࠹݂߭ଆඔऌކٚمᄜษં
ඔ࿐ࡹଆ֥ࠎЧٚمࠏٳ༅ҩ൫ٳ༅ႮႿग़ܴ൙ଽ҆ܿੰ֥گᄖࠣದૌಪ്ӱ؇֥ཋᇅ,مٳ༅ൌ࠽ؓའଽᄝ֥ၹݔܱ༢đࡹ৫ކެࠏܿੰ֥ඔ࿐ଆb๙ݖؓඔऌ֥࠹ٳ༅đᅳԛაඔऌކቋݺ֥ଆ݂߭ଆ൞Ⴈ࠹ٳ༅ٚمࡹ৫֥ቋӈႨ֥၂োଆ•҂ട݂ࠣ߭ٳ༅֥ඔ࿐ჰބٚم•๙ݖൌ২ษંೂޅ࿊ᄴ҂ো֥ଆ•ؓೈࡱ֤֥֞ࢲݔࣉྛٳ༅đؓଆࣉྛڿࣉ
࠹݂߭ଆ1 ֥ۛཧ൲ਈ2 ೈࡱषؿದჴ֥ྈࣁ3 ઽ՜ّႋ4 ሧحაݓളӁሹᆴބࡎᆷඔ
1֥ۛཧ൲ਈࡹ৫ۛཧ൲ਈაࡎ۬aܼۡೆᆭࡗ֥ଆ໙ყҩᄝ҂ࡎ۬ބܼۡٮႨ༯֥ۛཧ൲ਈี൬ࠢਔ30۱ཧ൲ᇛ௹Ч܄ඳۛཧ൲ਈaࡎ۬aܼۡٮႨđࠣ௹ఃӌࡅো֥ۛन൲ࡎཧ൲Ч܄ඳࡎఃӌࡅܼۡٮႨࡎ۬ҵཧ൲ਈ۬(ჭ)ࡎ۬(ჭ)(Ϥຣჭ)(Ϥຣᆦ)ᇛ௹čჭĎ………………
10yࠎЧଆ ~܄ඳۛཧ൲ਈ~ఃӌࡅაЧ܄ඳࡎ۬ҵ~܄ඳܼۡٮႨ=β+βx+βx+βx+εy=β+βx+ε011223201110yy~ФࢳэਈčၹэਈĎ, x~ࢳэਈ(݂߭эਈ, ሱэਈ) β, β, β, β~݂߭༢ඔε~ෛࠏ༂ҵčनᆴູਬ֥=β+βx+βx+εᆞٳ҃ෛࠏэਈĎ01222
MATLAB ࠹۽ऎདଆࢳ2y=β+βx+βx+βx+εႮඔऌy,x,xܙ࠹β011223212[b,bint,r,rint,stats]=regress(y,x,alpha)ൻೆy~nົඔऌཟਈൻԛb~β֥ܙ࠹ᆴ2bint~b֥ᇂྐࡗx= [1 x x x ] ~n×4ඔ122ऌइᆔ, ֻ1ਙູಆ1ཟਈr~җҵཟਈy-xbrint~r֥ᇂྐࡗalpha(ᇂྐඣ,)ҕඔҕඔܙ࠹ᆴᇂྐࡗStats~β[ ]0ဒ࠹ਈβ[ ]12βR,F, [ ]β[ ]2R= F= p=
2ࢲݔٳ༅y=β+βx+βx+βx+ε0112232ҕඔҕඔܙ࠹ᆴᇂྐࡗβ[ ]0β[ ]1β[ ]β[ ]2R= F= p=֥%ॖႮଆಒקFჹӑݖFဒ֥ਢࢸᆴpჹཬႿα=ଆՖᆜุഈुӮ৫β֥ᇂྐࡗЇݣਬׄxؓၹэਈy ֥22(Ⴗ؊ׄएਬׄޓ࣍) ႕ཙ҂ཁᇷ2xཛཁᇷॖࡼxЌᄝଆᇏ22
2ˆˆˆˆཧ൲ਈყҩˆy=β+βx+βx+βx0112232ࡎ۬ҵx=ఃӌࡅࡎ۬x-Ч܄ඳࡎ۬x134๙ݖx, xყҩyܙ࠹xטᆜx॥ᇅx12341॥ᇅࡎ۬ҵx=ჭđೆܼۡٮx=650ຣჭ122ˆˆˆˆˆy=β+βx+βx+βx=(Ϥຣᆦ)0112232ཧ൲ਈყҩࡗູ[đ]čᇂྐ؇95%ĎഈཋႨቔ९թ֥ܵଢѓᆴ༯ཋႨটϜ܄ඳ֥གྷࣁੀܙ࠹x=đഡקx=đᄵॖၛ95%֥Ϝ34ᆩ֡ཧ൲حᄝ×≈29čϤຣჭĎၛഈ
2y=β+βx+βx+βx+εଆڿࣉ0112232ҕඔҕඔܙ࠹ᆴᇂྐࡗxބxؓy12β[ ]0֥႕ཙ৫β[ ]1β[ ]2βxބxؓ[ ]122R= F= p=֥႕ཙႵ2y=β+βx+βx+βx+βxx+εࢌቔႨ0112232412ҕඔҕඔܙ࠹ᆴᇂྐࡗβ[ ]0β[ ]1β[ ]β[ ]3β[ ]42R= F= p=
ਆଆཧ൲ਈყҩбࢠ॥ᇅࡎ۬ҵx=ჭđೆܼۡٮx=Ϥຣჭ12ˆy=(Ϥຣᆦ)2ˆˆˆˆˆy=β+βx+βx+βx0112232ࡗ[đ]ˆy=(Ϥຣᆦ)2ˆˆˆˆˆy=β+βx+βx+βx+βxx0112232412ࡗ[đ] ˆyႵᄹࡆყҩࡗӉ؇۷؋
ˆyਆଆაx
xܱ༢֥бࢠ1222ˆˆˆˆˆˆˆˆˆˆy=β+βx+βx+βx+βxxy=β+βx+βx+βx01122324120112232ˆˆ=ˆyˆ=
2ˆˆˆˆˆy=β+βx+βx+βx+βxxࢌቔႨ႕ཙ֥ษં01122324122ˆy=−+ࡎ۬ҵx= x=ˆy=−+ࡎ۬ҵx==ˆˆˆy>yx<==ࡎ۬Ⴊ൝߶ཧ൲ਈᄹࡆ9x1==ࡆնܼۡೆཧ൲ਈᄹࡆ8čxնႿ6ϤຣჭĎࡎ۬ҵࢠཬൈᄹࡆࡎ۬ҵࢠཬൈ۷ླေौܼ֥ۡੱ۷նট་ႄܤग़֥င౯
ປಆؽՑ؟ཛൔଆ22y=β+βx+βx+βxx+βx+βx+ε011223124152MATLABᇏႵଁrstoolᆰࢤࢳˆˆˆˆˆˆˆˆβ=(β,β,β,β,β,β)ՖൻԛExport ॖ֤012345
2 ೈࡱषؿದჴ֥ྈࣁࡹ৫ଆ࣮ྈࣁაሧaܵᄳa࢝ტӱ؇֥ܱ༢ٳ༅ದ൙Ҧ֥ކྟđቔູྍௗႨದჴྈࣁ֥ҕॉ46ೈࡱषؿದჴ֥֖σሧਘщྈࣁሧܵ࢝щྈࣁሧܵ࢝ݼტݼტ011387611142278371612021160810343188381602031870111344174831601041128310245192071702……………46193462001ሧ~ Ֆ൙ህြ۽ቔ୍֥ඔĠܵ~ 1 ܵದჴđ0 ٤ܵದჴĠ࢝ტ~1 ᇏ࿐đ2 ն࿐đ3 ۷ۚӱ؇
y~ ྈࣁđx~ሧč୍Ďٳ༅აࡌഡ1 x 1~ ܵದჴđx 0~ ٤ܵದჴ2 2 1,ᇏ࿐⎧x=1 ᇏ࿐⎨3ᇏ࿐ğx=1, x=0 Ġ࢝340,ః⎩2 ն࿐ტն࿐ğx=0, x=1Ġ341,ն࿐⎧ۚx=3 ۷⎨4۷ۚğx=0, x=0 340,ః⎩ሧૄࡆ၂୍ྈࣁ֥ᄹӉ൞ӈඔĠܵa࢝ტaሧᆭࡗࢌቔႨy=a+ax+ax+ax+ax+εཌྟ݂߭ଆ011223344a, a, …, a൞րܙ࠹֥݂߭༢ඔđε൞ෛࠏ༂ҵ014
ଆࢳy=a+ax+ax+ax+ax+ε011223344ሧᄹࡆ1୍ྈҕඔҕඔܙ࠹ᆴᇂྐࡗࣁᄹӉ546 a11032[ 10258 11807 ]0a546[ 484 608 ]1ܵದჴྈࣁ؟a6883[ 6248 7517 ]6883 2a-2994[ -3826 -2162 ]3ᇏ࿐ӱ؇ྈࣁб۷a148[ -636 931 ]4֥ۚഒ2994 2R= F=226 p=ն࿐ӱ؇ྈࣁб۷2R,F, p→ଆᆜุഈॖႨ֥ۚ؟148 x~ሧ ୍
ᇏ࿐ğx=1, x=0;ն134aᇂྐࡗЇݣਬ4࿐ğx=0, x=1; ۷x 1~ ܵđx342 2 ׄđࢳ҂ॖौ 0~ ٤ܵۚğx=0, x=0. 34
ܵა࢝ტ֥ቆކҗҵٳ༅ٚمࢲݔٳ༅123456ቆކˆˆˆˆˆˆy=a+ax+ax+ax+ax011223344010101ܵˆe=y−yҗҵ112233࢝ტe აሧx֥ܱ༢eაܵ—࢝ტቆކ֥ܱ༢1200020001000100000-1000-1000-2000-200005101520123456җҵಆູᆞđࠇಆູڵđܵҗҵնۀٳӮ3۱ඣđ—࢝ტቆކԩ҂֒6ᇕܵ—࢝ტቆކࠁᄝႋᄝଆᇏᄹࡆܵxა࢝ტ2၂ఏđໃᆞಒّ႘bx, x֥ࢌཛ34
ᄹࡆܵxა࢝ტx, x֥ࢌཛࣉ၂֥҄ଆ234y=a+ax+ax+ax+ax+axx+axx+ε011223344523624500ҕඔҕඔܙ࠹ᆴᇂྐࡗ0a11204[11044 11363]0a497[486 508]-5001e ~ x1a7048[6841 7255]2-100005101520a-1727[-1939 -1514]3500a-348[-545 –152]40a-3071[-3372 -2769]5-500a1836[1571 2101]e ~ቆކ62-1000R= F=554 p=
FႵڿࣉđ෮Ⴕ݂߭༢ඔᇂྐཨԢਔ҂ᆞӈགྷའࡗ҂ݣਬׄđଆປಆॖႨၳӈඔऌ 33ݼ
ႋಀו
ಀוၳӈඔऌު֥ࢲݔ200e ~ x1ҕඔҕඔܙ࠹ᆴᇂྐࡗ100a11200[11139 11261]00-100a498[494 503]1-200a7041[6962 7120]051015202200a-1737[-1818 -1656]e ~ቆކ3100a-356[-431 –281]40a-3056[-3171 –2942]5-100a1997[1894 2100]6-2002123456R= F=36701 p=ğ → →җҵٳᆞӈFğ226 →554 →36701 ቋᇔଆ֥ࢲݔॖၛႋႨᇂྐࡗӉ؇۷؋
ˆˆˆˆˆˆˆˆy=a+ax+ax+ax+ax+axx+axxଆႋႨ011223344523624ᇅר6ᇕܵ—࢝ტቆކದჴ֥“ࠎԤ”ྈࣁ ሧູ0Ďx 0Ġx 1~ ܵđx 0~ ٤ܵ12 2 ᇏ࿐ğx=1, x=0 Ġն࿐ğx=0, x=1Ġ۷ۚğx=0, x=0 343434“ࠎԤ”ྈࣁቆކܵ࢝ტ༢ඔ101a+a946303211a+a+a+a134480235302a+a1084404412a+a+a+a198820246503a112000613a+a1824102ն࿐ӱ؇ܵದჴб۷ۚӱ؇ܵದჴ֥ྈࣁۚն࿐ӱ؇٤ܵದჴб۷ۚӱ؇٤ܵದჴ֥ྈࣁ֮
ೈࡱषؿದჴ֥ྈࣁؓקྟၹ ೂܵa࢝ტ
đॖၛႄೆ0 1эਈԩđ0 1эਈ֥۱ඔႋбקྟၹ֥ඣഒ1 җҵٳ༅ٚمॖၛؿགྷଆ֥ಌཊđႄೆࢌቔႨཛӈӈିܔڿଆัԢၳӈඔऌđႵᇹႿ֤֞۷ݺ֥ࢲݔᇿğॖၛᆰࢤؓ6ᇕܵ—࢝ტቆކႄೆ5۱0 1эਈ
3ઽ՜ّႋ࣮ઽ՜ّႋčઽբ߄ّႋĎᇏᕷᔒાّؓ໙ႋ؇აָčّႋĎ୩؇ᆭࡗܱ༢֥႕ཙีࡹ৫ඔ࿐ଆđّ႘ھઽ՜ّႋ֥؇აָ୩؇ၛࠣࣜᕷᔒાԩაڎᆭࡗ֥ܱ༢ٚഡ࠹ਔਆ۱ൌဒğઽࣜݖᕷᔒાԩĠઽໃσࣜᕷᔒાԩbൌဒඔऌ༯і:ָ୩؇(ppm)ԩ764797739921170ّႋ؇111312141516ໃԩ6751848698/514480
ཌྟ߄ଆβx11β1112y==+=θ+θ12β+xyββxx211ؓβ, β٤ཌྟؓθ, θཌྟ1212ࣜᕷᔒાԩުൌဒඔऌ֥ܙ࠹ࢲݔ--3ҕඔҕඔܙ࠹ᆴč10ᇂྐࡗč10Ď3Ďθ[ ]1θ[ ]22R= F= p=ˆˆˆˆˆβ=θ/θ=β=1/θ=
ཌྟ߄ଆࢲݔٳ༅1/=θ+θβ=β+
٤ཌྟଆҕඔܙ࠹MATLAB ࠹۽ऎད[beta,R,J] = nlinfit(x,y,’model’,beta0) βxൻೆ1x~ሱэਈඔऌइᆔbeta0~ཌྟ߄y=β+xଆܙ࠹ࢲݔ2y ~ၹэਈඔऌཟਈx= ; y= ;model ~ଆ֥ݦඔM໓ࡱbeta0=[ ];beta0 ~۳ק֥ҕඔԚᆴ[beta,R,J]=nlinfit(x,y,’f1’,beta0);beta ~ҕඔ֥ܙ࠹ᆴൻԛbetaci=nlparci(beta,R,J);R ~җҵđJ ~ܙ࠹ყbeta, betaciҩ༂ҵ֥Jacobiइᆔfunction y=f1(beta, x)beta֥ᇂྐࡗy=beta(1)*x./(beta(2)+x);betaci=nlparci(beta,R,J)
βx1٤ཌྟଆࢲݔٳ༅y=β+x2ҕඔҕඔܙ࠹ᆴᇂྐࡗ250β[ ]β[ ]ˆቋᇔّႋ؇ູβ= ~ჰඔऌ϶؇ׄ(ղ֞ቋᇔ؇၂϶+ ~ ކࢲݔ50ˆ0β=ൈ֥xᆴ)ູఃൻԛଁnlintool۳ԛࢌ߂૫250߂૫֥ሳཌđ֤200y֥ყҩᆴބყҩࡗ150100߂૫ቐ༯֥ٚExport 50ൻԛః࠹ࢲݔഺჅѓሙҵs=
ࠁކّႋଆᄝ၂ଆᇏॉ੮ᕷᔒાԩ֥႕ཙβxčβ+γxĎx11121y=y=β+x(β+γx)+x22221xָູ୩؇đxູ၂ൕྟэਈ12x=1іൕࣜݖԩđx=0іൕໃࣜԩ22Ȧ൞ໃࣜԩ֥ቋᇔّႋ؇1ȧ൞ࣜԩުቋᇔّႋ؇֥ᄹӉᆴ1Ȧ൞ໃࣜԩّ֥ႋ֥϶؇ׄ2ȧ൞ࣜԩުّႋ֥϶؇֥ׄᄹӉᆴ2
čβ+γxĎx1121y=ࠁކଆࢳႨnlinfitބnlintoolଁ(β+γx)+x22210000β=170,γ=60β=,γ=,(ࠎႿؓඔऌ֥ٳ༅)ҕඔԚᆴ1122ࣜԩܙ࠹ࢲݔބყҩໃࣜҕඔҕඔܙ࠹ᆴᇂྐࡗԩβ[ 1o ~ჰඔऌ]+ ~ކࢲݔβ[ ]γ[ 1ഺჅѓሙҵs= ]γ[ ᇂྐࡗЇݣਬׄđіૼγؓၹэਈy֥႕ཙ҂ཁᇷ]ࣜᕷᔒાԩ֥ቔႨ҂႕ཙ϶؇ׄҕඔ
čβ+γxĎxčβ+γxĎx11211121ࡥ߄֥ࠁކଆy=y=(β+γx)+xβ+x222121ܙ࠹ࢲݔބყҩҕҕඔܙࣜԩᇂྐࡗඔ࠹ᆴໃࣜԩ[ ]β[ ]βo ~ჰඔऌ2+ ~ކࢲݔ[ ]γ1ࡥ߄֥ࠁކଆྙൔࡥֆđҕඔᇂྐࡗ҂ݣਬׄഺჅѓሙҵs= đб၂Ϯࠁކଆն
၂Ϯࠁކଆაࡥ߄ࠁކଆყҩбࢠčβ+γxĎxčβ+γxĎx11211121ყҩࡗູy=y=β+x(β+γx)+x212221ყҩᆴ±ȐȐ(၂ϮଆĎȐ(ࡥ߄ଆĎൌ࠽ᆴ၂Ϯଆყҩᆴࡥ߄ଆყҩᆴ……………ࡥ߄ࠁކଆ֥ყҩࡗࢠ؋đ۷ູൌႨaႵི
ઽ՜ّႋࠏٳ༅ّႋ؇აָ୩؇֥ܱ༢٤ཌྟܱ༢ࢳཌྟଆࢳ٤ཌྟଆؿགྷ໙ีđ֤ҕඔԚᆴᕷᔒાԩّؓႋ؇აָ୩؇ܱ༢֥႕ཙࠁކଆࡥ߄ଆႄೆ0-1эਈҰҕඔᇂྐࡗ൞ڎЇݣਬׄᇿğ٤ཌྟଆކӱ؇֥ࡎمᆰࢤ০Ⴈ2ཌྟଆ֥ٚمđRაsಯಖႵིb
4 ሧحაݓളӁሹᆴބࡎᆷඔࡹ৫ሧحଆđ࣮ଖֹൌ࠽ሧحაݓ໙ളӁሹᆴ( GNP ) ࠣࡎᆷඔ(PI) ֥ܱ༢ี۴ऌؓໃটGNPࠣPI֥ܙ࠹đყҩໃটሧحھֹ৵࿃20୍֥࠹ඔऌ୍ٺሧحݓളӁࡎ୍ٺሧحݓളࡎݼሹᆴᆷඔݼӁሹᆴᆷඔ
ሧحაݓളӁሹᆴބࡎᆷඔٳྸ؟ࣜ࠶ඔऌᄝൈࡗഈႵ၂ק֥ᇌުྟ༅ၛൈࡗູ֥ඔऌđӫູൈࡗਙൈࡗਙᇏ၂эਈ֥ඨܴҩᆴᆭࡗթᄝሱཌྷܱҐႨ௴๙݂߭ଆᆰࢤԩđࡼ߶ԛགྷ҂ਅުݔླေᆐ؎ѩཨԢඔऌ֥ሱཌྷܱྟđࡹ৫ྍ֥ଆ୍ٺሧحݓളӁࡎ୍ٺሧحݓളࡎݼሹᆴᆷඔݼӁሹᆴᆷඔ……………………
ࠎЧ݂߭ଆt ~୍ٺđy~ ሧحđx~ GNP, x~ ࡎᆷඔt1t2t yyttxx1t2tሧحაGNPࠣࡎᆷඔࡗनႵޓ఼֥ཌྟܱ༢y=β+βx+βx+εβ, β, β~݂߭༢ඔt011t22tt012ε~ؓtཌྷ৫֥ਬनᆴᆞෛࠏэਈt
ࠎЧ݂߭ଆ֥ࢲݔაٳ༅ҕඔҕඔܙ࠹ᆴᇂྐࡗ[ ]β[ ]β[ ]β22R= F= p=ˆy=+−ഺჅѓሙҵt1t2ts= 2RĢđކ؇ۚଆႪׄଆಌׄીႵॉ੮ൈࡗਙඔऌ֥ᇌުྟ႕ཙॖିޭ൪ਔෛࠏ༂ҵթᄝሱཌྷܱĠೂݔթᄝሱཌྷܱྟđႨՎଆ߶Ⴕ҂ਅުݔ
ሱཌྷܱྟ֥קྟᆐ؎җҵᆐ؎مet20ˆe=y−yଆҗҵttt100eູෛࠏ༂ҵε֥ܙ࠹ᆴtt -10ᄝMATLAB۽ቔᇏൻԛ-20e-30ቔҗҵe~eׄt-1tt-1 -30-20-1001020ն҆ٳׄઋᄝֻ1, 3འཋεթᄝᆞ֥ሱཌྷܱtεթᄝڵ֥ሱཌྷܱն҆ٳׄઋᄝֻ2, 4འཋtࠎЧ݂߭ଆ֥ෛࠏ༂ሱཌྷܱྟᆰܴ؎ҵཛεթᄝᆞ֥ሱཌྷܱt
ሱ݂߭ྟ֥קਈᆐ؎D-Wဒy=β+βx+βx+ε,ε=ρε+uሱ݂߭ଆt011t22tttt−1tȵ~ሱཌྷܱ༢ඔ|ρ|≤1β, β, β~݂߭༢ඔ012u~ؓtཌྷ৫֥ਬनᆴᆞෛࠏэਈtȵ=0ሱཌྷܱྟȵ>0թᄝᆞሱཌྷܱྟթᄝڵሱཌྷܱྟȵ<0ೂޅܙ࠹ȵD-W࠹ਈܼၬҵٳمೂޅཨԢሱཌྷܱྟ
nnD-W࠹ਈაD-Wဒ2ˆρ=ee/e∑∑tt−1tnnt=2t=2⎡⎤2(e−e)ee∑tt−1∑tt−1⎢⎥t=2t=2DW=≈⎢⎥21−ˆ=č21−ρĎnn22⎢⎥enࢠնe∑t∑t⎢⎥t=2⎣t=2⎦ˆˆρ=1→DW=0ρ=−1→DW=4ˆ−1≤ρ≤1→0≤DW≤4ˆρ=0→DW=2dd4-d4-d024LUULDW҂ᆞ҂ڵဒඣ
ဢЧಸିሱିሱሱਈđ݂߭эਈඔଢಒཌྷಒཌྷཌྷקܱקܱܱD-Wٳ҃іႮDWᆴ֥նཬಒקሱཌྷܱྟဒਢࢸᆴdބdLU
DWܼၬҵٳэߐˆρ=1−ˆDW=č21−ρĎ2y=β+βx+βx+ε,ε=ρε+uჰଆt011t22tttt−1t**x=x−ρx,i=1,2y=y−ρy,эߐititi,t−1ttt−1*****y=β+βx+βx+uβ=β(1−ρ)ྍଆt011t22tt00*ၛβ, β, βູ݂߭༢ඔ֥௴๙݂߭ଆ012ሱཌྷܱჰଆ҄ᇧܼၬҵٳ࿃ՎD-WჰଆႵሱཌྷܱྍଆݖӱDWᆴဒᄹࡆඔऌਈĠ҂ିಒק࿊Ⴈఃٚم
n2ሧحྍଆ֥ࡹ৫(e−e)∑tt−1t=2DW=n2eDW=∑ჰଆtoldt=2җҵဢЧಸਈn=20đ݂߭ჰଆႵDW<doldLэਈඔଢk=3đα=ᆞሱཌྷܱҰіˆρ=1−DW/2=ਢࢸᆴd=, d=-d4-d024LUULቔэߐDW҂ᆞ҂ڵ*y=y−−1ିሱିሱሱಒཌྷಒཌྷཌྷ*x=x−,i=1,2קܱקܱititi,t−1ܱ
ሧحྍଆ֥ࡹ৫**y=y−=x−,i=1,2ttt−1ititi,t−1****y=β+βx+βx+ut011t22tt****Ⴎඔऌy,x,xܙ࠹༢ඔβđβđβt1t2t012ҕඔҕඔܙ࠹ᆴᇂྐࡗ*β[ ]0β[ ]1β[ ]22R= F= p=ሹุིݔਅݺഺჅѓሙҵs= < s=
dd4-dྍଆ֥ሱཌྷܱྟဒ024-d4LUULDW҂ᆞ҂ڵDW=ྍଆnewିሱିሱሱҗҵಒtཌྷಒཌྷཌྷקܱקܱܱဢЧಸਈn=19đ݂߭d< DW<4-dUnewUэਈඔଢk=3đα=Ұіྍଆሱཌྷܱྟਢࢸᆴd=, d=***ˆy=+−ྍଆt1t2tˆy=++−−11,t1,t−1ߎჰູ−+ჰэਈ2,t2,t−1၂ࢨሱ݂߭ଆ
ଆࢲݔбࢠˆy=+−ࠎЧ݂߭ଆt1t2tˆy=++−−11,t1,t−1၂ࢨሱ݂߭ଆ−+,t2,t−1җҵбࢠކбࢠ20500104000300-10200-201000-300510152005101520ྍଆe~ *đჰଆe~ +ྍଆŷ~ *đྍଆŷ~ +tttt၂ࢨሱ݂߭ଆҗҵeбࠎЧ݂߭ଆေཬt
ሧحყҩؓໃটሧحyቔყҩđླ༵ܙ࠹ԛໃট֥ݓtളӁሹᆴxބࡎᆷඔx1t 2t୍ٺሧحݓളӁࡎ୍ٺሧحݓളࡎݼሹᆴᆷඔݼӁሹᆴᆷඔˆy=၂ࢨሱ݂߭ଆഡၘᆩt=21ൈđx=3312đx= 2tˆy=ࠎЧ݂߭ଆtˆy=၂ࢨሱ݂߭ଆtŷࢠཬ൞ႮႿy=ݖཬ෮ᇁtt-1
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