# Chuong 8 Hien Tuong Tu Tuong Quan

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• CHNG 8HIN TNG T TNG QUAN (Autocorrelation)

• *T TNG QUAN

• NI DUNG*Bn cht hin tng hin tng t tng quan 1Hu qu23Cch khc phc t tng quan 4 Cch pht hin t tng quan

• 8.1 Bn chtT tng quan l g ?L tng quan gia cc sai s ngu nhin.cov(ui, uj) 0(i j)701003- T tng quan*

• T tng quan l g ?701003- T tng quan*Gi s Yt = 1 + 2Xt + ut

AR(p): T tng quan bc put = 1ut-1 + 2ut-2 + + put-p + vt

Qu trnh t hi quy bc p ca cc sai s ngu nhin

• 8.1 Bn chtS tng quan xy ra i vi nhng quan st theo khng gian gi l t tng quan khng gian.S tng quan xy ra i vi nhng quan st theo chui thi gian gi l t tng quan thi gian.

• t(a)ui, eiui, eiui, eiui, eiui, eiHnh 8.1 Mt s dng bin thin ca nhiu theo thi gian

• Nguyn nhn Nguyn nhn khch quan:Qun tnh: cc chui thi gian mang tnh chu k, VD: cc chui s liu thi gian v GDP, ch s gi, sn lng, t l tht nghipHin tng mng nhn: phn ng ca cung ca nng sn i vi gi thng c mt khong tr v thi gian: QSt = 1 + 2Pt-1 + ut tr: tiu dng thi k hin ti ph thuc vo thu nhp v chi tiu tiu dng thi k trc : Ct = 1 + 2It + 3Ct-1 + ut

• Nguyn nhn Nguyn nhn ch quanHiu chnh s liu: do vic lm trn s liu loi b nhng quan st gai gc.Sai lch do lp m hnh: b st bin, dng hm sai.Php ni suy v ngoi suy s liu

• V d b st bin*Vi Y: cu tht bX2: gi tht bX3: thu nhp ngi tiu dngX4: gi tht heot: thi gianM hnh ngM hnh b st bin

• 8.2 Hu qu ca t tng quanp dng OLS th s c cc hu qu:Cc c lng khng chch nhng khng hiu qu (v phng sai khng nh nht)Phng sai ca cc c lng l cc c lng chch, v vy cc kim nh t v F khng cn hiu qu.

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• 8.2 Hu qu ca t tng quan l c lng chch ca 2R2 ca mu l c lng chch (di) ca R2 tng thCc d bo v Y khng chnh xc

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• * thChy OLS cho m hnh gc v thu thp et. V ng et theo thi gian. Hnh nh ca et c th cung cp nhng gi v s t tng quan.8.3 Cch pht hin t tng quan

• t(e) Khng c t tng quana. thetetetetet

• *Thng k d ca Durbin Watson

Khi n ln th d 2(1-) vi

do -1 1, nn 0 d = 2: khng c t tng quan = 1 => d = 0: t tng quan hon ho dngb. Dng kim nh d ca Durbin Watson

• *Bng thng k Durbin cho gi tr ti hn dU v dL da vo 3 tham s: : mc ngha k: s bin c lp ca m hnhn:s quan st b. Dng kim nh d ca Durbin Watson

• *Cc bc thc hin kim nh d ca Durbin Watson:Chy m hnh OLS v thu thp phn sai s et.Tnh d theo cng thc trn.Vi c mu n v s bin gii thch k, tm gi tr tra bng dL v dU.Da vo cc quy tc kim nh trn ra kt lun.

b. Dng kim nh d ca Durbin Watson

• *Nu d thuc vng cha quyt nh, s dng quy tc kim nh ci bin:H0: = 0; H1: > 0Nu d < dU : bc b H0 v chp nhn H1 (vi mc ngha ), ngha l c t tng quan dng.

b. Dng kim nh d ca Durbin WatsonKhng c t tng quan dng

• *2. H0: = 0; H1: < 0Nu d > 4 - dU : bc b H0 v chp nhn H1 (vi mc ngha ), ngha l c t tng quan m.

b. Dng kim nh d ca Durbin WatsonC t tng quan m

• *3. H0: = 0; H1: 0Nu d 4 - dU : bc b H0 v chp nhn H1 (vi mc ngha 2), ngha l c t tng quan (m hoc dng).b. Dng kim nh d ca Durbin Watson

• *Lu khi p dng kim nh d:M hnh hi quy phi c h s chn.Cc sai s ngu nhin c tng quan bc nht: ut = ut-1 + et3. M hnh hi quy khng c cha bin tr Yt-1.

4. Khng c quan st b thiu (missing).b. Dng kim nh d ca Durbin Watson

• Xt m hnh:Yt = 1 + 2Xt + ut (8.1) ut = 1ut-1 + 2ut-2 + + put-p + vtKim nh gi thit H0: 1 = 2 = = = 0 -> khng c AR(p)H1: c t nht mt i khc 0

c. Dng kim nh Breusch Godfrey (BG)(Kim nh nhn t Lagrange)701003- T tng quan*

• *Bc 1: c lng (8.1) bng OLS, tm phn d etBc 2: Dng OLS c lng m hnh et = 1 + 2Xt + 1et-1 + 2et-2 + + pet-p + tt y thu c R2.Bc 3: vi n ln, (n-p)R2 c phn phi xp x 2(p) vi p l bc tng quan.- Nu (n-p)R2 > 2(p): Bc b H0, ngha l c t tng quan t nht mt bc no .- Nu (n-p)R2 2(p): Chp nhn H0, ngha l khng c t tng quan.c. Dng kim nh Breusch Godfrey (BG)

• *Kim nh BG c c im:p dng cho mu c kch thc lnp dng cho m hnh c bin c lp c dng Yt-1 , Yt-2 ..Kim nh c bc tng quan bt kc. Dng kim nh Breusch Godfrey (BG)

• *8.4 Khc phc

• 8.4 Khc phcTrng hp bit cu trc ca t tng quan: Phng php GLS:ut t hi quy bc p, AR(p)ut = 1ut-1 + 2ut-2 + + put-p + vtvi : h s t tng quan; < 1Gi s ut t hi qui bc nht AR(1)ut = ut-1 + et (*)et: sai s ngu nhin (nhiu trng), tha mn nhng gi nh ca OLS:E(et) = 0;Var(et) = 2;Cov(et, et+s) = 0

• Xt m hnh hai bin:yt = 1 + 1xt + ut(8.2)Nu (8.2) ng vi t th cng ng vi t 1yt-1 = 1 + 1xt - 1 + ut - 1 (8.3)Nhn hai v ca (8.3) vi yt-1 = 1 + 1xt - 1 + ut - 1 (8.4)Tr (8.2) cho (8.4)yt - yt-1 = 1(1 - ) + 1 (xt - xt 1) + (ut - ut 1) = 1(1 - ) + 1 (xt - xt 1) + et (8.5) 8.4 Khc phc

• 8.4 Khc phc

(8.5) gi l phng trnh sai phn tng qutt:1* = 1 (1 - )1* = 1 yt* = yt - yt 1xt* = xt - xt 1Khi (8.5) thnhyt* = 1* + 1*xt* + et(8.5*)

• 8.4 Khc phcV et tho mn cc gi nh ca phng php OLS nn cc c lng tm c l BLUE Phng trnh hi qui 8.5* c gi l phng trnh sai phn tng qut (Generalized Least Square GLS). trnh mt mt mt quan st, quan st u ca y v x c bin i nh sau:

• 2. 1 Phng php sai phn cp 1 Nu = 1, thay vo phng trnh sai phn tng qut (8.5)yt yt 1 = 1(xt xt 1) + (ut ut 1) = 1(xt xt 1) + etHay:yt = 1 xt + et(8.6)(8.6)phng trnh sai phn cp 1 ton t sai phn cp 1S dng m hnh hi qui qua gc to c lng hi qui (8.6)2.Trng hp cha bit

• Gi s m hnh ban u yt = 1 + 1xt + 2t + ut (8.7)Trong t bin xu thut theo m hnh t hi qui bc nhtThc hin php bin i sai phn cp 1 i vi (8.7) yt = 1xt + 2 + ettrong : yt = yt yt 1 xt = xt xt 1

2.1 Phng php sai phn cp 1

• Nu = -1, thay vo phng trnh sai phn tng qut (8.5)yt + yt 1 = 21 + 1(xt + xt 1) + etHay: (*) M hnh * gi l m hnh hi qui trung bnh trt.2.1 Phng php sai phn cp 1

• hay

i vi cc mu nh c th s dng thng k d ci bin ca Theil Nagar. Dng gi tr va c c lng chuyn i s liu nh m hnh 8.52.2 c lng da trn thng k d-Durbin-Watson

• Gi s c m hnh hai binyt = 1 + 1xt + ut (8.8)M hnh ut t tng quan bc nht AR(1)ut = ut 1 + et(8.9) Cc bc c lng Bc 1: c lng m hnh (8.8) bng phng php OLS v thu c cc phn d et.

2.3 Th tc lp Cochrance Orcutt c lng

• Bc 2: S dng cc phn d c lng hi qui:(8.10)Do et l c lng vng ca ut thc nn c lng c th thay cho thc.Bc 3: S dng thu c t (8.10) c lng phng trnh sai phn tng qut (8.5)Hay yt* = 1* + 1* xt* + vt (8.11)2.3 Th tc lp Cochrance Orcutt c lng

• Bc 4: V cha bit thu c t (8.10) c phi l c lng tt nht ca hay khng nn th gi tr c lng ca 1* v 1* t (8.11) vo hi qui gc (8.8) v c cc phn d mi et*:et* = yt (1* + 1* xt)(8.12)c lng phng trnh hi qui tng t vi (8.10) (8.13)(8.13) l c lng vng 2 ca . Th tc ny ti tc cho n khi cc c lng k tip nhau ca khc nhau mt lng rt nh, chng hn nh hn 0,05 hoc 0,005. 2.3 Th tc lp Cochrance Orcutt c lng

• Vit li phng trnh sai phn tng qutyt = 1(1 - ) + 1 xt 1xt 1 + yt 1 + et (8.14)Th tc Durbin Watson 2 bc c lng :Bc 1: Hi qui (8.14) yt theo xt, xt 1 v yt 1 Xem gi tr c lng h s hi qui ca yt 1 (= ) l c lng ca 2.4 Phng php Durbin Watson 2 bc c lng

• Bc 2: Sau khi thu c , thayv c lng hi qui (8.5*) vi cc bin c bin i nh trn. 2.4 Phng php Durbin Watson 2 bc c lng

• Thc hnh trn Eviews:Gi s m hnh hi quy Yi=1 + 2. Xi + UiB1. Hi qui Y theo X nh sau Y C XB2. So snh Durbin Watson d statistic vi dL v dU kim nh c t tng quan khng.Nu dng kim nh Breusch Godfrey (BG)Ti ca s Equation, chn View \ Residual Tests \ Serial Correlation LM Test, hin ra ca s nh cho nhp bc tng quan cn kim nh , v d ta nhp 2

• Xem gi tr Obs*R-squared (nR2) v gi tr p-value ca n bc b hay chp nhn gi thuyt H0. Gi thuyt H0: Khng c t tng quanB3. c lng ccB4: Bin i v thay vo cc biu thc sau

B5: Hi quy yt * theo xt*, ch Durbin Watson d statistic xem cn tng quan khng. Nu khng cn th m hnh bc ny c chn.

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• Khc phc bng th tc lp Cochrane-Orcutt Thc hin hi quyY c X AR(1) nu m hnh c t tng quan bc 1Y c X AR(1) AR(2) nu m hnh c t tng quan bc 2

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