡꅃ T∞∑jj=1덺륌RATS땻ꚡ꒧꒺ꯘ꒽ꚡꅁꕩꡄ녯ꑗ굺꒧ADF뭐PP샋ꥷꩫ꒧닎군뙱ꅁꣃ덺륌룓닎군뙱샋ꥷ꣤걏ꝟ떴돦껚꒧샋ꥷ AR-GARCH 볒ꮬ ꗑ꧳뛇닎꒧껉뚡Ꟈꙃ볒ꮬꅁ덱녠뎣낲덝Ꙁ엜늧볆꯭ꥷ(Covariance Stationary), 뇸ꗳ엜늧볆ꥷꅁ땍ꛓ맪믚꒧뿄엜볆롧샙엜볆ꅁꑪꙨ꙳Ꙣ뗛엜늧볆늧뷨꒧뉻뙈ꅁ걇Engle (1982)뒣ꕘꑆARCH (Autoregressive Conditional Heteroskedasticity Model)볒ꮬꅁ삳ꗎ꽓ꥷ꓆꒧덝ꥷꅁ꣓볒ꮬ꓆륷듺뇸ꗳ엜늧볆ꅁ엜볆꒧엜늧볆ꅁ걏ꗑ엜볆륌ꕨ꒧귈ꥍꛛ엜볆ꅂꕾꗍ엜볆꧒멣ꚨ꒧꣧볆꣓볒ꮬ꓆ꅃBollerslev (1986)ꭨ뒣ꕘꑆGARCH (Generalized ARCH)꣏덯볒ꮬꟳ뱳꩸꒧꣏ꗎ꧳ꙕ뫘꒧롧샙뻇꓀뻇곬ꑗꅆ꽓ꝏ걏끝냈ꑗ꒧껉뚡Ꟈꙃ꓀꩒ꅁꕩꕈ녱Bollerslev et al.ꅝ1992 ꅂ1994ꅞ, ꧒뒣ꕘ꒧돌꫱꒧뷕걤녯ꪾꅃꙢ둘귓귬ꙝ꒧ꑕꅁ뻇라띑볒ꮬ꓆ꩩ냊꧊륷듺ꩩ냊꧊ꅃꅝ1ꅞ꧒굮꓀꩒꒧뿄룪늣뿯뻜앶꒧믹귈꣣궷쁉꧊ꅁꅝ2ꅞ륷듺꒧ꭈ뿠냏뚡라쁈뗛껉뚡낵엜냊ꅆ꧒ꕈꅁ꙰ꩇ꿠득깴꒧엜늧떹볒ꮬ꓆ꅁ녎ꕩꕈ녯꣬룻뫫뵔꒧ꭈ뿠냏뚡ꅁꅝ3ꅞ꙰ꩇ득깴꒧늧뷨엜늧ꅁ꿠덑덂뉺ꪺ룜ꅁ녎ꕩꕈ녯꣬ꟳꚳ껄뉶꒧꛴군볆ꅃ 32
AR-GARCH 볒ꮬ꒧덝ꥷ ARCH(q)볒ꮬꅁ꣤꒤qꫭꗜARCH볒ꮬ꒧뚥볆쇶땍꿠꺷꺻꣬뿄꧊룪늣믹껦꒧ꛦ결ꅃ꣤ꛛ끪쉫듁볆덱녠ꯜꅁ꒣닅Ꙙ껉뚡Ꟈꙃ볒ꮬ덝ꥷ꧒굮ꡄ꒧냑볆뫫슲ꅝParsimoniousꅞ귬ꭨꅃꙐ껉Ꙣ맪믚꒧삳ꗎꑗꅁARCH(q)볒ꮬ결꣏뇸ꗳ엜늧볆결ꖿꅁꦹꦹ믝굮싇ꝕ곛럭듁볆꒧뵵꧊뮼듮뢨ꯡ듁떲멣ꅃꙝꚹꅁBollerslevꅝ1986ꅞ껚뻚뛇닎ARMA 볒ꮬ꒧ꓨꩫꅁ녎뢨ꯡ듁꒧뇸ꗳ엜늧볆 ht− jꕛꑊARCH 볒ꮬ꒤ꅃ낣꒹덜ꖼ꣓꒧뇸ꗳ엜늧볆꣼륌ꕨ득깴뚵ꖭꓨ꒧뱶암ꕾꅁ쇙ꕝ걁꣼륌ꕨ꒧뇸ꗳ엜늧볆뱶암ꅃꛓGARCHꅝp, qꅞ볒ꮬ결ꅇ Y=X+e, 뇸ꗳꖭꞡ볆ꓨ땻ꚡ ꅝꅞ ttt eΩ−1~N(0,h), tttX=EYΩh=VarYΩ=EY−X2(−1) ,(−1) [(Ω) Ω] tttttttY−1tt−1ttꅝꅞ ꑀ꿫ꕩꫭꚨ m Y=j+∑jY, ꅝ3t0eit−+.37) iti=1ꚹꝙ결뇸ꗳꖭꞡ볆볒ꮬARꅝmꅞꅁ pq h=a+∑20ae−+∑bh−. 뇸ꗳ엜늧볆ꓨ땻ꚡ ꅝꅞ titijtji=1i=1뇸ꗳꖭꞡ볆ꓨ땻ꚡ()ꕩ뱧ꚨꑆ득깴꒧ꕾꗍ엜볆ꅁ h걏껚뻚륌ꕨ꒧룪t끔ꅁ꧒멣ꚨ덯ꑀ듁륷듺엜늧엜볆ꅁꗧ뫙결뇸ꗳ엜늧볆(Conditional Variance)ꅁ뇸ꗳ엜늧볆꒧덝ꥷꅁ꙰뇸ꗳ엜늧볆ꓨ땻ꚡ()꧒ꗜꅁ걏ꑀ귓ꗑꑔ귓뎡ꗷ꧒닕ꚨ꒧꣧볆ꅃ ꅝ1ꅞ?ꖭꞡꅇa0 ꅝ2ꅞ?륌ꕨꩩ냊꒧끔꺧ꅁ걏ꗑ뇸ꗳꖭꞡ볆ꓨ땻ꚡ꒧득깴ꖭꓨ뚵꣓뿅뙱ꅇ2et−1ꅝARCH termꅞ ꅝ3ꅞ?륌ꕨ꒧륷듺엜늧볆ꅇht−1ꅝGARCH termꅞ 33
꣤꒤ a0ꅂb>0 , p 결 ARCH term ꒧뚥ꚸꅁꛓ q 결GARCH term꒧j뚥ꚸꅃ AR-GARCH볒ꮬ꒧꽓꧊ 1. 맯롳뭅꧊꣣ꚳꙮ꒧룑쓀꿠ꑏ 맯꧳룪늣돸륓ꩩ냊롳뭅꧊(Clusters)꣣ꚳꙮ꒧룑쓀꿠ꑏꅃ결꧶꧳셁룑ARCH볒ꮬ꒧꽓꧊ꅃ꙰ꕈ GARCH(1,1) 볒ꮬ결꣒뮡ꧺ꒧:Y=X+eꅁtttqeΩ−1~N(0,hꅁp)=a+a2httt0∑e−+∑bh−ꅁꗑꖻꚡꕩꪾ2et−1ꅁhtitijtjt−1뱗ꕛꞡi=1i=1라꣏녯 h 뱗ꕛꅆ꙰ꕈꓨ땻ꚡ뮡ꧺ꙰ꑕ: t Y=X+e, tttpq =a+∑a2h0e−+∑bh, titijt−ji=1i=1 e−1↑⇒h↑⇒h=Var(eΩ−1). ꅝꅞ ttttt꒽ꚡꅝꅞ꒤뮡ꧺ럭ꭥ듁꒧득깴뱗ꕛ껉녎뻉교득깴ꖭꓨ꒧뱗ꕛꅁꙐ껉ꗧ녡냊뇸ꗳ엜늧볆꒧뱗ꕛꅃꗧꝙꅁꚹ뫘뇸ꗳ엜늧볆꒧덝ꥷꓨꚡ쇴ꝴ뗛럭듁꒧엜냊ꅁ걏꣼꣬ꭥ듁엜냊꒧뱶암ꅁꝙ럭듁늣ꗍꑪ둔ꯗ엜꓆(ꕩ꿠ꚨꙐꙖꙖ)ꅁ녎꛱쁈뗛ꑕ듁룻ꚳꕩ꿠쇍뛕듂Ꙗꑪ둔엜냊ꅁꚹ뭐ARCH쏾ꅃ 2. ꕩ둹굺Ꟁ뫝ꭰ꓀끴ꅃ 3. 볒ꮬ뒣꣑ꩩ냊볒ꮬꚳ꡴닎꒧걛멣ꅃ 4. 쇗뙽뿲멼귈 (뭐ARCHꙐ)ꅇ덂뉺뇸ꗳ엜늧볆껉ꅁꕩꕈ쇗뙽뿲멼귈(뭐ARCHꙐ)ꅃ꙰ꕈGARCH(p,q)뮡ꧺꅇꙝ결 pqh=f(YY,Y)=[a+a2−1,−2....,−0∑e−+∑bh], ttttqitijt−ji=1i=1꣤꒤ei∈1,q]t−맯[ ꞡ결ꑷꪾꅁꙝꚹ꛴군a0ꅁaꅁb꒣교꧳ꚳ뿲멼귈늣ꗍꅃ iij5. 룻ARCH볒ꮬ뫫슲ꅇ뒣꣑ꑀ귓룻ARCH볒ꮬ냑볆뫫슲둹굺ꩩ냊ꓨ땻ꚡꅃ 34
ARCH LM 샋ꥷ뭐 Ljung-Box샋ꥷ Ꙣꞹꚨꑗ굺꒧GARCH 볒ꮬ꒧뮡ꧺꅁꑕꑀꡂꥼꖲ뚷샋ꥷ득깴Ꟈꙃ꒤ꅁ걏ꝟꚳARCH 껄ꩇ꙳Ꙣꅃ꙰ꩇꚳꪺ룜ꅁꫭꗜ볒ꮬ꿊껄뉶꧊ꅁ쇙뚷ꙁ귗ꖿꅃEngle (1982)뒣ꕘꅁARCH LM (Lagrange multiplier) 샋ꥷꅁARCH LM 샋ꥷ걏ꑀ귓ARCH볒ꮬ끪쉫ꚡ꒧쓝샋ꥷꅁ꣤뗪때낲꒧덝ꥷ걏:득깴ꖭꓨꟇꙃ꒧꒤ꖼ꙳Ꙣ낪ꯗ곛쏶ꅁꛓ끪쉫ꓨ땻ꚡ덝ꥷ꙰ꑕ: 2 e=b+b2e++b201−1......−q+, ꅝꅞ ttqentt꣤꒤eꫭꗜ득깴ꅁꛓ꒽ꚡꅝꅞ걏맯득깴꒧ꖭꓨꅁ녠볆득깴ꖭꓨ꒧뢨ꯡ뚵ꅁ꧒Ꝁ꒧끪쉫ꚡꅁꛓEngle꒧ LM 샋ꥷ뙱(ꑓ뫙결ARCH LM 닎군뙱) = Number of Observation × R-squared StatisticꅃARCH LM샋ꥷꙢꚳ궭꒧볋ꖻ궭꣮ꑕꅁ맯꧳뗪때낲덝뵔꓁닎군뙱꒧꓀끴ꅁ쇶땍때ꩫ녯ꪾꅃ걏ꅁꙢꑀ꿫꒧놡ꑕꅁARCH LM 닎군뙱ꅁ걏ꑀ귓꫱꧳ꕤꓨ꒧꓀끴ꅃꖦꕩꕈꗎ꣓Ꝁ볒ꮬ득깴ꖭꓨ꒧ARCH 껄ꩇ샋ꥷꅃ 끝냈껉뚡Ꟈꙃ룪껆Ꙣ뙩ꛦ볒ꮬ륷듺ꭥꅁ믝굮끷맯룪껆득깴ꖭꓨ뙩ꛦ곛쏶 ꧊샋ꥷꅁꗧꝙ꙰ꑕ꒧낲뮡ꅇ H0:r1=r2=....=0 H ꅝꅞ 1:r≠0,1≤j≤n,j꣤꒤rꫭꗜ결득깴ꖭꓨ꒧곛쏶ꭙ볆ꅁꛓ꣤샋ꥷꩫ걏뇄Ljung-Boxꅝ1978ꅞ꒧Qꅝmꅞ닎군ꩫ꣤ꚡꑬ꙰ꑕ꧒ꗜꅇ mr2 Q(mˆ)=T(T+2)∑i, ꅝꅞ =1T−iiꕂm≈ln(T)ꅁ룻꣣ꚳ껄뉶ꅃ꣤꒤ m 뭐 A ꓀ꝏ결몥꫱ꕤꓨ꓀끴꒧ꛛꗑꯗꅁꛓ T 결볋ꖻ귓볆ꅁꗧꝙ Qmx2 ()~m, ꅝꅞ 35
ꛓ꧒녯꒧ꕤꓨ닎군뙱ꅁꕩꗎꕈꡍꥷ볒ꮬ꒧득깴ꖭꓨ걏ꝟ꣣곛쏶꧊ꅃ AR-GARCH 볒ꮬ꒧꛴군 GARCH(p, q)볒ꮬꕩꕝꝴ덜Ꙩ꒧냊멁떲멣ꅁ맪쏒곣ꡳꙨꯘ쒳뇄ꗎGARCH(1,1)꣓낵결뇸ꗳ엜늧볒ꮬꅁ꙰Bollerslevꅝ1986ꅞEngleꅝ1982ꅞꅃ ꙢAR-GARCH 볒ꮬ꒤ꅁ득깴뚵ꛛ곛쏶껉ꅁ굙ꕈOLS ꧒꛴군꒧냑볆룻꒣꣣ꚳ껄뉶꧊ꅃꙝꚹꅁAR-GARCH 볒ꮬꞡ뇄ꗎ돌ꑪ랧ꩫꅝMaximum- Likelihood Methodꅞ뙩ꛦ꛴군ꅃb 뭐 h 결냑볆ꅁT 결볋ꖻ꒧왛맮귈귓볆ꅁtꛓGARCH볒ꮬ꒧맯볆랧꣧볆결ꅇ T logL=−(T2) ln(2pi)lnh−(1 h)YXt2t∑(−), ꅝꅞ 2ttt=1뇄ꗎ싐꛴군면뫢ꩫ랥ꑪ꓆맯볆랧꣧볆꣓ꡄ꣺냑볆꒧꛴군귈ꅁꛓꚹꑀ꛴군귈꒧군뫢륌땻녎덺륌RATS땻ꚡ꣓뙩ꛦ뇀꛴ꅃ AR-GARCH 볒ꮬ꒧륷듺 AR-GARCH 볒ꮬ꒧륷듺ꚡ꙰ꑕꅇ Yˆ=j+jYˆ++j−qe2−−qe2++−....Yˆ+−ˆ1+−1...ˆ011..titiptiptiqt+i−q+d ꅝꅞ ꝑꗎ샀Ꙙ꒧볆뻇볒ꮬꅁꡄ룑 Yt+1ꅁt 뫙결륷듺끟쉉ꅁ i 뫙결Ꙗꭥ륷듺듁볆꒧껉뚡ꅁ굙 i=1 ꝙ결Ꙗꭥ륷듺ꑀ듁ꛓ꣤볒ꮬ꙰ꑕꅇ Yˆ=j+jYˆ++j−qe2−−qe2+01....Yˆ+ˆ1−1.ˆ1...+1, ꅝꅞttptptqt−q+d ꣃ껚뻚륌ꕨ꒧룪껆ꅝꕝꝴ륷듺끟쉉ꅞꅁꝑꗎꑕ굺쏶ꭙꚡꅁꡄ룑꒧뇸ꗳ듁뇦귈결ꅇ Yˆ(i), i>0E (Y+)=, 뭐 ꅝꅞ tiYˆ+,i ≤0ti 36
0, i>0 E(e+)=. ꅝꅞ tieˆ+, i≤0ti껚뻚ꑗ굺꒽ꚡꅝꅞ뭐ꅝꅞꕩꪾꑕꑀ듁꒧륷듺귈Y깴뚵t+뭐왛맮득ieꑄ걏덺륌ꭥ듁꒧왛듺귈꧒군뫢ꡄ녯ꅃꙝꚹꅁ껚뻚ꚹꑀ덗ꭨꅁꖻ곣ꡳ녎륂t+iꗎRATS땻ꚡꡄ녯냑볆꛴군귈뭐왛맮득깴뚵 et−1,i≤0ꅁꕈ군뫢ꑕꑀ귓왛듺귈 Y꒧륷듺귈∧Y(l)ꅃ놵뗛ꅁꝑꗎꑗ굺ꡂ왊꒧뇸ꗳ듁뇦귈녎ꕩ뮼끪늣ꗍꑀꟇꙃt+ i꒧륷듺귈ꅃ AR-TGARCH볒ꮬ AR-TGARCH꒧볒ꮬꑄ걏ꝑꗎꭥꑀ듁득깴Ꟈꙃe−1ꖿ굴뢹꓀곉쉉ꅵ0ꅶ럭t쉥귈ꅁ녎GARCH볒ꮬ뎡꓀꓀ꚨ꣢뇸ꭄ뵵꧊GARCH볒ꮬꅁꗎꕈ룉꺻돸륓Ꟈꙃꭄ맯뫙뉻뙈ꅁ꿷녎곣ꡳ볒ꮬ뇔굺꙰ꑕꅇ Y=X+e ttt, eΩ−N( h)tt1~0, t , X=E(YΩ) ,h=Var(YΩ) =E [(Y−X2−1 t−1) Ω] ꅝꅞ tttttttt−1, ꑀ꿫ꕩꫭꚨ m Y=j0+∑jY−+e, ꅝꅞ tititi=1ꚹ결ꖭꞡ볆ꓨ땻ꚡAR(m) pqh=a∑a210+1e−+∑b1h− I(e0) titijtjt−1≤ i=1i=1 pq+(a+∑a2202e−+∑b2h−) I(e−1>0), ꅝꅞ itijtjti=1i=1 결 37
pqaae210+∑1−+∑b1h−, I(e0itijtjt−1≤)h=i=1i=1tpq (a+a)+∑+21020(a1a2) e−+∑(b1+b2)h−, I(e>). ꅝꅞiitijjtjt−10i=1i=1ꚹ결 Threshold GARCHꅃ ꒽ꚡꅝꅞ걏ꗎꕈ녎ꑀ귓ꭄ뵵꧊GARCH볒ꮬꅁ쉥엜볆꓀ꚨ꣢귓ꭄ뵵꧊볒ꮬGARCH볒ꮬꅃꙢ꓀꩒껉ꅁ궺ꗽꕈARMA볒ꮬ끴빁룪껆ꅁꣃ샋뗸꣤득깴꣣ꚳARCH껄ꩇꭨꙁꕈThreshold GARCH꣓덂뉺ARCH껄ꩇ득깴Ꟈꙃꭄ맯뫙뉻뙈ꅁꭨ돌닗볒ꮬ뫙결AR-TGARCH볒ꮬꅃ ꖻ볒ꮬ낣꣣ꚳGARCH볒ꮬ꒧꧊뷨ꕾꅁꕴꕾꚳꑕꙃ꯹꧊ ꅝ1ꅞ?쉥귈꒣Ꙑ둹뇸ꗳ엜늧볆ꅇ볒ꮬ꒤ꕈARMA(m, n)볒ꚡ둹굺룪껆Ꟈꙃ꣤ꑺ쉚뚵꒧쏶ꭙꅁꛓꕈ쉥꒣Ꙑꭨ뇄ꗎ꒣ꙐGARCH(p, q)ꕨ꣨릺ꕘꑺ쉚뚵ꖭꓨ꒧쏶ꭙꅃ ꅝ2ꅞ?ꑺ쉚뚵엜냊ꓨꙖ꒣Ꙑ맯ꩩ냊꒧뱶암땻ꯗ라꒣ꑀ볋ꅇꑺ쉚뚵엜냊맯ꩩ냊꒧뱶암ꅁ굙ꝑꗎ볆뻇ꚡ꣓ꫭꗜꝙ결∂h∂e−1ꅁꭨ룓귈엜냊ꑪꑰ라꣼ꑺtt쉚뚵ꓨꙖ꒣Ꙑꛓꚳ깴늧ꅃ ꅝ3ꅞ?Implied Volatility라쁈뗛ꑺ쉚뚵엜냊ꓨꙖ꒣Ꙑꛓ엜ꅃ ꓱ룻륷듺셚껄꒧ꓨꩫ ꖻꓥꝑꗎꑔ뫘꒣Ꙑ군뙱볒ꮬ꣓륷듺ꕾ맴ꗦ꧶뙱ꅁꛓ맯꒣Ꙑ볒ꮬ꒧륷듺꿠ꑏꅁꖲ뚷ꝑꗎ뿅뙱럇ꭨꕛꕈꓱ룻ꅁꕈꑕ꓀ꝏ꒶닐ꖻꓥ녎뇄ꛦ꒧ꑔ뫘뿅뙱ꑵ꣣ꅇ떴맯ꖭꞡ낾깴(Mean Absolute DeviationꅆMAD)ꅂꞡꓨ뭾깴(Root Mean Square ErrorꅆRMSE)뭐떴맯ꖭꞡꛊ꓀ꓱ뭾깴(Mean Absolute Percentage ErrorꅆMAPE)ꅃ 38
ꅝ1ꅞ?맯ꖭꞡ낾깴(MAD) MAD 군뫢ꓨꚡ결ꅇ n∑Y−Yˆtt MAD=t=1. ꅝꅞ n럭꓀꩒꒧볆ꙃ꣣곛Ꙑ꒧돦ꛬ껉ꅁMAD 결ꑀ뫘ꚳ껄꒧낾깴뿅뙱ꑵ꣣ꅃMAD 룻ꖭꞡ뭾깴결쁵꒧ꙡꓨꙢ꧳ꅇꖭꞡ뭾깴뿅뙱볆ꙃ륷듺귈뭐꽵맪귈꒧뚡꒧곛쏶꧊륷듺귈뭐꽵맪귈꒧뚡걏ꖿꙖ쏶ꭙ굴Ꙗ쏶ꭙꅃꖭꞡ뭾깴꒧귈꧶꣼꣢랥뫝귈꒧뱶암ꅁꝙ볒ꮬ꒧ꖭꞡ뭾깴ꑪꑰꣃ꒣꿠ꕎꫭ볒ꮬ륷듺꿠ꑏ꒧쁵Ꙉꅃ땍ꛓMAD 걏롧륌떴맯귈륂뫢ꅁ걇MAD 귈꒧ꑪꑰꕩꗎꕈ뗻꛴볒ꮬ륷듺귈뭐꽵맪귈꒧깴뙚ꅃ ꅝ2ꅞ?ꞡꓨ뭾깴(RMSE) RMSE 군뫢ꓨꚡ결ꅇ n∑(Y−Yˆ2)ttRMSE=t=1 . ꅝꅞ n RMSEꫭꗜ볒ꮬ륷듺귈맯꽵맪귈꒧득깴엜늧볆꒧뙽ꖭꓨ귈ꅁꚹ귈ꕩꫭꗜ볒ꮬ륷듺꿠ꑏ꒧ꙮ썡ꕂ맯꧳ꡃ귓륷듺뭾깴귈떹꒩꒣Ꙑ꒧ꖭꓨꕛ앶ꓨꚡꅁ꙰ꚹꕩ녯꣬룻결뫫뵔꒧ꓱ룻냲슦ꅃ ꅝ3ꅞ?떴맯ꖭꞡꛊ꓀ꓱ뭾깴(MAPE) MAPE 군뫢ꓨꚡ결ꅇ n∑Y−Yˆtt=1 MAPEYt=t. ꅝꅞ nMAD 쇶땍롧륌떴맯귈륂뫢ꕈ뗻꛴륷듺귈뭐꽵맪귈꒧깴뙚ꅁ걏MAD ꚳꑀ꿊쉉ꅇ럭꣢륷듺뭾깴곒결1 껉ꅁꛓ꣤꽵맪귈꓀ꝏ결100 뭐10 ꑇ볆ꅁ 39
꙰ꚹ꒧륷듺꿠ꑏ곛ꕨ곆뮷ꅁꑀ귓결1%ꅁꕴꑀ귓결10%ꅃ꧳걏ꕈ륷듺뭾깴ꙁꕈ꽵맪귈ꖭ듮ꯡꭋꕩ녯꣬ꑀ교돦ꛬ뭾깴ꛊ꓀ꓱ귈ꅃꙝ결ꑀ꿫ꛓꢥꅁMAPE ꙝ꓀ꗀ결맪믚귈ꅁ꧒ꕎꫭ결ꛊ꓀ꓱꅁ꒣라ꙝ볆귈꒧ꑪꑰꛓ늣ꗍꓱ룻냲슦꒣쎭꒧냝썄ꅃ 40
닄ꕼ뎹?맪쏒떲ꩇ꓀꩒? Ꙣꖻ뎹귌녎ꕈꕸ왗걙ꑀꕾ뛗ꗦ꧶믈ꛦ꒧냲ꖻ룪껆ꅁꕝꝴ과볚꒸꒧ꕾ뛗뙩ꕘꑦ떲뛗룪껆ꅁ럭Ꝁ냑ꛒ룪껆ꅃꣃꕈ볒샀ꓨꚡꯘꗟ룓믈ꛦ맪믚ꓩꗦ꧶뙱ꅁꙁꝑꗎ닄ꑔ뎹꧒뒣ꕘ꒧ꙕ뫘륂뫢ꓨꩫ뭐볒ꮬ뙩ꛦ뻞Ꝁꅁꕈ엧쏒ꖻ곣ꡳ볒ꮬ꒧ꕩꛦ꧊ꅃ뙩ꑀꡂꅁꙁ녎떲ꩇꕛꕈꓱ룻ꅁꕈꕘ돌꣎륷듺볒ꮬꅃ쁈ꯡꅁꙁ녎돌꣎륷듺떲ꩇ낵결ꕾ맴꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅃꣃ꓀ꝏꓱ룻돦뚵ꚡ뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒤ꖭꞡ믝ꡄ뙱볒ꮬ뭐믝ꡄ륷듺볒ꮬ꒧깴늧ꅃ결륆ꚹꗘ볐ꖻ뎹녎Ꟈ꓀결꒭론ꅇ닄ꑀ론볋ꖻ룪껆냲ꖻ꓀꩒ꅂ닄ꑇ론ARMA볒ꮬ꒧ꯘ멣ꅂ닄ꑔ론AR-GARCH뭐AR-TGARCH볒ꮬ꒧ꯘ멣ꅂ닄ꕼ론AR-GARCH뭐AR-TGARCH볒ꮬ꒧륷듺떲ꩇꓱ룻ꕈ닄꒭론꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧볆뻚꓀꩒ꅃ 볋ꖻ룪껆냲ꖻ꓀꩒ ꕾ뛗믈ꛦ맯꧳ꕾ맴꒧믝ꡄ뙱ꕄ굮ꕩ꓀결꣢쏾ꅁ꣤ꑀ결ꕾ뛗믈ꛦ결뒣꣑뙩ꕘꑦ뱴냓꒧ꕾ맴ꗦ꧶믝ꡄ꧒늣ꗍ꒧ꕾ맴꯹ꚳ믝ꡄꅁꚹꝙ결믈ꛦ결몡ꢬ롧녠꧊믝ꡄ꧒꯹ꚳ꒧ꕾ맴ꅁꗧꕩ뫙꒧결믈ꛦ맯ꕾ맴꒧롧녠믝ꡄ뙱ꅆ꣤ꑇꭨ결ꕾ뛗믈ꛦ결ꙝ삳뛗뉶ꩩ냊꒧깍ꝑꛦ결꧒늣ꗍ꒧ꕾ맴꯹ꚳ믝ꡄꅁꚹꝙ결믈ꛦ꧳몡ꢬꕾ맴놱꣮꒧믝ꡄ꧒꯹ꚳ꒧ꕾ맴ꅁꗧꕩ뫙꒧결믈ꛦ맯ꕾ맴꒧놱꣮믝ꡄ뙱ꅃꛓ뻚ꗽꭥ꧒굺ꕩꪾꅁꖻ곣ꡳꕄ굮끷맯믈ꛦ꒧롧녠믝ꡄ뙱땯깩ꕘꕾ맴믝ꡄ륷듺볒ꮬꕾ맴꙳뙱놱꣮볒ꮬꕈ궰ꝃ믈ꛦ꒧ꕾ맴꙳뙱ꚨꖻꅃ ꖻ곣ꡳ녎뿯꣺냪꒺걙ꑀꕾ뛗믈ꛦ꧳2001꙾1ꓫ3ꓩꛜ2002꙾7ꓫ31ꓩ꒧과꒸뭐볚꒸꒧뙩ꕘꑦ떲뛗ꗦ꧶뙱ꅁꛓꚹꑀꗦ꧶뙱ꕄ굮걏뻚룓믈ꛦ륌ꕨ 41
뭐뙩ꕘꑦ뱴냓꒧ꕾ맴ꗦ꧶떲ꩇ꧒녯ꅃꙝꛓꅁ뻚ꑗ굺꒧ꥷ롱ꅁꖻ곣ꡳ녎믈ꛦ륌ꕨ꒧뙩ꕘꑦ떲뛗ꗦ꧶뙱뗸결믈ꛦ륌ꕨ맯ꕾ맴꒧롧녠믝ꡄ뙱ꅃ꧳ꚹꅁꖻ곣ꡳꭋꕈꕾ뛗믈ꛦ륌ꕨ꒧뙩ꕘꑦ떲뛗ꗦ꧶뙱ꅁ낵결AR-GARCH뭐AR-TGARCHꕾ맴믝ꡄ뙱륷듺볒ꮬ꒧뿩ꑊ엜볆ꅃꣃ녎볒ꮬ꒧륷듺귈낵결ꯡ쓲꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧믝ꡄ뙱뿩ꑊ엜볆ꅃ Ꙣꖻ론꒤녎끷맯꣢뫘볒샀룪껆뙩ꛦ쁒멁닎군꓀꩒ꅁꕝꝴ룪껆꒧ꢫ뛕맏볋ꖻ룪껆꒧냲ꖻ닎군뙱꓀꩒ꅁꕈꭋ닊늤셁룑꧒ꗎ룪껆꒧냲ꖻ닎군꽓꧊ꅃ 볋ꖻ룪껆ꢫ뛕맏 ꕈꑕ녎2001꙾1ꓫ3ꓩꛜ2002꙾7ꓫ31ꓩꅁ룓ꕾ뛗믈ꛦ꒧과꒸ꓩꗦ꧶뙱ꅝ뙩ꑦ떲뛗ꅞ4꒧ꢫ뛕맏쎸꧳맏ꅝ볚꒸꒧ꗦ꧶뙱ꢫ뛕맏ꭨꚬ뿽꧳뿽꒤ꅞꅃ결ꡄ뙩ꑀꡂ샋뗸ꗦ꧶뙱땵듁꒧엜꓆쇍뛕ꅁꖻ곣ꡳ뙩ꑀꡂ뿯꣺2002꙾7ꓫ꒧ꓩꗦ꧶뙱ꅁꣃ녎꣤쎸뭳ꚨ맏ꅃ Ꙣ맏뭐꒤ꕩꕈ땯뉻ꕾ맴ꗦ꧶뙱꒧쇍뛕ꝥꑗꅂꑕꩩ냊꒧뉻뙈ꅃꙝꚹꅁ굙ꕈꖭꞡ믝ꡄ뙱낵결꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅁ녎뻉교꙳뙱볒ꮬ늣ꗍ꛴군ꑗ꒧낾깴ꅁꛓꚹꗧ결ꖻ곣ꡳ뇽땯깩꙳뙱륷듺볒ꮬ꒧ꕄꙝꅃ 4 ꗑ꧳룪껆꣓랽믝꒩ꕈꭏ녋ꅃꙝꚹꅁ녎끷맯ꕾ뛗믈ꛦ꒧룪껆ꕛꕈꛊ꓀ꓱ꒧귗ꅃ 42
$700,000$650,000$600,000$550,000$500,000$450,000$400,000$350,000$300,000 맏 과꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ 〰ⰰ〰㔰ⰰ〰〰ⰰ〰㔰ⰰ〰〰ⰰ〰㔰ⰰ〰〰ⰰ〰ꓩꓫ㈳ꓩ㌱ꓩ㤱꙾?ꓫ㈵ꓩ㤱꙾?ꓫ㈷ꓩ㤱꙾?ꓫ㈹㤱꙾?ꓫ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫㄱꓩ㤱꙾?ꓫㄳꓩ㤱꙾?ꓫㄵꓩ㤱꙾?ꓫㄷꓩ㤱꙾?ꓫㄹꓩ㤱꙾?ꓫ㈱ꓩ㤱꙾?맏 과꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ 43 㤰꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤰꙾ㄱꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ
볋ꖻ룪껆냲ꖻ닎군뙱꓀꩒ Ꙣ뙩ꛦ볒ꮬ꓀꩒꒧ꭥꅁꖻ론녎ꕈꑀ냲ꖻ닎군뙱ꅁ맯ꕾ맴ꗦ꧶뙱룪껆낵뙩ꑀꡂꪺ꓀꩒ꅃꕈꑕ꓀ꝏ쎸ꕘ맏꓀ꝏꫭ과꒸ꅂ볚꒸ꗦ꧶뙱ꚸ볆꓀끴뇸맏ꅁꣃ녎룓닎군뙱뻣뉺결ꫭꅃꗑ맏뭐ꫭ꒧떲ꩇ꣓곝ꕩꕈ땯뉻ꅁ꒣뷗Ꙣ과꒸볚꒸꒧ꗦ꧶뙱ꑗꅁ꣤낾멁ꭙ볆곒ꑪ꧳륳ꅁꗧꝙ꒣뷗Ꙣ과꒸볚꒸ꗦ꧶뙱Ꙣ꓀끴ꑗꞡꝥ뉻ꕫ낾꒧뉻뙈ꅃ뒫ꢥ꒧ꅁ꓀끴꒧ꮬ멁Ꙣꕫ뫝꧔ꪺ룻ꅁꕩꕈ뗸결걏꣢뫘ꕾ맴ꗦ꧶뙱꒧룪껆꒤ꝥ뉻Ꟁ뫝ꭰ꒧뉻뙈ꅃ ꫭ㐮ㄠ?ꕾ뛗ꗦ꧶뙱꒧냲ꖻ닎군뙱? 볋ꖻ볆 ꖭꞡ볆 볐럇깴 돌ꑰ귈 돌ꑪ귈 낾멁5 깰ꯗ6 Sample Mean Standard Min Max Skewness Kurtosis Size (µ) Deviation (s) (k) (σ) 과 395 480, 68, 338, 677, 볚꒸ 395 17, 2, 12, 24, 35x−m 낾멁ꭙ볆ꅝsꅞ꒧꒽ꚡ결ꅁE ꅁ꣤결볋ꖻ꓀끴꒧ꑔ뚥냊깴ꅃꕄ굮ꗎꕈꝐ쉟꓀끴꒧sꚡꅃ럭s>0껉ꅁꫭ꓀끴Ꟁ뫝낾ꕫꅁꗧꝙ꣤꓀끴ꖪ뫝ꝥꭰ꒧뉻뙈ꅆ꒧ꅁ굙s<0껉ꅁꫭ꓀끴Ꟁ뫝낾ꖪꅁꗧꝙ꣤꓀끴ꕫ뫝ꝥꭰ꒧뉻뙈 46 깰멁ꭙ볆ꅝkꅞ꒧꒽ꚡ결ꅁx−mE -3ꅁ꣤결볋ꖻ꓀끴꒧ꕼ뚥냊깴ꅃꕄ굮ꗎꕈꝐ쉟꓀s끴꒧깰ꯗꅃ럭k>0껉ꅁꫭ꓀끴ꝥ뉻낪꽕깰꒧ꮬ멁ꅁ꒧ꅁ럭k<0껉ꅁꫭ꓀끴ꝥ뉻ꝃ쇯깰꒧ꮬ멁 44
㐰㌰㈰볐럇깴?㴠㘸??㜰†ꚸ볆ꖭꞡ볆?㴠㐸〸〳???丠㴠㌹㐮〰㈲㌰㈵〰㔰㈸⸰〰㜰㌱〰㤰㌵㌸㌰㐱㐴⸰⸰〰⸰〰⸰〰㔰㜰㐷㤰㔱㔴㘰㜰㘳㘷㜰⸰〰⸰〰⸰〰⸰〰㌰㔷⸰〰㔰⸰〰⸰〰㤰⸰〰⸰〰㌰㜳㔰㜶〰㜰⸰〰⸰⸰〰⸰ 맏㐮㌠?과꒸ꗦ꧶뙱꒧ꚸ볆꓀끴맏?㜰㘰㔰㐰㌰㈰ꚸ볆볐럇깴?㴠㈴㤴?㜷†ꖭꞡ볆?㴠ㄷ㘲????丠㴠㌹㐮〰㠸㤴⸲㐷ㄲㄶㄮ〴ㄳ㈷㠱?㠮㘲ㄵ?㔮㈰㜷ㄸㄹ㈱㠮㌵㤳?ㄮ??㔮?㈮㔰㈳〸㈴㘮㘶㈶?㌮㈴?㤮??〮?㜮? 맏㐮㐠?볚꒸ꗦ꧶뙱꒧ꚸ볆꓀끴맏? 45
AR륷듺볒ꮬ꒧ꯘ멣 ꗑ꧳ꖻ곣ꡳ꒧볋ꖻ룪껆Ꟈꙃ결껉뚡Ꟈꙃ룪껆ꅃꙝꛓꅁ꣤ꭥꯡ듁녠꙳Ꙣ낪ꯗ꒧곛쏶꧊ꅃ결ꑆ끴빁껉뚡Ꟈꙃ꒧룪껆ꅁꖻ곣ꡳ녎륂ꗎAR뇸ꗳꖭꞡ볆볒ꮬ꣓뙩ꛦ볒ꮬ끴빁ꅃꛓꙢ뙩ꛦAR볒ꮬꯘ멣꒧ꭥꅁ믝뵔뭻볋ꖻ룪껆ꭥꯡ듁뚡걏ꝟꝥ뉻낪ꯗ곛쏶꧊ꅁꕈ볋ꖻ룪껆걏ꝟ결ꑀꥷ멁Ꟈꙃꅃ쇗ꝋ볒ꮬ륷듺떲ꩇ늣ꗍ뗪낲끪쉫꒧뉻뙈ꅁꕈꑕ녎둎볋ꖻ룪껆꒧곛쏶꧊뭐ꥷ멁꧊꒧샋ꥷ낵ꑀ뮡ꧺꅃ 볋ꖻ곛쏶꧊꒧샋ꥷ Ꙣꖻ론꒤ꅁ녎ꝑꗎ볋ꖻ룪껆꣓군뫢꣤ꛛ곛쏶ꭙ볆ꅝAutocorrelation Function슲뫙결ACF7ꅞ뭐낾ꛛ곛쏶ꭙ볆ꅝPartial ACF슲뫙결PACF8ꅞꅃ뉻녎과꒸뭐볚꒸ꗦ꧶뙱ACF뭐PACF쎸뭳뻣뉺ꚨ맏ꅂꅂꅂꫭꅃꙢ맏뭐꒧맏AC㐮F맏㐠꒤?볚ꑗ꒸ꑕꗦ꣢꧶뇸뙱쏤꒧곉ꚸ뵵볆걏꓀ꗑ끴B맏artlett9꒧꒽ꚡ꧒쎸ꕘꅁ꣤ꗎ꧳ꡍꥷMAꅝnꅞ볒ꮬ꒧뚥볆ꅃꙐ볋ꪺꅁꙢ맏뭐맏꒧PACF맏꒤ꑗ꣢뇸룻닓ꪺ쏤곉뵵ꭨ걏ꝑꗎQuenouille10꒧꒽ꚡ꧒쎸ꕘꅁ꣤ꗘꪺꙢ꧳ꡍꥷARꅝmꅞ볒ꮬ꒧뚥볆ꅃꙢ맏ꇣ뭐ꫭ꒤ꕩ곝ꕘꙢ과꒸볚꒸ꗦ꧶뙱꒧볋ꖻ곛쏶ꭙ볆귈ꣃꖼ룲쁈뢨ꯡ듁볆뱗ꕛꛓꕘ뉻뱗ꕛ꒧뉻뙈ꅁꛓꝥ뉻뵷멃뮼듮꒧뉻뙈ꅁ덯ꫭꗜꖻ곣ꡳ꒧볋ꖻ룪껆Ꟈꙃꝥ뉻ꑀ귓Ꟈꙃ곛쏶꒧ꪬ멁ꅃ 7 굙ꑀ룪껆Ꟈꙃ{xt∈Cov(x, x)0 , 1, 2..., T}ꅁꣃꥷ롱rtk=tt-kꅁ맯ꗴꑀVar(x) Var(x)tt−kk∈{ 0, 1, 2, .....}ꅁꭨrˆk뫙결닄k듁꒧ꛛ곛쏶ꭙ볆ꅁꕂ뫙ꛛ곛쏶ꭙ볆꣧볆결ACFꅝAutocorrelation Functionꅞꅃ 28 굙ꑀ룪껆Ꟈꙃ{xt∈0 , 1, 2..., T}ꅁꣃꥷ롱ˆ−rk1(1−rfk=1)ꅁ맯ꗴꑀk∈{ 0, 1, 2, .....}ꅁt1−r2(k−1)1ꭨfˆk 뫙결닄k듁꒧낾ꛛ곛쏶ꭙ볆ꅁꕂ뫙낾ꛛ곛쏶ꭙ볆꣧볆결PACꅝFPartial Autocorrelation Functionꅞꅃ 9 Bartlett꒽ꚡ결±Var(?kˆ)ꅁ꣤꒤rˆk결볋ꖻ꒧ꛛ곛쏶ꭙ볆ꅃ 10 Quenouille꒽ꚡ결±Var(fkˆ)ꅁ꣤꒤fˆk결볋ꖻ꒧낾ꛛ곛쏶ꭙ볆ꅃ 46
ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨ꯡ맏볆 과꒸ꗦ꧶뙱꒧곛쏶ꭙ볆(ACF) ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨ꯡ맏볆㐮㘠?과꒸ꗦ꧶뙱뉢곛쏶ꭙ볆⡐䅃䘩? 47 偁䍆䅃?
ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨ꯡ맏볆 볚꒸ꗦ꧶뙱곛쏶ꭙ볆(ACF) ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨ꯡ볆맏 볚꒸ꗦ꧶뙱뉢곛쏶ꭙ볆(PACF) 48 偁䍆䅃?
ꫭ ꣢뚵ꕾ맴ꗦ꧶뙱꒧볋ꖻ곛쏶ꭙ볆뭐낾곛쏶ꭙ볆귈 곛쏶뢨ꯡ듁볆ꅝpꅞ ꭙ볆 1 2 3 4 5 6 7 8 9 10 과 ꒸ACF () () () () () () () () () () ꗦ ꧶PACF ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞꅝꅞ ꅝꅞ ꅝꅞ 뙱 볚 ꒸ACF ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞꅝꅞ ꅝꅞ ꅝꅞ ꗦ ꧶PACF ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞꅝꅞ ꅝꅞ ꅝꅞ 뙱 뗹ꅇꅝꅞ꒤꒧볆꙲ꫭACF뭐PACF꒧볐럇뭾(Standard Error)ꅃ 볋ꖻꥷ멁꧊꒧샋ꥷ Ꙣꭥꑀꑰ론꒤ꅁꖻ곣ꡳꑷ삳ꗎ륌ACF뭐PACF맯볋ꖻ룪껆Ꟈꙃ뙩ꛦ륌볋ꖻ곛쏶꧊꒧샋ꥷꅃꙝꚹꅁꙢꖻ론꒤녎ꙁ끷맯볋ꖻ룪껆ꅁ륂ꗎADF뭐PP샋ꥷꩫ꣓샋ꥷ볋ꖻꟇꙃ꒧ꥷ멁꧊ꅃꕈꑕ녎RATS땻ꚡ꧒군뫢ꕘ꒧ADF뭐PP샋ꥷ뙱뻣뉺결ꫭꅃꙢꫭ꒧꒤ꅁ꒣뷗걏과꒸볚꒸ꗦ꧶뙱꒧샋ꥷ닎군뙱Ꙣ5ꉍꪺ엣뗛ꓴ럇ꑕꅁꞡ떴꣣ꚳ돦껚꒧뗪때낲덝ꅃꗧꝙꅁ볋ꖻ룪껆Ꟈꙃ결ꑀ쎭ꥷꪬ멁꒧껉뚡Ꟈꙃ룪껆ꅃ꧒ꕈꖻ곣ꡳ샀뇄ꗎꑷꝥꥷ멁Ꟈꙃ꒧과꒸볚꒸ꗦ꧶뙱Ꝁ결ꖻꓥꪺ곣ꡳ엜볆ꅃ 49
ꫭ 볋ꖻꥷ멁꧊샋ꥷ ꕾ맴ꗦ꧶뙱 샋ꥷꩫ 샋ꥷ닎군뙱 ADF샋ꥷꩫ ** 과꒸ (뢨ꯡ듁볆) ꅝp = 6ꅞ PP샋ꥷꩫ ** (뢨ꯡ듁볆) (p = 6) ADF샋ꥷꩫ ** 볚꒸ (뢨ꯡ듁볆) (p = 4) PP샋ꥷꩫ ** (뢨ꯡ듁볆) (p = 4) 뗹1ꅇꫭ꒤볆귈결 t 귈ꅁ ()ꫭ뢨ꯡ듁볆ꅃ p뗹2ꅇADF 볒ꮬꅇ꒽ꚡꅝꅞ ∆x=a+axaTbxe. t01t−1+2+∑∆it−+iti=1뗹T3ꅇPP샋ꥷꩫꅇ꒽ꚡꅝꅞ x=m~~+b~(t−)+ax tt−1+뗹4ꅇ“ꆯꆯꆯ”ꫭꗜꙢ엣뗛ꓴ럇1ꉈꑕ(Critical value=)ꅁ떴뗪때낲덝H0:a1=0ꅆ “ꆯꆯ”ꫭꗜꙢ엣뗛ꓴ럇5ꉈꑕ(Critical value=)ꅁ떴뗪때낲덝ꅆ “ꆯ”ꫭꗜꙢ엣뗛ꓴ럇10ꉈꑕ(Critical value=)ꅁ떴뗪때낲덝ꅃ AR-GARCH뭐AR-TGARCH볒ꮬ꒧ꯘ멣 Ꙣ1980꙾ꕎꯡꅁEngle떥뻇뒣ꕘARCH볒ꮬꅁꛓꚹꑀ볒ꮬꑄ걏끷맯득깴Ꟈꙃ낵뙩ꑀꡂ꒧꓀꩒ꅃꗧꝙ륂ꗎARCH볒ꮬ꧳꺷꺻껉뚡Ꟈꙃ엜볆껉ꅁꙢ걙걱듁뚡꒺꒧ꩩ냊롳뭅Ꟈꙃ꓀끴Ꟁ뫝꒧ꯡ뉻뙈ꅁꣃ귗ꖿ귬ꚳ꒧껉뚡Ꟈꙃ볒ꮬꛓ뛈ꛒ뱻엜볆ꛛꢭ꒧ꩩ냊뉻뙈꒣ꢬ꒧덂ꅃ뒫ꢥ꒧ꅁARCH볒ꮬ녎득깴ꖭꓨꟇꙃꕛꑊ끔꺧뚰Ꙙ뵤돲꒤ꕛꕈ꓀꩒ꅃꙝꚹꅁꙢ륂ꗎARCH볒ꮬ꓀꩒꣣ 50
ꚳꩩ냊롳뭅껄삳꒧끝냈룪껆껉ꅁARCH볒ꮬꟳ꿠룑쓀Ꟈꙃ꒧ꩩ냊놡ꅃꛓꯡ쓲뻇꧒땯깩뭐ARCH뇚곛쏶꒧볒ꮬ걏결꣏ARCH볒ꮬꙢ꓀꩒ꑗꟳ결닓뵯ꅃꙝꚹꅁꖻ곣ꡳꑝ걏냲꧳ꚹ귬ꭨꅁ꓀ꝏ뇄ꗎGARCH볒ꮬT-GARCH볒ꮬ꣓뙩ꛦꓱ룻꓀꩒ꅁ듁뇦꿠ꕘꟳ꣣룑쓀ꑏ꒧볒ꮬꅃ ARCH껄ꩇ꒧샋ꥷ 결샋엧꒽ꚡ()꒧득깴뚵(e)걏ꝟ꣣ꚳARCH 껄ꩇ꒧꽓꧊ꅁꖲ뚷ꗽ샋tꥷ득깴Ꟈꙃꖭꓨ걏ꝟ꣣ꚳ곛쏶꧊ꅃꙝꚹꅁꖻ곣ꡳꝑꗎ닄ꑔ뎹꧒뒣ꕘ꒧Ljung-Boxꅝꝙ꒽ꚡꅝ ꅞꅞ ARCH-LMꅝꝙ꒽ꚡꅝ3. 40ꅞꅞ샋ꥷ닎군뙱ꅁ맯볒ꮬ꒧득깴뚵뙩ꛦ샋ꥷꅃ꒵녎룪껆샋ꥷ닎군뙱군뫢떲ꩇ꓀ꙃ결맏ꇣꫭꅃ Ꙣ맏ꇣ꒤꒧ACFPACF11맏꒤엣ꗜꕘꅁꡃꑀ듁꒧곛쏶ꭙ볆ꅝACFꅞ뭐낾곛쏶ꭙ볆ꅝPACFꅞꞡꖼꝥ뉻덶몥뮼뱗꒧뉻뙈ꅃꙝꚹꅁ뻚ꚹꑀ뉻뙈ꕩꕈ뮡ꧺꅁꙢ과꒸볚꒸꒧ꕾ맴ꗦ꧶뙱꒧왛듺귈뭐꧒끴빁ꪺꖭꞡ볆볒ꮬ꒧득깴ꖭꓨꭥꯡꙕ듁ꞡꚳ엣뗛곛쏶ꅃ굙ꙁꗑꫭ꒧Ljung-Box꒧Qꅝmꅞ닎군샋ꥷ뙱ꛓꢥꅁꣃ껚뻚m≈ln(T)녎볋ꖻ귓볆ꅝTꅞ꣺맯볆ꅁꗧꝙm=&ln(395)=&6ꅃꙝꚹꅁ과꒸ꗦ꧶뙱꒧Qꅝ6ꅞ닎군뙱결ꅁꛓ볚꒸ꗦ꧶뙱꒧Qꅝ6ꅞ닎군뙱결ꅁ꣤p-valueꞡꑰ꧳ꅆꗧꝙꙢ5ꉍꪺ엣뗛ꓴ럇꒧ꑕꅁ꣤p-value때ꩫ떴득깴ꖭꓨꟇꙃ곛쏶꒧뗪때낲덝ꅁꫭꗜ꣤득깴ꖭꓨ꣣ꚳ엣뗛곛쏶ꅃ꣤ꚸꅁꙁ왛맮꣢엜볆꒧ARCH LM닎군뙱ꅁ꣤p귈ꗧꑰ꧳ꅃ뒫ꢥ꒧ꅁARCH LM샋ꥷ꒧떲ꩇꗧ뭐Ljung-Box꒧닎군뙱곛Ꙑꅃ 11 샋뗸볒ꮬ득깴걏ꝟ꣣ARCH껄ꩇꅁ믝샋ꥷ꣤득깴뚵걏ꝟ꣣곛쏶꧊ꅃꙝꚹꅁꖻꓥ낣륂ꗎARCH LM뭐Ljung-Box샋ꥷꕾꅁꣃꕛꑊACF뭐PACF맏ꕛꕈ뮡ꧺ꣤득깴Ꟈꙃ꒧곛쏶꧊ꅃ 51
ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨ꯡ맏볆 과꒸ꗦ꧶뙱득깴곛쏶ꭙ볆ꅝACFꅞ ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨맏ꯡ볆0 과꒸ꗦ꧶뙱득깴낾곛쏶ꭙ볆ꅝPACFꅞ 52 偁䍆䅃?
ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ뢨맏ꯡ4볆.11 볚꒸ꗦ꧶뙱득깴곛쏶ꭙ볆ꅝACFꅞ ㄮ?⸵〮??ꭙ볆궭꣮ⴱ⸰ꭙ볆?????ㄱㄳㄵ????ㄲㄴㄶ맏뢨4ꯡ.12볆 볚꒸ꗦ꧶뙱득깴낾곛쏶ꭙ볆ꅝPACFꅞ 53 偁䍆䅃?
ꫭ ꕾ맴ꗦ꧶뙱득깴ꖭꓨ꒧곛쏶ꭙ볆뭐뉢곛쏶ꭙ볆귈 곛쏶뢨ꯡ듁볆ꅝpꅞ ARCH test ꭙ볆 1 2 3 4 5 6 7 Ljung-Box LM test 닎군뙱Qꅝ6ꅞ c2(4) 과ACF ꒸() () () () () () () [] [] ꗦPACF ꧶ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ뙱 볚ACF ꒸ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ[] [] ꗦPACF ꧶ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ ꅝꅞ뙱 뗹1ꅇꅝꅞ꒤꒧볆꙲ꫭACF뭐PACF꒧볐럇뭾ꅃ 뗹3ꅇ[ ] ꒤꒧볆꙲ꫭARCH LM뭐Ljung-Box샋ꥷ꒧p-valueꅃ 뗹2ꅇQꅝmꅞ=Qꅝ6ꅞꅁ6 = lnꅝ395ꅞꅆc2(4)ꅆARCH test샋ꥷ꒧돌빁뢨ꯡ듁볆ꗑSAS닎군덮엩군뫢ꛓ녯ꅃ AR-GARCH볒ꮬ냑볆꛴군뭐빁Ꙙ꧊샋ꥷ Ꙣꚹ론꒤녎끷맯GARCH볒ꮬ꣓뙩ꛦ냑볆꛴군ꅁꣃ뇄ꗎRATSꅝRegression Analysis for Time Seriesꅞ깍룋덮엩뙩ꛦ땻ꚡ꒧벶뱧ꅁꣃ륂ꗎBHHH12ꩫ뙩ꛦ냑볆꛴군ꅃ 12 BHHHꩫ결RATS땻ꚡ꒧꒺ꯘ냑볆꛴군ꩫꅁꚹ면뫢ꩫ걏ꗑBerndt, Hall, Hall and Hausman(1974) 땯깩ꕘ꣓ꪺ면뫢ꩫꅁꚹꗎ꧳ꡄ꣺랧꣧볆귈결돌ꑪ꒧냑볆꛴군귈ꅁ꣤군뫢ꚡ꙰ꑕ꧒굺ꅇ q(i+1)=q(i)+S+q(i)−1gq(i)[1()]*()ꅃ i 54
AR-GARCH볒ꮬ냑볆꛴군 뉻녎꒽ꚡꅝꅞ뇸ꗳꖭꞡ볆ꓨ땻ꚡYˆ=j+∑jYˆ+q2+0+1e−1ꕈ꒽ꚡtiititi=0ꅝꅞ뇸ꗳ엜늧볆ꓨ땻ꚡpq=a+∑a2h0e−+∑bh꒧ꕾ뛗ꗦ꧶뙱볒ꮬ꒧titijt−ji=1i=1땻ꚡ륂뫢떲ꩇ뻣뉺결ꫭꅃꙢꫭ꒧꒤ꕩꕈ땯뉻과꒸ꗦ꧶뙱꒧AR(3)-GARCH(1,1)륷듺볒ꮬꙢ뇸ꗳꖭꞡ볆ꑗ꒧끴빁떲ꩇꅝAICSBC13ꞡ룻꣤ꕌ꣢귓볒ꮬAR(2)-GARCH(1,1)ꕈAR(1)-GARCH(1,1)ꑰꅞꅁꗧꝙ쁵꧳AR(2)-GARCH(1,1)ꕈAR(1)-GARCH(1,1)꒧떲ꩇꅃ꣤ꚸꅁꙢꫭ꒤ꗧꕩ땯뉻Ꙣ볚꒸ꗦ꧶뙱꒧륷듺볒ꮬ꒤ꅁAR(3)-GARCH(1,1)볒ꮬ꒣뷗Ꙣ뇸ꗳꖭꞡ볆ꑗ꒧끴빁떲ꩇ룻쁵ꅃ ꗑꫭꕩꪾꖻ곣ꡳ맯과꒸ꗦ꧶뙱륷듺볒ꮬ꒧꛴군떲ꩇꕈAR(3)-GARCH(1,1)결돌꣎ꅁꝙ결꒽ꚡ()꧒ꗜꅇ Y=231,+−1+−2+−3,eΩ−1~N(0,h), ttttttth=−1. () Ꙣ꒽ꚡꅝꅞ꒤ꅁꗑ꧳GARCH볒ꮬ꒧녠볆뚵뭐ARCH뚵꒧ꭙ볆ꞡ꒣엣뗛ꅃꙝꚹꅁ녎Ꙣ과꒸ꗦ꧶뙱꒧륷듺볒ꮬ꒤꒩ꕈ귧낣ꅃ ꛓꗑꫭ꒤ꕩꪾꖻ곣ꡳ맯볚꒸ꗦ꧶뙱륷듺볒ꮬ꒧꛴군떲ꩇꕈAR(3)-GARCH(1,1)결돌꣎ꅁꝙ결꒽ꚡ()꧒ꗜꅇ Y=7,+−1+−2+−3,eΩ−1~N(0,h), ttttttth=. tt−1 () Ꙣ꒽ꚡꅝꅞ꒤ꅁꗑ꧳GARCH볒ꮬ꒧녠볆뚵뭐ARCH뚵꒧ꭙ볆ꞡ꒣엣뗛ꅃꙝꚹꅁ녎Ꙣ볚꒸ꗦ꧶뙱꒧륷듺볒ꮬ꒤꒩ꕈ귧낣ꅃ 13 AIC뭐SBCꞡ결SAS땻ꚡ꒧군뫢떲ꩇꅁ꣤ꗎ덾Ꙣ꧳Ꝑ쉟볒ꮬ뚥볆ꅁAIC뭐SBC꒧귈뙖ꑰ뙖ꙮꅃ 55
ꫭ 과꒸AR-GARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 냑볆 냑볆꛴군귈 AR(1)-GARCH(1,1) AR(2)-GARCH(1,1) AR(3)-GARCH(1,1) j0 328, 272, 231, (t-value) () () () j1 AR (t-value) () () () 볒ꮬ j2 (t-value) () () j3 (t-value) () a0 +009 +008 +008 (t-value) () () () GARCH a1 -003 볒ꮬ (t-value) () () () b1 (t-value) () () () 득깴 Q (6) 볒ꮬ뙅쉟 (p-value) () () () 득깴 Q (6) ꖭꓨ (p-value) () () () AIC럇ꭨ SBC럇ꭨ 56
ꫭ 볚꒸AR-GARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 냑볆 냑볆꛴군귈 AR(1)-GARCH(1,1) AR(2)-GARCH(1,1) AR(3)-GARCH(1,1) j0 12, 9, 7, (t-value) () () () j1 AR (t-value) () () () 볒ꮬ j2 (t-value) () () j3 (t-value) () a0 829, 965, (t-value) () () () GARCH a1 볒ꮬ (t-value) () () () b1 (t-value) () () () 볒ꮬ득뙅깴쉟 Q (6) (p-value) () () () 득깴 Q (6) ꖭꓨ (p-value) () () () AIC럇ꭨ SBC럇ꭨ 57
AR-GARCH볒ꮬ꒧빁Ꙙ꧊뙅쉟 놵ꑕ꣓ꅁꖻꑰ론녎끷맯꒽ꚡꅝꅞꅝꅞ꒧득깴ꕈ득깴ꖭꓨꟇꙃ꒧Q(m)닎군뙱낵ꑀ뮡ꧺꅃ궺ꗽꅁꙢ뙩ꛦQ(m)닎군뙱샋ꥷ꒧ꭥꖲ뚷ꗽ뵔ꥷ룓닎군뙱꒧ꛛꗑꯗꅁ굙껚뻚m≈ln(T)녎볋ꖻ귓볆ꅝTꅞ꣺맯볆ꅁꗧꝙm=&ln(395)=&6ꅁꭨꕩ녯ꪾ꣤ꕤꓨ꓀끴꒧ꛛꗑꯗ결6ꅃꛓ룓떲ꩇꭨ뻣뉺Ꙣꫭꕈ꒤ꅁ껚뻚ꑗ굺꒧뮡ꧺꕩꕈ녯ꪾ과꒸륷듺볒ꮬQꅝ6ꅞ닎군뙱꒧p-value결ꅁꛓ볚꒸륷듺볒ꮬQꅝ6ꅞ닎군뙱꒧p-valueꭨ꓀ꝏꅁ걇Ꙣ5ꉍꪺ엣뗛ꓴ럇꒧ꑕꅁ꣢ꞡ놵꣼뗪때낲덝꒧득깴Ꟈꙃ때곛쏶꒧낲ꥷꅃꛓ둎득깴ꖭꓨ꒧곛쏶꧊낲ꥷꗧ땍ꅁ꣤샋ꥷ뙱꒧p-value꓀ꝏ결ꅃꙐ볋둎5ꉍꪺ엣뗛ꓴ럇꣓뮡ꅁ꣢볒ꮬ꒧득깴Ꟈꙃꖭꓨꗧ때곛쏶꒧뉻뙈늣ꗍꅃ뒫ꢥ꒧ꅁꙢ꣢ꕾ뛗꒧AR-GARCH꒧륷듺볒ꮬꞡ꣣ꚳ륷듺꒧껄뉶꧊ꅃ AR-TGARCH볒ꮬ냑볆꛴군뭐빁Ꙙ꧊샋ꥷ 둎ꫭ뭐ꫭꅂ꒧ꓱ룻ꕩꕈ땯뉻ꅁ꣢뫘ꕾ뛗ꗦ꧶뙱륷듺볒ꮬ꒧ꭄ뇸ꗳꖭꞡ볆ꅝ꓀ꝏ결231,뭐7,ꅞ뭐볋ꖻꖭꞡ볆ꅝ꓀ꝏ결480,뭐17,ꅞ꒧깴늧곛럭ꙡ엣뗛ꅁꛓ덯ꫭꗜꙢAR-GARCH볒ꮬ꒤ꕩ꿠ꥼꚳ걙룪끔걏덑뿲멼ꅃꙝꚹꅁꖻ곣ꡳ륂ꗎ꒽ꚡꅝꅞꕈet−1꒧ꖿ굴뢹낵결쉥녎GARCH볒ꮬꪺ뇸ꗳ엜늧볆볒ꮬ귗결ꕈꑕ꒧ꮬ멁ꅇ pqh=α+t∑α2101ε−+βhI iti∑1, (ε1≤0) ;jt−jt−i=1i=1pqh=aa∑a22(10+20)+(1e−+a2e−)+∑(b1h−+b2h−), I(e−1>0) . titiitijtjjtjti=1i=1ꣃ륂ꗎꭄ맯뫙ꩩ냊볒ꮬ꣓끴빁룪껆ꅁꛓꚹꑀ볒ꮬꝙ결ꖻ곣ꡳ꒧TGARCH볒ꮬꅁꕈꑕꖻ곣ꡳ녎Ꟈ뮡ꧺ륱뢣땻ꚡ군뫢떲ꩇ뭐볒ꮬ꒧빁Ꙙ꧊뙅쉟ꅃ 58
AR-TGARCH볒ꮬ꒧냑볆꛴군 Ꙣ덯ꑀ론꒤ꅁꖻ곣ꡳ녎륂ꗎRATS깍룋덮엩꣓벶뱧땻ꚡꅁꛓ꛴군귈ꪺ군뫢ꗧ걏덺륌BHHHꩫꅃ뉻녎꣢뫘ꕾ뛗꒧TGARCH볒ꮬ꒧냑볆꛴군귈뻣뉺결ꫭꅁꕈꑕ녎둎볒ꮬ꒧꛴군떲ꩇ낵ꑀ뮡ꧺꅃ ꗑꫭ꒤ꕩꪾ과꒸ꗦ꧶뙱꒧륷듺볒ꮬ결AR(3)-TGARCH(1,1)ꅁꛓ꣤꛴군ꚡꭨ꙰꒽ꚡꅝꅞ꧒ꗜꅝꑕꚡ꒤ꑷ녎꒣엣뗛꒧ꭙ볆귈꒩ꕈ귧낣ꅞꅇ Y=404,−−3 ;eΩ−1~N(0,h) , ttttth=142,328,+−1 ; I(e0) ,ttt−1≤ h=304,828,+ ; I(e0) .tt−t−1> ()볚꒸ꗦ꧶뙱꒧륷듺볒ꮬ결AR(3)-TGARCH(1,1)ꅁ꣤꛴군ꚡꭨ꙰꒽ꚡꅝꅞ꧒ꗜꅝꑕꚡ꒤ꑷ녎꒣엣뗛꒧ꭙ볆귈꒩ꕈ귧낣ꅞꅇ Y=20,−−2 ;εΩ~N(0,h) , tttt−1th=249+2,+− ; I(e0) ,tt−t1t−1≤ h=6441,+−1− ; (0) .t−1Ie ttt−1> () AR-TGARCH볒ꮬ꒧빁Ꙙ꧊샋ꥷ ꦵ쓲ꑗ론꒧볒ꮬ꛴군떲ꩇꅁꖻ론녎Ꟈ맯꒽ꚡꅝꅞꅝꅞ뙩ꛦ볒ꮬ득깴꒧샋ꥷꅁꣃ덺륌Ljung-Box꒧Qꅝmꅞ닎군뙱꣓샋ꥷ꣢ꗦ꧶뙱볒ꮬ꒧득깴뭐득깴Ꟈꙃꖭꓨꅃ꣤떲ꩇꭨ뻣뉺결ꫭꅁ둎ꫭ꒧떲ꩇ엣ꗜꙢ뢨ꯡ듁볆결6듁ꑕ(m=&ln(395)=&6)ꅁ과꒸ꗦ꧶뙱볒ꮬ꒧득깴뭐득깴ꖭꓨQꅝ6ꅞ닎군뙱꒧p-value꓀ꝏ결뭐ꅁꙢ5ꉍꪺ엣뗛ꓴ럇ꑕꅁ꓀ꝏꞡ떴득깴Ꟈꙃꕈ득깴ꖭꓨꟇꙃ곛쏶꒧낲ꥷꅃꛓꙢ볚꒸ꗦ꧶뙱ꪺ뎡꓀ꅁ꣤볒ꮬ꒧득깴뭐득깴ꖭꓨꪺQꅝ6ꅞ닎군뙱꒧p-value꓀ꝏ결뭐ꅃꙐ볋ꪺꅁꙢ5ꉍꪺ엣뗛ꓴ럇ꑕꗧ떴Ꟈꙃ곛쏶꒧낲ꥷꅃꙝꚹꅁꙢ꣢ꕾ맴 59
AR-TGARCH륷듺볒ꮬꞡ꣣ꚳ륷듺ꑗ꒧껄뉶꧊ꅃ ꫭ ꕾ맴AR-TGARCH볒ꮬ꒧냑볆꛴군떲ꩇ뙅쉟 냑볆 냑볆꛴군귈 과꒸ 볚꒸ j0 404, 20, (t-value) () () AR j1 볒ꮬ (t-value) () () j2 -003 (t-value) () () j3 -003 (t-value) () () a10 142,328, 249, (t-value) () () a11 (t-value) () () T-GARCH b11 -003 볒ꮬ (t-value) () () a20 +009 (t-value) () () a21 (t-value) () () b21 (t-value) () () 볒ꮬ뙅득쉟깴 Q (6) (p-value) () () 득깴ꖭꓨ Q (6) (p-value) () () 60
AR-GARCH뭐AR-TGARCH볒ꮬ륷듺떲ꩇ꒧ꓱ룻 뻚ꑗ굺AR-GARCH뭐AR-TGARCH륷듺볒ꮬ꒧뻞Ꝁꅁꖻ론녎륷듺떲ꩇ뻣뉺ꚨꫭꅁꣃ녎꣤꒺깥쎸뭳ꚨ맏뭐ꅝ볚꒸꒧ꗦ꧶뙱륷듺떲ꩇ녎ꚬ뿽꧳뿽꒧꒤ꅞꅃꙢꫭ꒤ꅁꖻ곣ꡳ륂ꗎ닄ꑔ뎹꒤꒶닐꒧ꑔ뫘륷듺셚껄ꓨꩫꅁꓱ룻AR-GARCH볒ꮬ뭐AR-TGARCH볒ꮬꙢꕾ맴믝ꡄ뙱륷듺ꑗ셚껄꒧쁵Ꙉꅃ Ꙣꫭ꒤ꅁ뻣뉺ꑆꑔ뫘셚껄륷듺볒ꮬMADꅂRMSEꕈMAPE꒧군뫢떲ꩇꅁ굙왛맮ꫭ꒧떲ꩇꅁ과꒸AR-GARCH뭐AR-TGARCH볒ꮬ꒧MADꅁ꓀ꝏ결25,뭐16,ꅃꙝꚹꅁꙢMAD럇ꭨ꒧ꑕꅁAR-TGARCH볒ꮬ꒧MAD귈ꑰ꧳AR-GARCH꒧MAD귈ꅁꗧꝙAR-TGARCH볒ꮬ꒧륷듺뭾깴ꑰ꧳AR-GARCH볒ꮬꅃꙐ뉺ꅁꙢRMSE뭐MAPE 럇ꭨꑕꅁAR-TGARCH볒ꮬ꒧륷듺셚껄ꞡ룻AR-GARCH볒ꮬ결꣎ꅃꚹꕾꅁꙢ맏뭐맏꒧ꓱ룻ꛓꢥꅁAR-TGARCH볒ꮬꙢ륷듺셚껄ꑗ엣땍쁵꧳AR-GARCH볒ꮬꅁꓗ꣤AR-TAGRCH볒ꮬꙁ덺륌득깴쉥귈꒧귗ꖿꯡꅁ맯꧳낻듺ꖿꙖꩩ냊뉻뙈ꅁ녎룻AR-GARCH볒ꮬꟳꚳ껄뉶ꅃ ꣢뚵ꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧볆뻚꓀꩒ Ꙣ뙩ꛦ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ볆뻚꓀꩒꒧ꭥꅁ뚷ꗽ녎NIR-EOQ꙳뙱볒ꮬ꒧냲ꖻ룪껆Ꝁꑀ덂뉺ꅁꣃ녎NIR-EOQ꙳뙱볒ꮬ꒧냲ꖻ룪껆뻣뉺결ꫭꅃ 61
ꫭ 과꒸믝ꡄ뙱볒ꮬ륷듺떲ꩇ셚껄ꓱ룻 ꓩ듁 2002꙾8ꓫꅝ왛듺귈ꅞ 2002꙾8ꓫꅝ륷듺귈ꅞ 과꒸ 과꒸ꅝGARCHꅞ 과꒸ꅝTGARCHꅞ 8/01 450, 429, 435, 8/02 478, 450, 488, 8/03 424, 444, 410, 8/04 427, 409, 436, 8/05 512, 458, 495, 8/08 506, 464, 520, 8/09 504, 488, 487, 8/10 483, 478, 464, 8/11 513, 480, 488, 8/12 446, 466, 418, 8/15 430, 457, 406, 8/16 452, 478, 478, 8/17 438, 424, 421, 8/18 501, 446, 485, 8/19 463, 428, 501, 8/22 473, 428, 451, 8/23 556, 451, 524, 8/24 539, 467, 547, 8/25 535, 502, 519, 8/26 497, 514, 473, 8/29 516, 503, 500, 8/30 515, 526, 535, 8/31 558, 512, 546, Total11,225, 10,714, 11,035, MAD--------------------- 25, 16, RMSE--------------------- 29, 5, MAPE--------------------- 62
왛듺귈륷듺귈$650,000$600,000$550,000$500,000$450,000$400,000$350,0001234567891011121314151617181920212223 맏 과꒸AR-GARCH볒ꮬ륷듺꒧떲ꩇꅝ2002꙾8ꓫꅞ 왛듺귈륷듺귈$650,000$600,000$550,000$500,000$450,000$400,000$350,0001234567891011121314151617181920212223 맏 과꒸AR-TGARCH볒ꮬ륷듺꒧떲ꩇꅝ2002꙾8ꓫꅞ 63
ꫭ NIR-EOQ꙳뙱볒ꮬ꒧냲ꖻ엜볆룪껆 과꒸ꅝꉃꅞ 볚꒸ꅝꏡꅞ ꯹ꚳꚨꖻꅝwꅞ ꅝNTꉃꅞ ꅝNTꉃꅞ 륷듺믝ꡄ뙱 AR-GARCH 2,192,ꅝꉃꅞ 95,ꅝꏡꅞ ꅝdꅞ AR-TGARCH 2,065,ꅝꉃꅞ 92,ꅝꏡꅞ ꖭꞡ믝ꡄ뙱ꅝdꅞ 2,293,ꅝꉃꅞ 97,ꅝꏡꅞ 룉뙱ꚨꖻꅝkꅞ ꅝNTꉃꅞ ꅝNTꉃꅞ ꖭꞡ뙒뛗뉶ꅝpꅞ 133,078,ꅝꉃꅞ 4,868,ꅝꏡꅞ ꕾ맴믝ꡄ뉶ꅝrꅞ 101,271,670ꅝꉃꅞ 3,705,ꅝꏡꅞ ꙳뙱셠썂ꅝQꅞ 7,200 뗹ꅇ꯹ꚳꚨꖻꅝwꅞ꒧군뫢ꖻ곣ꡳꛒ뱻륂ꗎ꣢뫘ꕾ맴꒧ꥷ꙳ꝑ뉶ꅁ땍둎ꗽꭥ꒧ꥷ롱ꖻ곣ꡳ믝덺륌ꑕ굺꒧꒽ꚡwr=c*1−신뒫결ꖻ곣ꡳ꒧꯹ꚳꚨꖻꅁꚹꕾꅁꑗ굺꒧꯹ꚳꚨꖻꥼ뚷덺륌꣢p뫘ꕾ맴꒧믹껦꒩ꕈ신뒫결Ꙑ볋꒧돦ꛬꕈꓨꭋ군뫢ꅆꛓꖭꞡ믝ꡄ뙱ꅝdꅞꭨ뇄꣺ꭥ듁꒧ꖭꞡ믝ꡄ뙱ꅆ룉뙱ꚨꖻꅝkꅞꭨ걏ꕈ믈ꛦ쇊뙒ꕾ맴꒧ꓢ쓲뙏뭐ꕾ뛗롧샙냓꒧ꗲ꒶뙏ꅁ땍ꕾ뛗롧샙냓꒧ꗲ꒶뙏때ꩫ녯ꪾꅃꙝꛓꅁꖻ곣ꡳ뛈꿇ꑊ믈ꛦ쇊뙒ꕾ맴꒧ꓢ쓲뙏ꅁꗑ꧳ꑗ굺꒧꯹ꚳꚨꖻꕈ신뒫ꚨꕸ맴군뫢ꅁꓞꚹ룉뙱ꚨꖻꗧ믝덺륌뛗뉶꒧뒫뫢ꅆ돌ꯡꙢꖭꞡ뙒뛗뉶ꅝpꅞꕈꕾ맴믝ꡄ뉶ꅝrꅞꭨ둎NIR-EOQ볒ꮬ꒧ꥷ롱ꕈ믈ꛦ륌ꕨꑀ꙾꒧뙒ꅂ뷦ꕾ맴뙱꣓ꕎꑊꅆ꙳뙱셠썂ꅝQꅞ꒧귈걏뇄q1+q2=Q꧒녯ꅃ ꑀ꿫NIR-EOQ꙳뙱볒ꮬ꣤믝ꡄ뙱곒ꕈ륌ꕨ꒧ꖭꞡ믝ꡄ뙱결ꛒ뙱ꅁꛓꚹ뫘꙳덦볒ꚡ꧳믝ꡄ뙱ꝥ뉻쎭ꥷꪬ멁ꑕꑾ꣣ꚳ빁ꗎ꧊ꅃ럭믝ꡄ뙱Ꟗ덴엜냊꒧놡맒ꑕꅁ꙳뙱볒ꚡ녎ꙝ결륌ꕨꖭꞡ믝ꡄ뙱뭐맪믚믝ꡄ뙱꒧뭾깴쉘ꑪꅁꛓ뻉교꙳뙱볒ꮬ군뫢ꑗ늣ꗍꟳꑪ꒧낾뭾ꅃꚹꕾꅁ굙ꕈ맏뭐맏꒧믝ꡄ뙱ꢫ뛕꣓곝ꅁ과꒸꒧믝ꡄ뙱Ꙣ2002꙾8ꓫꗷ꒧ꢫ뛕ꝥ뉻Ꙗꑗꩩ냊꒧ꢫ뛕ꅃꙝꚹꅁ굙ꕈꖭꞡ믝ꡄ뙱낵결꙳뙱볒ꮬ꒧뿩ꑊ냑볆녎뻉교볒ꮬꕘ뉻낪꛴ꝃ꛴ꖫ돵믝ꡄ뙱ꪺ뉻뙈ꅃꙝꛓꅁ뻉교꙳뙱볒ꮬ셠ꚨꖻꡄ뫢꒣ꖿ뵔꒧놡ꩰꅃ ꙝꚹꅁꙢꖻ론꒤녎ꛒ뱻륂ꗎ꒣Ꙑ믝ꡄ뙱륷듺볒ꮬ뭐꣢뚵ꚡꕾ맴 64
NIR-EOQ꙳뙱볒ꮬ결ꛒ뙱ꛓꯘꗟ볆귓꒣Ꙑ놡ꩰ꒧닕Ꙙꅁꣃꓱ룻ꙕ귓꙳뙱볒ꮬ셠ꚨꖻ꒧깴늧ꅃꕈꑕ녎둎ꖭꞡ믝ꡄ뙱ꕈAR-GARCH볒ꮬ뭐AR-TGARCH볒ꮬ꒧꣢뫘륷듺믝ꡄ뙱Ꙁꑔ뫘꒣Ꙑ꒧믝ꡄ뙱ꅁꕈ낵결돦뚵ꚡꕾ맴뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅃꣃ꓀ꝏꓱ룻Ꙣ꒣Ꙑ륷듺볒ꮬꑕ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꙢ꙳뙱셠ꚨꖻ꒧깴늧ꅁꕈ꙳뙱놱꣮ꑗ꒧엜냊ꅁꕈꑕ녎ꕈꖭꞡ믝ꡄ뙱ꕈ꣢뫘륷듺믝ꡄ뙱낵결룓꙳뙱볒ꚡ꒧뿩ꑊ엜볆ꅁꣃ녎룓꙳뙱볒ꮬ꒧군뫢떲ꩇ뻣뉺결ꫭ뭐ꅃ ꫭ 돦뚵ꚡNIR-EOQ꙳뙱볒ꮬ꒧돌꣎꯹ꚳ뎡ꛬ뭐꙳뙱셠ꚨꖻ ꖭꞡ GARCH TGARCH 믝ꡄ뙱볒ꮬ 륷듺볒ꮬ 륷듺볒ꮬ 과꒸ 6, 5, 5, q* i볚꒸ 셠ꚨꖻꅝꉃꅞ 7, 7, 7, ꫭ ꣢뚵ꚡNIR-EOQ꙳뙱볒ꮬ꒧돌꣎꯹ꚳ뎡ꛬ뭐꙳뙱셠ꚨꖻ ꖭꞡ GARCH TGARCH 믝ꡄ뙱볒ꮬ 륷듺볒ꮬ 륷듺볒ꮬ l* 과꒸ 6, 5, 4, q* i볚꒸ 셠ꚨꖻꅝꉃꅞ 7, 6, 6, 뗹ꅇꑗ굺ꫭ뭐ꫭ볆귈꒧ꡄ녯ꅁ걏싇ꗑWINQSB땻ꚡ륂뫢꧒ꡄ녯ꅃ ꓱ룻ꫭ뭐ꫭ꒧떲ꩇꕩꕈ땯뉻ꅁ꒣뷗륂ꗎꖭꞡ믝ꡄ뙱볒ꮬ륷듺믝ꡄ뙱볒ꮬ꒧NIR-EOQ꙳뙱볒ꮬ꒤ꅁ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ룻돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꟳ꿠ꚳ껄ꪺ궰ꝃ셠ꚨꖻꅃ굙ꕈAR-TGARCH륷듺볒ꮬꛓꢥꅁ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧셠ꚨꖻ결$6,ꅁꛓ돦 65
뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧셠ꚨꖻ결$7,ꅁ꣢곛ꓱ룻꣤셠ꚨꖻ곹궰ꝃꑆ$ꅝꉍꅞꅃ 껚뻚ꫭꅁ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧꓀꩒떲ꩇꛓꢥꅁꙢꕛꑊ륷듺볒ꮬ꒧ꕾ맴NIR-EOQ꙳뙱볒ꮬꅁ꣤믝ꡄ뙱ꟳ꿠뙋꫱맪믚ꪬꩰꅁ꣏녯꧒ꡄ녯꒧돌꣎꯹ꚳ뎡ꛬꟳ꿠ꕒ꓀삳뉻맪놡맒ꅃꙝꚹꅁ굙ꙁꓱ룻ꖭꞡ믝ꡄ뙱뭐AR-TGARCH볒ꮬꙢ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧꓀꩒떲ꩇꅃꕩꕈ땯뉻ꅁꙢAR-TGARCH볒ꮬ꒤꧒ꡄ녯꒧셠ꚨꖻ결ꉃ6,ꅁꛓꖭꞡ믝ꡄ뙱볒ꮬ꧒ꡄ녯꒧꙳뙱셠ꚨꖻ결ꉃ7,ꅁ꣢Ꙣ꙳뙱셠ꚨꖻꑗ꒧깴늧결ꉃ1,ꅝ ꉍꅞꅃ덺륌ꑗ굺꒧ꓱ룻ꯡꅁꕩꕈ땯뉻ꅁ싇ꗑLagrange궼볆귗ꖿ꒧꣢뚵ꚡNIR-EOQ꙳뙱볒ꮬꅁꕩ궰ꝃ돦뚵ꚡNIR-EOQ꙳뙱볒ꮬꙢ꙳뙱셠ꚨꖻꑗꅃꙝꚹꅁꕩꪾ꣢뚵ꚡNIR-EOQ꙳뙱볒ꮬꙢ돌꣎꙳뙱뭐셠ꚨꖻꑗ꒧ꡄ룑ꑗꟳ꿠뙋꫱뉻맪놡ꩰꅃ 66
닄꒭뎹?떲뷗뭐ꯘ쒳? ꖻ뎹녎끷맯뻣엩곣ꡳ떲ꩇ낵ꑀ셠떲뭐뮡ꧺꅃ꣤ꚸꅁ뮡ꧺꖻ곣ꡳ꒧곣ꡳ궭꣮꒧꧒Ꙣꅃ돌ꯡꅁꣃ끷맯ꯡ쓲곛쏶곣ꡳ뒣ꕘꑀꯘ쒳ꅃ 떲뷗 꿷녎곣ꡳ떲ꩇ꓀굺꙰ꑕꅇ ꅝ1ꅞ?ꕾ맴믝ꡄ뙱륷듺볒ꮬ꒧ꓱ룻 ꗑ꧳ꕾ맴꒧믝ꡄ뙱녠ꙝ뛗뉶꒧ꩩ냊ꛓ뻉교믝ꡄ뙱ꝥꙖꑗꙖꑕ쇍뛕꒧뉻뙈ꅃꙝꚹꅁ굙ꕈꖭꞡ믝ꡄ뙱낵결NIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅁ녎뻉교꙳뙱볒ꮬ늣ꗍ낪꛴ꝃ꛴믝ꡄ꒧뉻뙈ꅃꖻ곣ꡳ결룑ꡍNIR-EOQ꙳뙱볒ꮬ꒤ꅁꖭꞡ믝ꡄ뙱꧒늣ꗍꪺ꙳뙱놱꣮냝썄ꅁ뻚GARCH볒ꮬꅁ낵결ꕾ맴믝ꡄ뙱륷듺꒧냲슦ꅁꛓ땯깩ꕘAR-GARCH륷듺볒ꮬꅃꕂꙝ껉뚡Ꟈꙃ룪껆ꅁ녠ꕘ뉻ꭥ듁꒧ꖿꙖ뭐굴Ꙗꩩ냊ꅁꙝꛓ맯ꑕꑀ듁녎늣ꗍ꒣Ꙑ땻ꯗ꒧뱶암ꅃꙝꚹꅁꖻ곣ꡳ뻚TGARCH볒ꮬ땯깩ꕘAR-TGARCH륷듺볒ꮬꅃ Ꙣ곣ꡳ떲ꩇ꒤땯뉻ꅁAR-TGARCH볒ꮬꙢꕾ맴믝ꡄ뙱륷듺셚껄ꑗꧺ엣쁵꧳AR-GARCH볒ꮬꅃ꓀꩒꣤떲ꩇꅁꗑ꧳AR-TGARCH볒ꮬ싇ꗑꕾ맴믝ꡄ뙱득깴꒧ꖿꅂ굴Ꙗ낵결꓀곉쉉ꅁ녎AR-GARCH볒ꮬ꓀결꣢귓ꭄ뵵꧊AR-GARCH볒ꮬꅁ꓀ꝏ낻듺ꭥꑀ듁ꖿꅂ굴Ꙗ꒧엜냊ꅃꙝꚹꅁAR-TGARCH볒ꮬ맯꧳ꖿꙖꩩ냊뵵Ꙗ꒧낻듺ꧺ엣쁵꧳AR-GARCHꅃ ꅝ2ꅞ?Lagrange궼볆뭐꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧ꯘ멣 뫮Ꙙ꒧ꭥ뎹론꧒굺ꅁꖻ곣ꡳꕄ굮싇ꗑLagrange궼볆귗ꖿ돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬꅃꗑ꧳돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ삳ꗎ꧳Ꙑ껉ꛒ뱻꣢뚵ꕾ맴꙳뙱놱꣮껉ꅁꙝꖼꛒ뱻ꕾ맴꙳뙱셠썂꒧ꑗ궭ꛓ꣏녯돦뚵ꚡꕾ맴 67
NIR-EOQ꙳뙱볒ꮬ뭐Ꙑ껉ꛒ뱻꣢뚵ꕾ맴꒧놡ꩰ늣ꗍ깴늧ꅃꙝꚹꅁꖻ곣ꡳ륂ꗎLagrange궼볆녎꙳뙱셠썂꒧궭꣮ꕛꑊ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧꒤ꅁꕈ듁꣏꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꿠궰ꝃꙝ꙳뙱ꑗ궭꧒뻉교꙳뙱놱꣮꒧뭾깴ꅃ껚뻚꒧ꭥ뎹론꧒굺ꅁ녎Lagrange궼볆ꕛꑊ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒤ꅁꕈ뙩ꛦ돌꣎꓆ꡄ룑껉녎꣼꣬Lagrange궼볆꒧뱶암ꅃꕂꙝLagrange궼볆결ꑀꭄ굴꒧궼볆ꅃ굙껚뻚KKT뇸ꗳꅝ꒽ꚡꅝꅞ뭐ꅝꅞꅞꅁꭨ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꧒ꡄ룑ꕘ꒧돌꣎꙳뙱녎ꑰ꧳돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧돌꣎꙳뙱ꅃ 껚뻚ꖻ곣ꡳ꒧맪쏒곣ꡳ땯뉻ꅁ꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꧒ꡄ룑ꕘꕾ맴돌꣎꙳뙱엣뗛ꑰ꧳돦뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꧒ꡄꕘ꒧ꕾ맴돌꣎꙳뙱ꅃꕂ굙뻚ꡃꑀ돦ꛬ꙳뙱셠ꚨꖻ돌ꑰ꓆꒧ꗘ볐ꚡꅝ꒽ꚡꅝꅞꅞꕩꪾꅁ돌꣎꙳뙱꒧군뫢떲ꩇ녎맯셠ꚨꖻ덹ꚨꑀꪽ놵꒧뱶암ꅃ럭돌꣎꙳뙱뙱궰ꝃ껉ꅁ녎덳녡뻉교셠ꚨꖻ꒧ꑕ궰ꅃꗧꝙꅁ럭NIR-EOQ볒ꮬ꿠ꡄ룑ꕘꟳ뫫뵔꒧돌꣎꙳뙱껉ꅁ녎ꚳꝕ꧳셠ꚨꖻ꒧궰ꝃꅃ ꅝ3ꅞ?ꕾ맴믝ꡄ뙱륷듺볒ꮬ뭐꣢뚵ꚡNIR-EOQ꙳뙱볒ꮬ떲Ꙙ륂ꗎ ꑀ꿫ꛓꢥꅁNIR-EOQ꙳뙱볒ꮬꞡ걏륂ꗎꖭꞡ믝ꡄ뙱낵결볒ꮬ꒧뿩ꑊ엜볆ꅃ땍ꛓꅁꙢ믝ꡄ뙱ꝥ뉻Ꙗꑗ뚵ꑕ꒧쇍뛕껉ꅁ녎교꣏NIR-EOQ꙳뙱볒ꮬꕘ뉻뭐맪믚뉻뙈꒣닅꒧뉻뙈ꅃꙝꚹꖻ곣ꡳ링룕뒣ꕘAR-GARCH뭐AR-TGARCH볒ꮬꅁꕈ떽NIR-EOQ꙳뙱볒ꮬ뿩ꑊ엜볆꒧꿊ꖢꅃ 덺륌닄ꕼ뎹꒧맪쏒꓀꩒녯ꪾꅁ굙ꕈꖭꞡ믝ꡄ뙱볒ꮬ낵결꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅁ녎늣ꗍ룻ꑪ꒧꙳뙱놱꣮낾깴ꅃꙐ껉ꅁꗧ덹ꚨ셠ꚨꖻ꒧뱗ꕛꅃ꒧ꅁ굙ꕈAR-GARCH뭐AR-TGARCH볒ꮬ꒧륷듺떲ꩇ낵결꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ꒧뿩ꑊ엜볆ꅁꭨ꣤셠ꚨꖻ녎ꕘ뉻엣뗛꒧ꑕ궰ꅃꚹꕾꅁꙢꗽꭥ꒧꓀꩒꒤ꗧꚳ뒣ꅁꙢꖻ곣ꡳ꧒륂ꗎꪺ꣢뫘륷듺볒ꮬ꒤ꅁꕈAR-TGARCH볒ꮬ꒧륷듺셚껄룻꣎ꅃꙝꚹꅁ굙뙩ꑀꡂꓱ룻AR-GARCH뭐AR-TGARCH볒ꮬ륂ꗎ꧳꣢뚵ꚡꕾ맴NIR-EOQ꙳뙱볒ꮬ떲ꩇꅁꕩꕈ땯뉻 68
AR-GARCH볒ꮬꙢ륷듺떲ꩇꑗꕘ뉻뎡ꗷꝃ꛴꒧뉻뙈ꅃꙝꛓꅁ뻉교꣤꯹ꚳꚨꖻꑕ궰룉덦ꚨꖻꕘ뉻ꑗ꒧쇍뛕ꅃꛓꚹꑀ뉻뙈뻉교AR-GARCH볒ꮬꙢ꙳뙱놱꣮ꑗ늣ꗍ룻AR-TGARCH볒ꮬ결낪ꪺ셠ꚨꖻꅃ꣣엩ꛓꢥꅁAR-GARCH볒ꮬꙢ꙳뙱볒ꮬ꒤꒧셚껄쇶룻ꖭꞡ믝ꡄ뙱볒ꮬ결꣎ꅁ꒴룻AR-TGARCH볒ꮬ결깴ꅃꙝꚹꅁꕩꕈ뵔뭻ꪺ걏뫫뵔꒧ꕾ맴믝ꡄ뙱륷듺떲ꩇ녎ꚳꝕ꧳셠ꚨꖻ꒧궰ꝃꅃ 곣ꡳ궭꣮ 덂뉺ꕾ맴꙳뙱냝썄결ꑀ냊멁꒧냝썄ꅃꙝꚹꅁꥼꕩ꿠궱셻ꑀꝸ쏸ꯗꅃꙝꚹꅁꖻ곣ꡳ꧒ꚨ꒧궭꣮ꅁ삳ꕩ쉫덛결ꕈꑕꑔ쉉ꅇ ꅝ1ꅞ?ꗑ꧳믈ꛦꙢ뙩ꛦꕾ맴ꗦ꧶껉ꅁ꧒ꛒ뙱ꪺ궫쉉꒣뛈ꓮ꧳ꖼ꣓압ꯈꖫ돵믈ꛦ뚡ꖫ돵맯ꕾ맴꒧믝ꡄꅃꥼꕝꝴ결ꙝ삳ꖼ꣓뛗뉶ꩩ냊꒧깍ꝑ뭐쇗쁉ꛦ결꧒늣ꗍ꙳뙱꒧꯹ꚳꛦ결ꅃꛓꖻ곣ꡳ뛈끷맯압ꯈꖫ돵믈ꛦ뚡ꖫ돵꒧믝ꡄ뙱룪껆뙩ꛦ놴끑ꅃ ꅝ2ꅞ?Ꙣ륷듺믈ꛦ꒧ꕾ맴믝ꡄ뙱껉ꅁ뇄뽗ꗟ꒧륷듺ꓨꚡꅃ땍ꛓꅁꙢ냪꒺믈ꛦ꧒꯹ꚳ꒧ꖻ냪덦맴ꚳꑀꥷ꒧뎡ꛬ궭꣮ꅃꙝꛓ럭믈ꛦꕈ띳ꕸ맴ꝉ과꒸꒧ꓱ꣒뱗ꕛ껉ꅁꭨꕈ띳ꕸ맴ꝉꓩ뛪꒧ꓱ꣒녎라ꑕ궰ꅃꚹ뫘ꕾ맴뛗ꝉ껉ꅁꕾ맴꒧뚡ꖲ땍꙳Ꙣ꒬냊쏶ꭙꅁ땍ꛓꖻ곣ꡳ결슲꓆군뫢낲덝꣤꒣꣣꒬냊쏶ꭙꅁꚹ녎뻉교곣ꡳ꒧떲ꩇ뭐뉻맪꒧놡맒ꚳ꧒깴늧ꅃ ꅝ3ꅞ?결슲꓆ꖻ곣ꡳ꧒뒣ꕘ꒧볒ꮬ꒧군뫢ꅁꙢ믈ꛦꕾ맴꯹ꚳꚨꖻ뛈ꛒ뱻뛗뉶뭐ꝑ꺧꒧ꩩ냊ꅃ땍뛗뉶꒧ꩩ냊냟ꑀ냊멁륌땻ꅁꙝꚹ굙ꕈ꽂냊뛗뉶꣓군뫢ꅁꭨ믝ꕈ뿯뻜앶볒ꮬ꣓뙩ꛦ군뫢ꅃꚹ뫘볒ꮬ륂뫢쇶룻꫱뉻맪꒧놡맒ꅁ꣤뛕ꖲ뱗ꕛ볒ꮬ륂뫢꒧뷆싸꧊ꅁꙝꚹꅁꙢ곣ꡳ꒤귌뛈ꛒ뱻ꕈꥷ뛗뉶꒧ꓨꚡ꣓뙩ꛦꅃ 69
ꯡ쓲곣ꡳꯘ쒳 ꖻ곣ꡳ귬륷군땯깩꣬꣢뚵ꚡꕈꑗ꒧ꕾ맴꙳뙱볒ꮬꅁꙝ쎪꧳곣ꡳ껉뚡뭐볆뻇륂뫢꒧궭꣮ꛓ뛈땯깩ꛜ꣢뫘ꕾ맴꒧꙳뙱볒ꮬꑷ빁Ꙙ꧳냪꒺ꕾ뛗믈ꛦ꒧꣏ꗎꅃꙝ냪꒧ꕾ뛗ꖫ돵꒤과꒸꒧ꗦ꧶뙱뮷뙗륌꣤ꕌ맴ꝏ꒧ꗦ꧶뙱ꅃ둎ꕈꖻ곣ꡳ꒧귓껗룪껆ꛓꢥꅁ과믈ꛦ꒧ꗦ꧶ꓱ꣒낪륆82ꉍꅁꛓ볚꒸뛈3ꉍꅃꙝꚹꅁ굙ꕈꙨ뫘덦맴꙳뙱볒ꮬ뙩ꛦ놴끑ꅁ녎ꑪꑪ뱗ꕛ볒ꮬꙢ돌꣎꓆꒧ꡄ룑ꑗ꒧뷆싸ꯗꅁꗧ녎궰ꝃ볒ꮬꙢ맪냈ꑗ꒧삳ꗎꅃ땍ꛓꅁ맯ꯡ쓲곣ꡳꛓꢥꅁꕩ덺륌꒣Ꙑ꙳뙱볒ꮬ꒧ꯘ멣ꅁ꣏ꗎ꣤ꕌꭄ뵵꧊돌꣎꓆ꓨꩫ궰ꝃꙨ뫘덦맴꙳뙱볒ꮬ꒧뷆싸ꯗꅃ꣤ꚸꅁꙢꖻ곣ꡳ꒧귓껗꓀꩒꒤ꕩꕈ땯뉻ꅁ믝ꡄ뙱륷듺볒ꮬ맯꧳꙳뙱놱꣮볒ꮬꙢ꣢뚵ꚡNIR-EOQ꙳뙱놱꣮ꑗꚳ엣뗛꒧ꕜ껄ꅃꙝꚹꅁꯡ쓲곣ꡳꕩ덺륌꣤ꕌ끝냈륷듺ꓨꩫ꙰ꅁCARRꅝConditional Autoregressive Range ModelꅞOrthogonal GARCH떥꣤ꕌ끝냈륷듺볒ꮬ륂ꗎ꧳꒣Ꙑꕾ맴꙳뙱놱꣮볒ꮬꅃꟳꕩ뙩ꑀꡂ뵔뭻믈ꛦꕾ맴꙳뙱놱꣮맯믈ꛦꕾ맴뫞뉺셚껄꒧떽ꅃ 70
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31. ꓽꓥꅁꅵ꙳덦놱꣮뭐ꕾ뛗ꓩ꒺믹뙱꒧쏶ꭙ곣ꡳꅶꅁ냪ꗟ멛ꑪ뻇냪믚ꗸ띾곣ꡳ꧒뫓ꑨ뷗ꓥꅁ2000ꅃ 32. ꓽꓬ땞뵳뗛ꅁꅵꗍ늣뫞뉺ꅶꅁꕸꅁꕸ왗둟ꓥ꒽ꕱꅁ1995ꅃ 33. ꓽ쒣뾳ꅁꅵ냪뿄꣮ꯗ뭐걆떦ꅶꅁ끝걆뎡뿄ꞽꅁ1999ꅃ 34. ꩌ뙩끝ꥍ뛀쑒둦ꅁꅵ믈ꛦ과꙳뙱ꓴ럇꒧곣ꡳꅶꅁ뫞뉺뭐꡴닎ꅁ닄ꕼꣷꅁ닄ꑇ듁ꅁ17-26궶ꅁ1997ꅃ 35. ꩌ랡뚯ꅁꅵ꒣맯뫙GARCH볒ꮬ꒧ꯘꗟ:냪늼ꖫ돵꒧맪쏒곣ꡳꅶꅁ냪ꗟ꒤ꑳꑪ뻇ꗸ띾뫞뉺곣ꡳ꧒돕ꑨ뷗ꓥꅁ1997ꅃ 36. ꮸꓥ꧉ꅁꅵ늼돸륓륷듺늣ꕘ꒧꒣맯뫙꧊껄ꩇꅶꅁꡰꗟ뉈ꚿꑪ뻇끝냈뿄뫓ꑨ뷗ꓥꅁ1997ꅃ 37. 녩늱쉅ꅁꡌꞵ띏ꅁꝤ꺶엯ꅁꩌ꧳ꟶꅁꟵ녯늱ꅁꓽꙷ늻ꅁ룫듉ꦾꥍ남ꓟ꧉ꅁꅵꗍ늣군땥뭐뫞뉺ꅶꅁ1998ꅃ 38. 뎢쳉솾ꅁꅵꕢ뻉엩덝돆꣑삳냓꒧Ꟗ덴걹냊륳ꗳ꙳덦볒ꚡꅶꅁꡰꗟ믊뛇ꑪ뻇뫞뉺곬뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅁ2002ꅃ 39. 뎯ꓟꑀꅁꅵ땵듁뛗뉶륷듺ꅇARIMA뭐GARCH볒ꮬ꒧ꓱ룻곣ꡳꅶ냪ꗟ꒤ꑳꑪ뻇끝냈뫞뉺곣ꡳ꧒뫓ꑨ뷗ꓥꅁ1996ꅃ 40. 빇ꓑ뱷ꅁꅵARMA-TGARCH볒ꮬ꒧ꯘꗟꅶꅁ냪ꗟꗦ덱ꑪ뻇롧샧뫞뉺곣ꡳ꧒뫓ꑨ뷗ꓥꅁ2002ꅃ 74
뿽A 볚꒸ꗦ꧶뙱꒧땻ꚡ냵ꛦ떲ꩇ 㘬〰?㐬〰?㈬〰?〬〰?㠬〰?㘬〰?㐬〰?㈬〰? 맏 볚꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ $26,000$24,000$22,000$20,000$18,000$16,000$14,000$12,000 맏 볚꒸ꗦ꧶뙱ꢫ뛕맏ꅝꅞ 75 㤰꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ?ꓩ㤰꙾?ꓫ?ꓩ㤱꙾?ꓫㄱꓩ㤱꙾?ꓫㄳꓩ㤰꙾?ꓫ?ꓩ㤱꙾?ꓫㄵꓩ㤰꙾ㄱꓫ?ꓩ㤱꙾?ꓫㄷꓩ㤱꙾?ꓫㄹꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ㈱ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ㈳ꓩ㤱꙾?ꓫ㈵ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ㈷ꓩ㤱꙾?ꓫ㈹ꓩ㤱꙾?ꓫ?ꓩ㤱꙾?ꓫ㌱ꓩ
ꫭ 볚꒸믝ꡄ뙱볒ꮬ륷듺떲ꩇ셚껄ꓱ룻 ꓩ듁 2002꙾8ꓫꅝ왛듺귈ꅞ 2002꙾8ꓫꅝ륷듺귈ꅞ 볚꒸ 볚꒸ꅝAR-GARCHꅞ 볚꒸ꅝAR-TGARCHꅞ 8/01 19, 19, 18, 8/02 17, 17, 16, 8/03 20, 18, 19, 8/04 21, 19, 20, 8/05 18, 19, 21, 8/08 18, 17, 17, 8/09 17, 17, 17, 8/10 20, 18, 19, 8/11 19, 19, 20, 8/12 18, 18, 19, 8/15 20, 17, 21, 8/16 16, 17, 17, 8/17 19, 17, 18, 8/18 17, 18, 18, 8/19 21, 18, 20, 8/22 22, 19, 23, 8/23 19, 17, 21, 8/24 18, 16, 17, 8/25 18, 17, 17, 8/26 19, 17, 18, 8/29 18, 18, 19, 8/30 19, 18, 19, 8/31 20, 19, 22, Total443, 421, 444, MAD--------------------- 1, 1, RMSE--------------------- 1, 1, MAPE--------------------- 76
왛듺귈륷듺귈㈵ⰵ〰㈳ⰵ〰㈱ⰵ〰ㄹⰵ〰ㄷⰵ〰ㄵⰵ〰ㄳⰵ〰?????????ㄱㄲㄳㄴㄵㄶㄷㄸㄹ㈰㈱㈲㈳ 맏 볚꒸AR-GARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ 왛듺귈륷듺귈㈵ⰵ〰㈳ⰵ〰㈱ⰵ〰ㄹⰵ〰ㄷⰵ〰ㄵⰵ〰ㄳⰵ〰?????????ㄱㄲㄳㄴㄵㄶㄷㄸㄹ㈰㈱㈲㈳ 맏 볚꒸AR-TGARCH볒ꮬ꒧륷듺떲ꩇꅝ2002꙾8ꓫꅞ 77
