kinh tế lượng_chương 9

Chng trnh Giang day Kinh te Fulbright Nien khoa 2003-2004

Phng phap phan tch Bai oc

Nhap mon kinh te lng vi cac ng dung Chng 9: Tng quan chuoi

Ramu Ramanathan 1 Thuc oan/Hao Thi

CHNG 9

Tng Quan Chuoi Phng phap bnh phng toi thieu a chng to mang lai cac c lng ve thong so co mot vai tnh chat mong muon, vi ieu kien cac so hang sai so (ut) thoa man mot so gia thiet. ac biet, cac c lng co tnh khong thien lech, nhat quan, va hieu qua nhat. Khi mot nha nghien cu x ly d lieu dang chuoi thi gian, mot so van e ac biet phat sinh thng dan en ket qua la vi pham vai gia thiet can e phat ra nhng tnh chat tot a liet ke. Trong chng nay, chung ta se khao sat mot dang vi pham cac gia thiet c ban ve cac so hang nhieu. Th nhat ta xem xet nhng an y cua viec bo qua s vi pham nay va dung thu tuc bnh phng toi thieu thng (OLS). Ta co the ky vong rang, nh trong trng hp phng sai cua sai so thay oi, vai tnh chat co the khong con gi c na. Th hai, ta kiem nh s co mat cua s vi pham nay, va cuoi cung thao luan cac phng phap co the la chon cho cac van e.

Gia thiet 3.6 trong Chng 3 phat bieu rang cac so hang sai so ut va us, cho cac quan sat khac nhau t va s, la phan phoi oc lap. Tnh chat nay goi la oc lap chuoi. T Chng 2, Phan 2.3, ut va us an y oc lap rang chung khong tng quan. Khi mot nha nghien cu ang phan tch d lieu chuoi thi gian, gia thiet nay thng se b vi pham. Cac so hang sai so cho cac thi oan khong qua cach xa co the co tng quan. Tnh chat nay c goi la tng quan chuoi hay t tng quan (cac thuat ng nay se c s dung thay the nhau). Trong Chng 3 ta a liet ke mot so nhan to giai thch cho s co mat cua so hang sai so ut. o la (1) cac bien b loai bo, (2) bo qua s phi tuyen, (3) cac sai so o lng, va (4) hoan toan ngau nhien, cac tac ong khong d oan c. Ba nhan to au tien trong cac nhan to nay co the dan en cac sai so tng quan chuoi. V du, gia s mot bien phu thuoc Yt tng quan vi cac bien oc lap Xt1 va Xt2, nhng nha nghien cu khong tnh en bien Xt2 trong mo hnh. Tac ong cua bien nay se c bao gop qua so hang sai so ut. Bi v nhieu bieu hien chuoi thi gian kinh te co chieu hng theo thi gian, Xt2 co the phu thuoc vao Xt-1,2, Xt-2,2, . . .. ieu nay se bien thanh s tng quan ro rang gia ut va ut-1, ut-2, . . ., do o vi pham gia thiet oc lap chuoi. Vay, cac chieu hng trong cac bien b loai bo co the tao s t tng quan trong cac sai so.

Tng quan chuoi cung co the c gay nen bi ac trng sai ve dang ham so. V du, gia s moi quan he gia Y va X la bac hai nhng ta gia thiet la ng thang. Vay so hang sai so ut se phu thuoc vao X2. Neu X tang hoac giam theo thi gian, ut cung se bieu hien chieu hng nh vay, cho thay s t tng quan.

Sai so co he thong trong o lng cung gay nen s t tng quan. V du, gia s mot cong ty ang cap nhat so lieu hang hoa ton kho trong mot thi oan cho trc. Neu co mot sai sot co tnh he thong xay ra trong cach o lng, d tr ton kho tch luy se phan anh cac sai so o lng tch luy. Cac sai so nay se cho thay nh la s tng quan chuoi.

Mot v du cua tng quan chuoi, xet s tieu thu ien theo cac gi khac nhau trong ngay. Bi v dang thay oi nhiet o la tng t gia cac thi oan lien tiep, ta co the ky vong dang





tieu thu la tng quan gia cac thi oan lan can. Neu mo hnh khong c ac trng mot cach thch hp, tac ong nay co the e lo s tng quan cao gia cac sai so t cac thi oan gan ke. Mot v du khac cua tng quan chuoi c tm thay trong d lieu th trng chng khoan. Gia cua mot chng khoan ac biet nao o hoac mot ch so th trng chng khoan tai thi iem ong ca cua nhng ngay lien tiep hoac trong nhng gi lien tiep co the tng quan theo chuoi.

} V DU 9.1 DATA6-6 co d lieu hang nam ve dan so nong trai theo phan tram tong dan so tai My. Hnh 9.1 la o th cua dan so nong trai va gia tr phu hp thu c t xu hng thi gian tuyen tnh cua dang ham FARMPOP = + TIME + u, trong o TIME la t t 1 en 44. Phan May Tnh Thc Hanh 9.1 co cac hng dan e chay lai v du nay. T bieu o ta lu y rang trong nhng thi oan ban au th cac gia tr thc te nam pha tren ng bnh phng toi thieu, trong nhng thi oan gia cac iem phan tan tu hop pha di ng thang, va trong cac thi oan sau cung chung lai nhat quan nam pha tren ng thang. Do o ta ky vong s tng quan cao gia cac sai so cua cac thi oan lien tiep va gan ke nhau, nh vay vi pham gia thiet oc lap chuoi. Thc te, he so tng quan gia ut va ut-1 la 0,97. Mot phng cach hu dung e nhan dang s co mat cua tng quan chuoi la bieu o phan d. ay n gian la mot o th cua cac so d c lng ut theo thi gian t, Hnh 9.2 minh hoa bieu o so d nay cho trng hp dan so nong trai. Ta quan sat thay mot xu hng ro rang cac phan d lien tiep tu tap ve mot pha cua ng thang so khong hoac pha kia. ay la mot dau hieu theo dang o th cho thay s co mat cua t tng quan. Neu ut la oc lap, s tu hop nay co the se khong xay ra. } Hnh 9.1 Minh Hoa cua T Tng Quan

0 5 10 15 20 25 30 35 40 45

18 16 14 12 10

8 6 4 2 0 Time

Farmpop





} Hnh 9.2 Minh Hoa cua Bieu o Phan D

T s thao luan va cac v du nay ro rang s t tng quan thc s vi pham Gia thiet 3.6.

Bay gi ta tiep tuc thao luan cac he qua khi bo qua s t tng quan, trnh bay cac kiem nh thch hp e nhan dang s co mat cua tng quan chuoi, va cuoi cung thao luan cac phng phap c lng co the chon la.

} 9.1 Tng Quan Chuoi Bac Nhat au tien, ta xet trng hp ac biet nhat cua tng quan chuoi goi la tng quan chuoi bac nhat. Mac du ta dung mo hnh hoi qui tuyen tnh n e khao sat cac van e, tat ca ket qua cung khai quat hoa cho trng hp hoi qui boi. Neu tng quan chuoi ton tai, th Cov(ut, us) 0 vi t s, ngha la, sai so cho thi oan t la tng quan vi sai so cho thi oan s. Gia thiet cua t tng quan bac nhat c phat bieu chnh thc nh sau: GIA THIET 9.1 Yt = + Xt + ut (9.1) ut = ut-1 + t 1 < < 1 (9.2)

Vay sai so ut quan he vi sai so cua thi oan trc (ut-1), mot so hang sai so mi (t), va mot thong so mi , phai co tr tuyet oi nho hn 1, neu khong, tac ong bung no co the xay ra. Bi v la he so cua so hang sai so tre mot thi oan, c goi la he so t tng quan bac nhat. Qua trnh c mo ta bi Phng trnh (9.2) c goi la qua trnh t hoi qui bac nhat, c biet en pho bien hn la AR(1). Sau nay trong chng nay (Phan 9.5) ta xet cac qua





trnh t hoi qui bac cao hn. Cac sai so mi t c gia thiet e thoa man cac ieu kien sau ay:

GIA THIET 9.2 Cac sai so t tuan theo phan phoi mot cach oc lap va ong nhat vi tr trung bnh la 0 va phng sai khong oi sao cho E(t) = 0, E(2t) = 2 < , va E(tt-s) = 0 vi s 0.

Vay cac so hang sai so mi c gia thiet e co cung tnh chat vi cac tnh chat ma thu tuc OLS gia thiet ut phai co. Trong tai lieu chuoi thi gian, mot chuoi tuan theo Gia thiet 9.2 c goi la chuoi co tnh nhieu trang vi tr trung bnh la 0. Bi v ut phu thuoc vao ut-1, ta co the ky vong la chung tng quan. Lu y rang ut khong phu thuoc trc tiep vao ut-2; tuy nhien, lai phu thuoc gian tiep qua ut-1 bi v ut-1 phu thuoc trc tiep vao ut-2. Vay, ut tng quan vi tat ca sai so qua kh. Neu ong phng sai la dng, th co t tng quan dng, va khi ong phng sai am, ta co t tng quan am. Trong Phu luc Phan 9.A.2 cho thay Cov(ut, ut-1) = 2s, vi s 0.

} 9.2 Cac He Qua khi Bo Qua Tng Quan Chuoi Trong Chng 3 ta a chng minh rang theo Gia thiet 3.3 va 3.4, (ngha la ut co tr trung bnh la 0 va khong tng quan vi Xt), cac c lng OLS la khong thien lech va nhat quan. V s chng minh cac tnh chat nay khong phu thuoc vao Gia thiet 3.6, gia thiet b vi pham bi s co mat cua t tng quan, cac c lng OLS (va cac d bao da tren chung) la khong thien lech va nhat quan ngay ca khi cac so hang sai so tng quan theo chuoi. Van e la s hieu qua cua cac c lng. Trong chng minh nh ly Gauss-Markov a thiet lap s hieu qua (Phan 3.A.4), mot trong cac bc lien quan viec cc tieu phng sai cua to hp tuyen tnh atut: ( )

+=

ststst

22ttt )u,u(CovaaauaVar (9.3)

trong o tong kep la theo moi t va s co gia tr khac nhau. Neu Cov(ut, us) 0, so hang th hai ben tay phai se khong triet tieu. Do vay, cc tieu at22 (se a ra cac phng trnh chuan OLS) khong tng ng vi viec cc tieu Phng trnh (9.3). V ly do nay, c lng khong thien lech tuyen tnh tot nhat (BLUE) cc tieu phng trnh (9.3) se khong giong nh c lng OLS. Noi cach khac, c lng OLS khong phai BLUE va do vay khong hieu qua. Vay, he qua khi bo qua s t tng quan giong nh khi bo qua phng sai cua sai so thay oi; ngha la cac d bao va c lng la khong thien lech va nhat quan nhng khong hieu qua. Tuy nhien, co mot ieu nen biet trc. Neu cac bien X co bao gom mot bien phu thuoc co hieu ng tre nh Yt-1 th tng quan chuoi se cho ra cac c lng OLS khong nhat quan. ieu nay c chng minh trong chng ke tiep.





Ta co the cho thay rang neu tng quan chuoi trong ut la dng va bien oc lap Xt tang len theo thi gian (trng hp thng thay), th phng sai phan d c lng ( 2 ) se la mot c lng qua thap va gia tr cua R2 se la mot c lng qua cao. Noi cach khac, o thch hp se b phong ai va cac sai so chuan c lng se nho hn cac sai so chuan thc s. Cac iem nay c minh hoa trong Hnh 9.3, mot bieu o phan tan tieu bieu, vi s tr giup cua mo hnh hoi qui n. ng am la ng hoi qui thc +X. Gia s co t tng quan dng; ngha la, ong phng sai gia hai so hang nhieu ngau nhien lien tiep la dng. Gia s them rang iem phan tan au tien (X1, Y1) nam pha tren ng hoi qui thc. ieu nay ngha la u1 se dng. Bi v u2 va u1 la tng quan dng, u2 co the dng, lam cho (X2, Y2) cung nam pha tren ng thang. Do o, mot vai iem phan tan au tien co the nam pha tren ng hoi qui thc. Gia s mot trong cac iem phan tan ngau nhien nam pha di ng hoi qui thc bi do ban chat ngau nhien cua cac so hang u. Nh vay mot vai iem ke tiep cung co the nam pha di ng hoi qui thc. } Hnh 9.3 c Lng Qua Thap cua Phng Sai Phan D

Bi v thu tuc bnh phng toi thieu lam cc tieu tong bnh phng cac o lech, ng

thch hp se trong nh ng t net. Phng sai thc cua cac sai so c xac nh bi o lech cua (Xt, Yt) so vi ng hoi qui thc, ro rang se ln hn phng sai phan d c lng, c tnh t cac o lech xung quanh ng thch hp. Do o, tong bnh phng sai so tnh toan (ESS) se nho hn gia tr thc, va R2se ln hn gia tr thc.

Trong trng hp tong quat, cac phng sai cua cac he so hoi qui se b thien lech. e biet them phan tch chi tiet ban chat cua thien lech, ban oc co quan tam nen tham khao Phan 8.3 sach cua Kmenta (1986).

ng thc (true line)

ng thch hp (fitted line)

Y

X





Tac ong Len cac Kiem nh cac Gia Thuyet Chung ta va bien luan rang trong trng hp thong thng khi ma tng quan chuoi la dng va bien oc lap tang len theo thi gian, cac sai so chuan c lng nho hn cac sai so thc, va do o se la c lng qua thap. ieu nay co ngha la cac tr thong ke t se la cac c lng qua cao, va do vay mot he so hoi qui co ve co y ngha nhng thc te co the la khong. Cac phng sai c lng cua cac thong so se thien lech va khong nhat quan. V vay, cac kiem nh t va F khong con hp le. Tac ong Len D Bao Mac du cac d bao se khong thien lech (bi v cac c lng khong thien lech), nhng chung khong hieu qua vi cac phng sai ln hn. Bang cach lu y en tng quan chuoi trong cac phan d, co the se phat ra cac d bao tot hn cac d bao phat ra theo thu tuc OLS. ieu nay c chng minh cho cau truc sai so cua qua trnh t hoi qui bac nhat AR(1) c nh ro trong Phng trnh (9.2).

Gia s ta bo qua Phng trnh (9.2) va thu c cac c lng OLS va . Ta a thay trong Phan 3.9 rang d oan OLS se la tt XY += . Bi v ut la ngau nhien, no khong the d oan; va do vay ta at no bang vi gia tr trung bnh cua no, bang khong. Tuy nhien, trong trng hp cua tng quan chuoi bac nhat, ut co the d oan t Phng trnh (9.2), vi ieu kien co the c lng c (goi la ). Ta co 1tt uu = . Tai thi iem t, phan d cho thi oan trc ( 1tu ) la biet. Do o, d oan AR(1) se la

)XY(XuXY~ 1t1tt1ttt ++=++= (9.4)

tan dung s viec 1t1t1t XYu = . Phng trnh (9.4) s dung s co mat cua tng quan chuoi e phat ra d oan; vay Yt se hieu qua hn Yt thu c theo thu tuc OLS. Thu tuc c lng c mo ta trong Phan 9.3.

Cac ket qua thu c trong phan nay c tom tat trong Tnh chat 9.1. Tnh chat 9.1 Neu tng quan chuoi gia cac so hang nhieu ngau nhien trong mo hnh hoi qui b bo qua va thu tuc OLS c dung e c lng cac thong so, th se co cac tnh chat sau: a. Cac c lng va cac d bao da tren chung se van khong thien lech va nhat quan. Tuy

nhien tnh chat nhat quan se khong con neu cac bien phu thuoc co hieu ng tre c gop vao xem nh cac bien giai thch.





b. Cac c lng OLS khong con BLUE na va se khong hieu qua. Cac d bao cung se khong hieu qua.

c. Cac phng sai c lng cua cac he so hoi qui se thien lech va khong nhat quan, va do o cac kiem nh cac gia thuyet se khong con hp le. Neu tng quan chuoi la dng va bien oc lap Xt tang len theo thi gian, th cac sai so chuan se la cac c lng qua thap cua cac gia tr thc. ieu nay co ngha rang R2 tnh toan se la mot c lng qua cao, cho thay mot s thch hp tot hn so vi ton tai tren thc te. Cung vay, cac tr thong ke t trong trng hp nh vay se co khuynh hng co y ngha hn gia tr thc s cua chung.

} 9.3 Kiem nh Tng Quan Chuoi Bac Nhat Trong phan nay, ta gii han trong kiem nh t tng quan bac nhat. Thu tuc c tong quat hoa trong Phan 9.5 cho trng hp cua cac bac cao hn. Kiem nh Durbin-Watson Mac du bieu o phan d la mot phng phap o th hu ch e nhan dang s co mat cua tng quan chuoi, cac kiem nh chnh thc cho t tng quan van la can thiet. Trong phan nay, ta trnh bay kiem nh pho bien nhat cho tng quan chuoi bac nhat, goi la kiem nh Durbin-Watson (DW) (Durbin and Watson, 1950, 1951). Mot kiem nh da tren phng phap nhan t Lagrange c thao luan trong Chng 6 va 8 c trnh bay trong phan tiep theo.

Cac bc thc hien kiem nh Durbin-Watson cho AR(1) c mo ta cho mo hnh hoi qui boi sau ay:

Yt = 1 + 2Xt2 + 3Xt3 + . . . + kXtk + ut (9.5) ut = ut-1 + t -1 < < 1 Bc 1 c lng mo hnh bi bnh phng toi thieu thong thng va tnh toan cac

phan d tu la tkktttt XXXXY ... 3333221 Bc 2 Tnh toan thong ke Durbin-Watson:

=

=

=

=

= nt1t

2t

2nt

2t1tt

u

)uu(d (9.6)

sau nay se cho thay co gia tr trong khoang t 0 en 4. Phan phoi chnh xac cua

d phu thuoc vao cac quan sat tren cac bien X. Durbin va Watson a cho thay





rang phan phoi cua d b gii han bi 2 phan phoi. Cac phan phoi nay c dung e xay dng cac vung gii han cho kiem nh Durbin-Watson.

Bc 3a e kiem nh H0: = 0 oi lai > 0 (kiem nh mot pha), tm trong Bang A.5, Phu luc A, cac gia tr ti han cho thong ke Durbin-Watson, va viet cac so dL va dU. Lu y rang bang nay cho gia tr k, la so cac he so hoi qui c c lng, ngoai tr so hang hang so. Bac bo H0 neu d dL. Neu d dU, ta khong the bac bo H0. Neu d L < d < dU, kiem nh cha the ket luan.

Bc 3b e kiem nh tng quan chuoi am (ngha la, cho H1: < 0), dung 4 d. ieu nay c thc hien khi d ln hn 2. Neu 4 d dL, ta ket luan rang co t tng quan am y ngha. Neu 4 d dU, ta ket luan rang khong co t tng quan am. Kiem nh cha the ket luan neu d L < 4 d < dU.

S cha the ket luan cua kiem nh DW phat sinh t thc te rang phan phoi mau nho cho

tr thong ke DW d phu thuoc vao cac bien x va d kho tnh toan. e khac phuc ieu nay, Durbin va Watson xep thanh bang cac gia tr ti han cho cac phan phoi cua cac gii han oi vi d, vi cac gia tr khac nhau cua kch thc mau n va so cac he so k, khong bao gop so hang sai so. Savin va White (1977) m rong ket qua nay cho trng hp cua nhieu bien giai thch. Khi kiem nh la cha the ket luan, ta co the th dung kiem nh nhan t Lagrande c mo ta tiep sau. Cac dang ham hoac cac thu tuc c lng khac co the c chon la e th. Vai chng trnh nh SHAZAM co tnh en gia tr p co lu y en ieu thc te la phan phoi cua d phu thuoc vao cac gia tr cua cac bien giai thch.

T cac phan d c lng ta co the thu c mot c lng cua cac he so tng quan chuoi bac nhat la

=

=

=

=

= nt1t

2t

nt

2t1tt

u

uu (9.7)

c lng nay xap x bang vi c lng thu c khi hoi qui tu theo 1tu ma khong co mot so hang khong oi. Trong Phu luc 9.A cho thay rang tr thong ke DW d xap x bang 2(1 - ). Vay d 2(1 - ) (9.6a) Bi v co the sap t 1 en + 1, khoang gia tr cho d la 0 en 4. Khi bang 0, d bang 2. Vay th, mot tr thong ke DW co gia tr gan bang 2 ngha la khong co tng quan chuoi bac nhat. T tng quan dng manh ngha la gan vi +1. ieu nay bieu hien cac gia tr thap cua d. Tng t, cac gia tr cua d gan 4 cho biet mot s tng quan chuoi am manh; ngha la gan





vi 1. Cac trang thai khac nhau co the co c mo ta trong bieu o sau. Gia thuyet khong la H0: = 0.

Kiem nh DW la khong hp le neu vai bien X la hieu ng tre cua bien phu thuoc

ngha la, neu chung co dang Yt-1, Yt-2, . . . . Cac bai toan phat sinh bi cac bien co hieu ng tre c khao sat trong Chng 10.

} V DU 9.2 B Trong v du dan so nong trai, bieu o phan d c trnh bay trong Hnh 9.2, tr thong ke DW la d = 0,056. (Xem Phan May Tnh Thc Hanh 9.1.) So quan sat la 44 va k = 1. oi vi kiem nh mot pha, cac gia tr gii han thu c (theo phep noi suy) t Bang 5.A la dL = 1,47 va dU = 1,56. V d < dL, kiem nh nay b bac bo tai mc 5 phan tram. V vay ta ket luan rang tng quan chuoi trong cac phan d co y ngha tai mc 5 phan tram.

} V DU 9.3 B

V du th hai, xet Mo hnh C trong Bai tap 4.17, lien ket ty le t vong do benh tim mach vanh vi tieu thu thuoc la tnh tren au ngi, tieu thu thc an beo va dau tnh tren au ngi, tieu thu ru cat tnh tren au ngi, va tieu thu bia tnh tren au ngi (xem DATA4-7). Trong v du nay, ta co n = 34, k = 4, d = 1,485, dL = 1,21, va dU = 1,728. (xem Phan May Tnh Thc Hanh 9.2.) Bi v d nam trong khoang dL va dU, ta co mot kiem nh cha the ket luan. Vai chng trnh may tnh (v du, SHAZAM) tnh toan chnh xac gia tr p da tren cac quan sat cua ngi s dung. Gia tr p la 0,017, la gia tr thap, va v vay ta bac bo H0: = 0 va ket luan rang co t tng quan y ngha.

K l

Bac bo = 0 Chap nhan = 0 Bac bo = 0 Cha the ket luan

Cha the ket luan

T tng quan dng T tng quan amH1: > 0 H1: < 0

0 dL dU 2 4 dU 4 dL 4





} BAI TOAN THC HANH 9.1 Trong V du 5.1 cua Chng 5 ta a lien ket lng nha mi vi cac bien nh GNP va lai suat va a dung d lieu chuoi thi gian e c lng vai mo hnh khac nhau. Dung kiem nh Durbin-Watson cho cac mo hnh nay e kiem nh tng quan chuoi bac nhat. Can than khi phat bieu cac gia thuyet khong va gia thuyet ngc lai cung nh cac tieu chuan chap nhan hoac bac bo gia thuyet khong. Da tren cac ket qua cua ban, ban co ket luan g ve cac tnh chat cua cac c lng OLS thu c trong Chng 5?

Kiem nh Durbin-Watson co vai han che lam cho kiem nh khong hu dung trong nhieu trng hp. V du, ta han a thay rang kiem nh co the cho cac ket qua khong the ket luan. Cung vay, kiem nh la khong hp le neu cac bien X bao gom cac bien phu thuoc co hieu ng tre (thong tin them ve ieu nay trong Chng 10). Th ba, kiem nh la khong the ap dung neu cac sai so t hoi qui co bac cao hn (v du, la 4 trong trng hp d lieu theo quy). Cuoi cung, neu so bien giai thch la ln, gii han dL va dU co the khong san co. Neu bat c trng hp nao trong cac trng hp nay xay ra, mot la chon khac la kiem nh LM c ban luan tiep theo ay, khong b cac han che nay (tuy nhien, chac chan phai co t nhat 30 bac t do, bi v kiem nh LM la kiem nh mau ln). Kiem nh Nhan T Lagrange Kiem nh LM mo ta trong Chng 6 hu dung trong viec nhan dang tng quan chuoi khong ch vi bac nhat ma cung cho ca cac bac cao hn, nhng ay ta t han che cho trng hp bac nhat. Trng hp tong quat c xet en trong Phan 9.5.

e bat au kiem nh nay, lu y rang Phng trnh (9.5) co the c viet lai la

Yt = 1 + 2Xt2 + . . . + kXtk + ut-1 + t Do o kiem nh oi vi = 0 co the c x ly nh kiem nh nhan t Lagrange (LM) oi vi viec them bien ut-1 (la cha biet, va do o ta co the dung 1tu e thay vao). Cac bc thc hien kiem nh LM nh sau: Bc 1 Bc nay ung nh Bc 1 cua kiem nh DW; ngha la c lng Phng trnh

(9.5) theo OLS va tnh toan cac phan d cua no. Bc 2 Hoi qui tu theo mot hang so, Xt2, . . . , Xtk va 1tu , dung n 1 quan sat t 2 en

n. ieu nay tng t nh hoi qui phu trong Bc 4 cua Phan 6.14. Ke en tnh toan LM = (n 1)R2 t hoi qui phu nay. n 1 c dung bi v so quan sat hieu qua la n 1.





Bc 3 Bac bo gia thuyet khong cua t tng quan co gia tr bang khong va cung co gia thuyet 0 neu (n 1)R2 > 21 (), gia tr 21 trong phan phoi chi-square vi 1 bac t do sao cho dien tch vung ben phai cua no la . Mot cach khac, tnh toan gia tr p = Prob( 21 > LM), vung ben phai cua LM trong phan phoi 21 . Neu gia tr p < , chac chan bac bo H0: = 0 va ket luan rang t tng quan la co y ngha.

Neu a co tng quan chuoi trong cac phan d, ta co the ky vong tu co quan he vi 1tu .

ay la ong lc hau thuan hoi qui phu trong o 1tu c ke en cung vi tat ca cac bien oc lap trong mo hnh. Lu y rang kiem nh LM khong co tnh trang khong the ket luan nh cua kiem nh DW. Tuy nhien, o la kiem nh mau ln va can t nhat 30 bac t do e co y ngha.

} V DU 9.4 B

Trong v du benh tim, hoi qui phu se nh sau (xem Phan May Tnh Thc Hanh 9.3):

tu = 113,628 4,675 CIG 1,579 EDFAT + 0,361 SPIRITS (1,4) (1,1) (1,6) (0,1)

+ 0,207 BEER + 0,259 1tu (0,3) (1,4)

R2 = 0,137 n = 34 (n-1)R2 = 4,521 Gia tr chi-square ti han la 21 (0,05) = 3,841, nho hn (n-1)R2. Cung vay, gia tr p cho 4,521 la 0,033. Vay kiem nh LM bac bo gia thuyet khong cua t tng quan co gia tr bang khong, trong khi kiem nh DW cho ket qua khong the ket luan.

K l

} BAI TOAN THC HANH 9.2 Lam lai Bai Toan Thc Hanh 9.1 dung phng phap kiem nh LM.

} 9.4 X Ly Tng Quan Chuoi Thay oi Dang Ham So Khong co thu tuc c lng nao co the am bao loai bo tng quan chuoi bi v ban chat va nguyen nhan cua t tng quan noi chung cha biet. Nh Hendry va Mizon (1978) a bien luan ay thuyet phuc, tng quan chuoi co the la trieu chng cua mo hnh b ac trng sai hn la cau truc sai so b ac trng sai. V du, gia s rang quan he la bac hai va ang ra ta hoi qui Y





theo X va X2. Neu X tang hoac giam co he thong theo thi gian, hoi qui cua Y ch theo X se hien nhien the hien s tng quan chuoi. Khong co thu tuc c lng tinh vi nao co the hieu chnh van e ma no thc s do ac trng sai trong phan xac nh hn la trong so hang sai so. Giai phap ay la thiet lap lai mo hnh co tnh en so hang bac hai sao cho khong co tng quan chuoi xuat hien. Mot cach khac la dung mo hnh log-hai lan. Cac van e nay c minh hoa trong V du 9.5. ng dung Phan 9.7 trnh bay mot v du khac trong o mo hnh au tien boc lo s t tng quan, nhng khi cac ac trng c cai thien, tng quan chuoi khong con co mat na

} V DU 9.5 S dung d lieu trong bang DATA6.6, chung ta nhan thay rang o th bieu dien so phan tram tren tong so dan so cua My song nh vao nganh nong nghiep co xu hng i xuong va khong tuyen tnh t 1947 en 1991. Neu chung ta lam thch hp bang mot ng xu hng tuyen tnh theo thi gian cho tap d lieu nay, chung ta co the ky vong rang mot nhom cac iem phan d nam lien tiep nhau bieu hien moi tng quan chuoi (xem hnh 9.2). Cac gia tr c lng tren ng xu hng tuyen tnh c cho nh sau (xem Phan Thc Hanh May Tnh 9.4 e biet cach tnh ra cac ket qua nay):

farmpopt = 13,777 0,325t d = 0,056 (31,55) (- 19,2)

2R = 0,895

Nhng gia tr trong ngoac n la cac tr thong ke t. Lu y rang tr thong ke Durbin Watson (DW) rat gan bang zero, cho thay moi tng quan chuoi rat manh. V ly do nay ma tr thong ke t va ai lng thch hp b lam tang qua mc. T hnh 9.1, ngi ta nhan thay rang se thch hp hn neu xem ay moi quan he phi tuyen tnh. ng xu hng theo thi gian c thch hp bang ham bac hai va ket qua c tnh ra nh sau:

farmpopt = 17,026 0,749t + 0,00942t2 d = 0,601 (113,5) (- 48,7) (28,4)

2R = 0,995 Mac du tr thong ke DW a tien en en gan gia tr 2 hn, nhng no van cho thay tnh t tng quan dng kha manh. Phep lay sai phan bac nhat gia cac gia tr logarit c tnh toan tiep theo ay. Cu the hn, chung ta at

gfarmpopt = ln(farmpopt) ln(farmpopt 1)





Lng nay con c goi la ty le tang trng tc thi va co dang ng tang trng ham mu. e co c lng nay, chung ta gia s rang ham Yt tang trng theo ham mu vi Yt = Y0 egt (g la ty le tang trng, co the co dau am, bieu th ham Y co khuynh hng suy giam theo dang mu). Lay logarit hai ve, chung ta co

ln(Yt) = ln(Y0) + gt theo bien thi gian t ln(Yt -1) = ln(Y0) + g(t 1) theo bien thi gian (t 1)

Lay phng trnh th nhat tr i phng trnh th hai, ta co

g = ln(Yt) ln(Yt -1) V vay, hieu so gia cac gia tr logarit tren la ty le tang trng. Gia tr qua he c lng oi vi dan so nong nghiep la (xem bang 9.2)

gfarmpopt = - 0,064 + 0,00058t d = 2,266 (- 3,9) (0,92)

2R = - 0,004 Lu y rang, v bien phu thuoc nay khac vi hai hoi quy trc ay nen gia tr 2R la khong tng thch e co the so sanh vi nhau. Tr thong ke DW xap x bang 2 va khong co chng c nao ve tnh t tng quan bac nhat (v d > 2 nen chung ta s dung 4 d = 1,734). V the, mot s hieu chnh hp ly oi vi dang ham so la co the loai bo tnh chat t tng quan chuoi bieu kien. ieu nay co ngha dang cong thc th ba la tot nhat? Cau tra li phu thuoc vao y ngha cua t tot nhat la g? Mot nha nghien cu rat quan tam en viec d bao dan so nong nghiep se at cac anh gia tren c s kha nang d bao cua mo hnh. Van e nay se c e cap mot cach he thong hn chng 11. ac Trng Mot Cau Truc ong va Tong Quat Hn De dang nhan thay rang mo hnh vi mot so hang sai so t hoi quy la mot trng hp ac biet cua mo hnh co cau truc ong tong quat hn cho phan tat nh (xem tham khao tac gia Sargan, 1964, va tac gia Hendry va Mizon, 1978). Hay xem xet mo hnh sau ay (thng c s dung trong cac bai toan kinh te hoc v mo) ve moi quan he gia bien phu thuoc vi gia tr tre cua chnh no, mot bien giai thch, va vi o tre cua no:

yt = 0 + 1yt 1 + 2xt + 3xt 1 + t 1 < 1 (9.8) So hang sai so t c gia nh co gia tr trung bnh bang zero, gia tr phng sai khong oi, va co tnh chat oc lap chuoi. Phng trnh (9.1) co dang nh sau





yt = + xt + ut (9.1) Tm ut theo cac bien con lai va thay the no vao phng trnh (9.2), chung ta co

yt xt = (yt 1 xt 1) + t Phng trnh co the viet lai nh sau

yt = (1 ) + yt 1 + xt xt 1 + t (9.1a) So sanh gia phng trnh (9.8) va (9.1a), chung ta thay rang

0 = (1 ), 1 = , 2 = , va 3 = Co the nhan thay rang cac tham so thoa man gii han phi tuyen tnh 3 + 12 = 0. Neu gii han nay c thoa man trong phng trnh (9.8) th mo hnh se c rut gon lai thanh mo hnh tnh trong phng trnh (9.1) vi cau truc sai so t hoi quy trong phng trnh (9.2). Phng trnh (9.8) co bon thong so e c lng, trong khi phng trnh (9.1) va (9.2) ch co ba thong so cha biet. V the ma tnh tng quan chuoi la mot s n gian hoa e mang lai s thuan tien ch khong phai la s kho khan nh tac gia Hendry va Mizon (1978) a ch ra. Cac tac gia nay cung vi tac gia Sargan (1964) a e ngh rang bc au tien la thiet lap mo hnh mot cach tong quat nh phng trnh (9.8), sau o kiem nh cac gii han phi tuyen tnh len mo hnh nay, va neu no c chap nhan th hay lam n gian hoa mo hnh theo cach tng t nh phng trnh (9.1) va (9.2). Neu mo hnh khong thoa man gii han phi tuyen tnh th giai quyet bai toan nh trong trng hp mo hnh tnh co so hang sai so t hoi quy va viec can c tren tr thong ke Durbin Watson co y ngha co the dan en cac ket qua khong chnh xac. Thiet Lap Mo Hnh Trong Cac Sai Phan Bac Nhat Tac gia Granger va Newbold (1974 va 1986) a neu len mot so nghi van ve s hoi quy gia tao co the co khi mot qua trnh hoi quy da tren nhieu mc bien xu hng, ac biet khi tr thong ke DW co y ngha. Trong viec nghien cu kinh te lng thc nghiem, cach thc ma ngi ta thng s dung e vt qua van e nay la thiet lap mot so mo hnh theo sai phan bac nhat, ngha la hieu so gia gia tr tai moc thi gian t va t 1. Trong trng hp nay, chung ta se c lng yt = 0 + xt + t, trong o yt = yt yt 1 va xt = xt xt 1 . Tuy nhien, giai phap s dung sai phan bac nhat nay khong phai luc nao cung thch hp. e hieu ro hn, hay lu y en mo hnh sai phan bac nhat co the c viet lai nh sau:

yt = yt 1 + 0 + xt xt 1 + t





So sanh phng trnh tren vi phng trnh (9.8), chung ta nhan ra rang mo hnh nay chnh la trng hp ac biet khi 1 = 1 va 2 + 3 = 0. V the, mot cach tiep can khac thng c s dung la kiem nh hai gii han nay trc, va neu ca hai c chap nhan th hay s dung ac trng sai phan bac nhat. Nhng Thu Tuc c Lng Khi mot ham a c hieu chnh ma khong the loai bo c tnh chat t tng quan, ngi ta co the s dung mot so thu tuc khac e a ra cac con so c lng nhng gia tr nhan c t phng phap OLS. Nhng thu tuc nay se c e cap tiep theo ay. Tuy nhien, nen lu y rang viec co nh mot cach may moc oi vi tnh t tng quan co the ngam cha mot so gii han ve thuoc tnh chuoi thi gian khong nhat quan vi d lieu cua mo hnh. Cung nen lu y rang cac phng phap nay ch c ap dung cho loai d lieu chuoi thi gian. oi vi loai d lieu cheo, ngi ta co the tai sap xep cac gia tr quan sat theo bat c hnh thai nao va nhan c mot tr thong ke DW chap nhan c. Tuy nhien, ieu nay cung noi len rang thc hien kiem nh DW cho loai d lieu cheo la khong co y ngha. V d lieu chuoi thi gian khong the tai sap xep c nen nha nghien cu can quan tam en moi tng quan chuoi co the co gia chung. Thu Tuc Tnh lap Cochrane Orcutt Thu tuc Tnh lap Cochrane Orcutt (CORC) (tac gia Cochrane va Orcutt, 1949) yeu cau co s bien oi mo hnh hoi quy (9.5) thanh dang mo hnh co the ap dung bang thu tuc OLS. Phng trnh (9.5) c viet lai theo thi oan t 1, chung ta co

Yt 1 = 1 + 2 X(t 1)2 + 3 X(t 1)3 + + k X(t 1)k + ut 1 (9.5) Lay (9.5) tr i (9.5) sau khi a nhan tng so hang cua (9.5) vi , chung ta co

Yt Yt 1 = 1(1 ) + 2[Xt 2 X(t 1)2] + 3[Xt 3 X(t 1)3] + + k[Xt k X(t 1)k] + t

Vi bieu thc ut = ut 1 + t, phng trnh tren co the viet lai nh sau:

t*tkk

*3t3

*2t2

*1

*t X...XXY +++++= (9.9)

Trong o

*tY = Yt Yt 1, *1 = 1(1 ), va *tiX = Xti X(t 1)i vi t = 2, 3, , n va i = 2, , k





Qua trnh bien oi tao ra bien Y* va cac bien X* con c goi la phep lay sai phan gan ung, hay phep lay sai phan tong quat. *1 ch la so hang hang so mi. Lu y rang so hang sai so trong phng trnh (9.9) thoa man moi tnh chat can thiet e co the ap dung c thu tuc bnh phng toi thieu. Neu biet c gia tr cua , chung ta co the ap dung phng phap OLS cho phng trnh (9.9) va gia tr c lng nhan c la BLUE. Tuy nhien, gia tr cha biet nen chung ta can phai c lng chung t mau quan sat. Cac bc tien hanh thu tuc Cochrane Orcutt c trnh bay nh sau: Bc 1 c lng phng trnh (9.5) bang phng phap OLS va tnh toan phan d cua no tu . Bc 2 c lng he so tng quan chuoi bac nhat (con goi la ) t phng trnh (9.7). Bc 3 Bien oi cac bien nh sau:

*tY = Yt Yt 1, *2tX = Xt2 X(t 1)2 , va .v.v.

Lu y rang cac bien co dau hnh sao (*) c xac nh ch vi t nhan gia tr t 2 en n v co t 1 so hang xuat hien.

Bc 4 Hoi quy *tY theo hang so, theo *2tX ,

*3tX , ,

*tkX va tnh gia tr c lng cua phng

trnh (9.9) c bien oi bang phng phap OLS. Bc 5 S dung nhng gia tr c lng nay cho cac gia tr trong phng trnh (9.5) va tnh

c mot tap mi cac gia tr c lng ut . Sau o, quay tnh lap bc 2 vi nhng gia tr mi nay cho en khi co the ap dung c quy tac dng tiep theo ay.

Bc 6 Thu tuc tnh lap tren ay co the dng lai khi hieu so gia tr c lng cua t hai ket qua lien tiep tnh c khong ln hn gia tr chon trc nao o, nh 0,001 chang han. Gia tr cuoi cung nay se c dung e tnh gia tr c lng CORC t phng trnh (9.9).

V so hang hang so cung c nhan vi 1 nen gia tr 1 nhan c se bang *1 / (1 ), vi *1 la so hang hang so c lng trong phng trnh bien oi (9.9). Hau het nhng chng trnh hoi quy tieu chuan thc hien tat ca cac bc thu tuc tren bang cac lenh n gian, va giai phong ngi s dung khoi cong viec tnh toan tnh lap nang nhoc. Hau het cac chng trnh eu xuat ra ket qua so hang hang so cua mo hnh ban au (la 1 ), v vay ma ngi s dung khong can thiet (va khong nen) chia no cho (1 ). Ngi s dung cung nen can than khi xac nh ket qua R2, tong bnh phng sai so, va .v.v. Neu chung co lien quan en phng trnh (9.9) th nhng gia tr nay khong the so sanh vi gia tr c lng bang phng phap OLS tng ng v ve ben trai cua hai phng trnh (9.5) va (9.9) kha khac nhau. Tng t, tr thong ke Durbin Watson nhan c thng lien quan en phan d cua phng trnh (9.9) ma khong lien quan en phng trnh (9.5). Kiem nh DW ve van e nay se kiem





nh moi tng quan chuoi bac hai cho phan d tu v ngam nh di mo hnh nay la qua trnh t hoi quy bac nhat AR(1) theo t . Thu tuc Cochrange Orcutt co the c chng minh hoi tu ve gia tr c lng thch hp cc ai. S hoi tu nay nay co tnh chat nhat quan va tien en tiem can. Thu tuc tnh lap thng hoi tu nhanh va khong can lap lai nhieu hn ba en sau lan. Nen lu y rang so lan quan sat dung e c lng trong phng trnh (9.9) ch la n 1 v chung ta bo qua lan quan sat au tien. Vi k thong so th bac t do la n k 1. Kiem nh gia thuyet co the c thc hien theo cach thong thng. Co the s dung ket qua cho lan quan sat au tien bang phep bien oi sau ay oi vi t =1 (cac ieu chnh trong bc nay c trnh bay trong phan phu luc 9.A):

*1Y = Yt (1 2) 1/2 va *i1X = X1i (1 2) 1/2 vi i = 1 k

} V DU 9.6

Tnh t tng quan cua mau quan sat benh tim trnh bay trong v du 9.4 c chng minh la co y ngha (theo ket qua cua kiem nh LM), va v the chung ta se tai c lng mo hnh bang kiem nh CORC. Phng trnh c lng c cho ay la ket qua tnh toan cua chng trnh GRETL, bo qua lan quan sat au tien (xem them trong phan thc hanh may tnh 9.5). V cac chng trnh khac nhau ve tieu chuan hoi tu nen ket qua se khac nhau mot vai iem gia cac chng trnh vi nhau. Tuy nhien, s khac nhau nay khong nen qua cach biet.

CHD = 341,023 + 2,903 CIG + 0,373 EDFAT + 12,045 SPIRITS 2,206 BEER (4,2) (0,6) (0,4) (1,83) (- 2,5)

Cac gia tr trong ngoac n la cac tr thong ke t. So vong lap can thiet la 12 va gia tr cuoi cung la 0,613. Chung ta co the thc hien mot kiem nh DW oi vi cac gia tr c lng t phng trnh bien oi (9.9) e kiem tra xem cac phan d co tnh chat t tng quan bac nhat hay khong. Gia tr d cua phng trnh trong kiem nh DW la 2,232. T bang A.5, chung ta co (vi n = 33 va k = 4) dL = 1,19 va dU = 1,73. V hieu so 4 d = 1,771 > dU nen chung ta co the ket luan rang cac phan d khong co tng quan chuoi.

Thu Tuc Tm Kiem Hildreth Lu Mot giai phap thng c dung e thay the thu tuc Cochrange Orcutt la thu tuc tm kiem Hildrth Lu (HILU) (cua tac gia Hildreth Lu, 1960). Thu tuc nay bao gom cac bc sau: Bc 1 Chon mot gia tr (goi la 1). S dung gia tr nay, bien oi cac bien va c lng

phng trnh (9.9) bang thu tuc OLS.





Bc 2 T cac gia tr c lng nay, tnh t t phng trnh (9.9) va tnh ra gia tr tong bnh phng sai so tng ng. Goi gia tr nay la ESS(1). Tiep tuc chon mot gia tr khac na cho (goi la 2) va lap lai bc 1 va 2.

Bc 3 Bang cach thay oi gia tr cua t 1 en + 1 theo vi bc nhay co tnh he thong nao o (nh vi bc nhay la 0,05 hoac 0,01), chung ta se nhan c mot chuoi cac gia tr ESS(). Hay chon nao co gia tr ESS nho nhat. ay la gia tr cuoi cung co the cc tieu hoa mot cach bao quat tong bnh phng sai so cua mo hnh bien oi. Phng trnh (9.9) c lng vi gia tr cuoi cung nay la ket qua toi u.

} V DU 9.7

Tai lieu goc cua tac gia Hildreth Lu trnh bay gan hai ta v du ve c lng bang thu tuc HILU. Chung ta se thc hanh lai mot trong nhng v du o. D lieu DATA9-1 trong phan phu luc D trnh bay so lieu ve nhu cau kem. Cac so lieu mau quan sat c thc hien theo tng thi oan 4 tuan t ngay 18/03/1951 en ngay 11/07/1953. nh ngha cac bien c cho nh sau: DEMAND = Nhu cau tieu thu kem tnh tren moi au ngi, n v tnh bang panh (1 panh =

0.58 lt) PRICE = Gia moi panh kem tnh bang dollar INCOME = Thu nhap hang tuan cua gia nh tnh bang dollar TEMP = Nhiet o trung bnh tnh bang o Fahrenheit Bang 9.1 trnh bay cac he so hoi quy c lng va tong bnh phng sai so cua phng trnh (9.9) cua moi bc trong thu tuc tm kiem. Hang tng ng vi = 0 trnh bay cac gia tr c lng bang thu tuc OLS (tng ng mau quan sat 2 en 30). Thu tuc HILU cc tieu hoa ESS() khi = 0,41. Lu y rang cac gia tr c lng theo OLS va HILU khac nhau mot cach ang ke. Thu tuc CORC cung c ap dung cho nhng d lieu nay. Thu tuc nay ch can hai vong lap e co the tien ti hoi tu. Gia tr sau cung la 0,40083, va gia tr c lng bang thu tuc CORC va tr thong ke t c tnh toan nh sau (xem phan thc hanh may tnh 9.6 e thc tap tnh toan lai):

DEMAND = 0,157 0,892 PRICE + 0,0032 INCOME + 0,00356 TEMP (0,5) (1,1) (2,07) (6,42) Nhng gia tr c lng nay kha gan vi tr c lng theo thu tuc HILU. Tr thong ke DW cho phng trnh (9.9) la 1,55. Vi n = 29 va k = 3, ta co dL = 1,198 va dU = 1,65. Co the chng minh rang kiem nh DW a khong bac bo gia thuyet khong ve tng quan chuoi co gia tr bang khong cua cac phan d trong phng trnh (9.9). ac biet, kiem nh nay van cha the ket luan c.





} BAI TAP THC HANH 9.3 Dung d lieu trong bang DATA9-1 e c lng mo hnh log-hai lan bang phng phap OLS. Mo hnh log hai lan se cho biet o co gian cua bien thu nhap (income), gia (price), va nhiet o (temp). Hay thc hien mot kiem nh DW len cac phan d. Co chng c nao cho thay tnh t tng quan bac nhat khong? Neu co, hay ap dung cac thu tuc CORC va HILU e tnh toan va so sanh cac gia tr c lng. } Bang 9.1 c Lng Nhu Cau Ve Kem Bang Phng Phap Hildreth Lu

CONST. PRICE INCOME TEMP ESS 1.0 .64927 .9358 .00197 .00272 .025823

.9 .64166 .9824 .00149 .02284 .027317

.8 .53264 1.0064 .00044 .00303 .026854

.7 .41572 1.0001 .00075 .00321 .026470

.6 .30779 .9728 .00182 .00336 .026022

.5 .22084 .9342 .00264 .00348 .026522

.42 .16779 .9004 .00311 .00354 .025459

.41 .16229 .8967 .00316 .00355 .025452

.4 .15653 .8916 .00321 .00356 .025453

.39 .15136 .8876 .00325 .00357 .025454

.3 .11148 .8502 .00357 .00361 .025674

.2 .08025 .8101 .00379 .00364 .026395

.1 .05903 .7733 .00392 .00364 .027666 0 .04406 .7378 .00398 .00364 .029521

.1 .03387 .7058 .00400 .00363 .031964 .2 .02680 .6766 .00400 .00362 .034995 .3 .02210 .6505 .00398 .00360 .038612 .4 .01895 .6270 .00395 .00359 .042810 .5 .01695 .6060 .00392 .00357 .047585 .6 .01580 .5872 .00388 .00355 .052933 .7 .01538 .5707 .00384 .00354 .058846 .8 .01544 .5560 .00380 ..00352 .065324 .9 .01587 .5432 .00376 .00350 .072361

1.0 .01651 .5315 .00372 .00349 .079958 Nguon: Hildreth va Lu (1960), Bang 19, 36. Tai xuat ban di s cho phep cua Michigan State University





So Sanh Hai Thu Tuc Mot cach can ban, thu tuc HILU se tm kiem cac gia tr nam trong khoang -1 va +1 ma khien cho gia tr tong bnh phng phan d cua phng trnh (9.9) at cc tieu. Neu khoang cach gia cac bc nhay la nho th thu tuc phai thc hien rat nhieu so lan hoi quy; v the khi so sanh vi thu tuc CORC, phng phap HILU oi hoi s ho tr tnh toan cua may tnh rat ln. Ngc lai, thu tuc CORC lap lai nhieu lan e gia tr ESS() at cc tieu cuc bo (local minimum) va nh vay thu tuc co the bo qua gia tr cc tieu toan cuc (global minimum) neu mo hnh co nhieu hn mot iem cc tieu cuc bo. iem nhan xet nay c trnh bay trong hnh 9.4, trong o co hai iem cc tieu cuc bo la A va B. Cac iem c bieu dien bang cham tron nho bieu hien cac bc nhay tng ng cua thu tuc HILU. Ky thuat CORC se lap lai va at en iem cc tieu cuc bo la A, va nh vay no a bo qua iem cc tieu toan cuc B. Lu y rang phng phap HILU se chon iem tng ng vi gia tr H va bo qua iem cc tieu toan cuc thc s, nhng s chenh lech nay la khong ang ke. Tac gia Hildreth va Lu a tien hanh thc nghiem vi gan hai ta bo d lieu nhng khong tm thay cac iem cc tieu boi (multiple minima), va ket luan rang co le trng hp xuat hien cac iem a cc tieu la khong thng xuyen. Mot thu tuc lai ket hp (hybrid procedure) nen c s dung vi nhng bc nhay ln, bang 0,1 chang han, ch can 19 lan hoi quy (khong bao gom cac iem mut 1 va +1). Chon iem co gia tr ESS nho nhat trong phan tnh toan th au tien e lam iem khi au cua thu tuc CORC va lap lai cho en ket qua cuoi cung. V the trong hnh 9.4, phng phap HILU se chon gia tr H trong lan th au tien, va thu tuc CORC sau o lap lai cac bc nhay e at en iem cc tieu toan cuc B. Hau het cac chng trnh may tnh tot eu cho phep ap dung ca hai thu tuc lap lai va tm kiem; ay la mot giai phap toi u khi dung ca hai thu tuc nham bao am rang phng phap CORC se khong bo qua gia tr cc tieu toan cuc. Nen lu y rang thu tuc Hildreth Lu va thu tuc lai ket hp ch thch hp cho qua trnh AR(1), va ay chnh la mot iem gii han rat ln. V ly do tren ma thu tuc tm kiem nay khong c ng dung pho bien.





} Hnh 9.4 So Sanh Hai Thu Tuc HILU Va CORC

} V DU 9.8 Bay gi chung ta hay xem xet mot v du trong o cac gia tr c lng theo phng phap CORC va HILU la hoan toan khac nhau (phan thc hanh may tnh 9.7 trnh bay chi tiet cach thc thc hien v du nay). Xem xet mo hnh c c lng trong chng 4 s dung d lieu trong bang DATA4-2 di ay:

Ct = 1 + 2Wt + 3Pt + ut Trong o Ct la chi ph tieu dung tong hp, Wt la tong chi ph boi thng cho nhan vien, va Pt la tong li nhuan, tat ca ai lng tren eu la so lieu thc te vi n v tnh bang ty dollar My trong giai oan t 1959 1994. Tr thong ke Durbin Watson oi vi tnh t tng quan bac nhat la 0,969, bieu hien moi tng quan chuoi manh (hay kiem tra lai nhan nh nay). Phng phap CORC bat au vi gia tr c lng (0,494) co c t viec tnh toan phan d bang phng phap OLS, va sau o thc hien sau vong lap e at en gia tr cuoi cung la 0,562. Phng phap HILU se ap dung thu tuc lai ket hp nh a e ngh trc ay va bat au tm kiem trong khoang t 0,9 en + 0,9 vi bc nhay 0,1 va cung thc hien tng t trong khoang t 0,99 en + 0,99. Trong lan th au tien, ESS at gia tr cc tieu la 0,99. Chng trnh sau o se gia tr nay e lam iem khi au va thc hien mot vong lap CORC e at en gia tr cuoi cung la 0,9903 va hoan toan khac vi gia tr cuoi cung 0,562 tnh c bang thu tuc CORC. Hnh 9.5 se giai thch tai sao hai phng phap nay cho ra cac ket qua khac nhau. Trong hnh 9.5, cac iem ESS c

Cc tieu toan cuc(Glocal Minimum)

Cc tieu cuc bo (Local Minimum)

C H

A

B

ESS()

0





xac nh da tren cac gia tr nam trong khoang 0,1 en 1,0. Lu y rang thu tuc CORC bat au vi gia tr bang 0,494 va sau o hoi tu ve gia tr cc tieu cuc bo 0,562. Trong luc o phng phap lai ket hp HILU CORC a chon ngay gia tr cc tieu la 0,99. V the, thong qua v du nay chung ta co the chng minh rang phng phap hon hp HILU CORC tot hn han ngay ca khi ch s dung mot mnh v no khai thac c cac li the so sanh cua moi phng phap. } Hnh 9.5 Ve ESS Theo T 0.1-0.99

} 9.5 Tng Quan Chuoi Bac Cao Nh a e cap trc ay, ban chat cua cau truc sai so thng la cha biet. V vay, nha nghien cu phai thiet lap mot mo hnh cang tong quat cang tot oi vi phan tat nh cung nh oi vi cau truc sai so va thc hien phan biet d lieu gia cac phng trnh khac nhau. Cac nguyen ly c trnh bay trong cac phan trc ay co the ap dung cho tng quan chuoi bac cao hn. Trong phan nay, chung ta se thao luan ve cac thu tuc e kiem nh tnh t tng quan bac cao hn va e c lng cac thong so mo hnh khi cac so hang nhieu tuan theo tnh tng quan bac tong quat. Cac ac trng chung cua mo hnh vi so hang sai so t hoi quy c cho nh sau:

Yt = 1 + 2Xt2 + 3Xt3 + + kXtk + ut (9.10)

ut = 1ut 1 + 2ut 2 + 3ut 3 + + put p + t (9.11) Phng trnh (9.11) con c goi la qua trnh t hoi quy bac p cua cac phan d hay AR(p). Neu chung ta co d lieu theo tng quy, chung ta co the ky vong rang mo hnh t hoi quy bac bon la





hp ly. Tng t, d lieu theo thang co kha nang co tnh t tng quan bac 12 va d lieu theo gi co the co tnh tng quan chuoi bac 24. V the, chung ta can nhng ai lng e xac nh cau truc sai so t hoi quy bac tong quat cung nh cac thu tuc c lng co the ap dung cho trng hp bac cao hn. Kiem nh Tnh T Tng Bac Cao LM Breusch Godfrey Kiem nh LM, mo ta trong phan 9.3 c dung e kiem nh tnh tng quan chuoi bac nhat, de dang c m rong ap dung cho bac cao hn vi c mau khong c nho. Kiem nh nay c goi la kiem nh Breush (1978) Godfrey (1978). Viec thc hien thu tuc nay se ro rang hn neu chung ta ket hp hai phng trnh (9.10) va (9.11) nh sau:

Yt = 1 + 2Xt2 + 3Xt3 + + kXtk + 1ut 1 + 2ut 2 + 3ut 3 + + put p + t Gia thuyet khong la moi gia tr trong so cac gia tr eu bang zero (ngha la 1 = 2 = = p = 0) oi vi gia thuyet ngc lai cho rang t nhat mot trong cac gia tr nay khac zero. Gia thuyet khong nay rat giong gia thuyet ma chung ta a trnh bay trong chng 6 e kiem nh s them vao cac bien mi. Trong trng hp nay, nhng bien mi la ut 1, ut 2, , ut p ma co the c lng bang phan d 1tu , 2tu , , ptu . Cac bc tien hanh kiem nh nh sau:

Bc 1 c lng phng trnh (9.10) theo phng phap OLS va tnh ra cac gia tr phan d tu .

Bc 2 Hoi quy phan d tu theo tat ca cac bien oc lap trong phng trnh (9.10) cung nh cac phan d ut 1, ut 2, , ut p . So lan quan sat hieu qua cho bc hoi quy phu nay phai la n p v t p c xac nh cho thi oan t p +1 en n.

Bc 3 Tnh toan gia tr (n p)R2 trong phan hoi quy phu bc 2. Neu gia tr nay ln hn )(2p th gia tr cua phan phoi Chi-square vi p bac t do la phan dien tch pha ben

phai iem , va t ay chung ta se bac bo gia thuyet H0: 1 = 2 = = p = 0 va chap nhan gia thuyet H1: co t nhat mot trong so cac gia tr khac khong.

Mac du ban than thu tuc kiem nh th khong phc tap nhng nha nghien cu can phai quyet nh so bac p oi vi mo hnh t hoi quy cho trc bi phng trnh (9.11). Tnh nh ky cua d lieu (theo quy, thang, tuan, hay theo bat c khoang thi gian nao) se gop phan xac nh bac p. Trong bc 2, ngi ta a ch ra rang c mau thch hp la n p. Hn na, bc hoi quy phu co he so t hoi quy p cong them cac he so k cho k 1 bien giai thch va so hang hang so. V vay, n p toi thieu phai bang p + k (neu khong chung ta se co bac t do am). ieu nay co ngha la n toi thieu phai bang k +2p trc khi co the c lng c phan hoi quy phu. Neu c mau khong tng xng, chung ta co the bo bt mot vai so hang t hoi quy. V du, vi d lieu theo thang, chung ta co the thiet lap cac bien tre ng vi t = 1, 2, 3, va 12 va at cac he so t hoi quy khac bang zero. ng dung trong phan 9.7 trnh bay v du ve kiem nh tnh t tng quan bac cao.





c Lng Mot Mo Hnh Vi Sai So T Hoi Qui Bac Tong Quat Neu kiem nh Breusch-Godfrey bac bo gia thiet khong cho rang khong co tng quan chuoi, chung ta phai c lng mot cach hieu qua cac thong so cua phng trnh (9.10) va (9.11). Dang tong quat bac p cua phng trnh (9.9) la

Yt - 1Yt-1 - 2Yt-2 - 3Yt-3 - . . . - pYt-p (9.12) = 1 (1 - 1 - 2 - . . . -n) + 2 [Xt2 - 1 X(t-1)2 - . . . - n X(t-p)2] + . . . + k [Xtk - 1 X(t-1)k - . . . - n X(t-p)k] + t

Thuat toan Cochrance-Orcutt trong trng hp tong quat la nh nhau oi vi phng trnh (9.11) va (9.12) va ve mat khai niem cung tng t trng hp tng quan chuoi bac nhat. Trong thc te, cac chng trnh hoi quy chuan eu co kha nang thc hien cac bc tnh toan can thiet.

Bc 1 c lng phng trnh (9.10) theo OLS va gi lai cac phan d tu

.

Bc 2 Ke tiep hoi qui tu

theo -1tu

, 2-tu

, . . . , p-tu

(khong co so hang hang so) e thu c cac c lng 1

, 2

, ... cua cac thong so trong phng trnh (9.11). ay ch s

dung n-p quan sat. Bc 3 Dung cac c lng nay, bien oi cac bien oc lap va phu thuoc e co cac bien mi

trong phng trnh (9.12) Bc 4 c lng mo hnh a c bien oi (9.12) va tnh lan hai cac c lng . Bc 5 T cac c lng , tnh c lng a hieu chnh cua phan d ut bang cach s dung

phng trnh (9.10). Sau o quay lai bc 2 va lap lai cho en khi mot so tieu chuan c thoa man. V du, ta tnh tong bnh phng sai so cua phng trnh (9.12) va viec lap lai ket thuc khi cac ket qua tnh toan nay sai lech nho hn 0.1 phan tram hay mot so gia tr khac. Noi cach khac, qua trnh lap co the tiep tuc cho en khi gia tr logarit cua ham so thch hp cua phng trnh (9.12) khong thay oi vt qua mot mc phan tram qui nh trc.

Cac cuoi cung tnh c bc 5 sau o co the c dung e thc hien bien oi d lieu

lan cuoi e c lng (9.12). Tai moc hoi tu, cac c lng cua va co tnh thch hp cc ai. Cac sai so chuan va tr thong ke t lay c t phng trnh (9.12) se nhat quan va hieu qua mot cach tiem can tr khi mot so X co cha cac bien phu thuoc co hieu ng tre (v du nh Yt-1, Yt-2). Van e cua bien phu thuoc co hieu ng tre c e cap trong chng 10. Phng phap tren c trnh bay trong phan ng dung 9.7 vi chng trnh GRETL, trongo co lenh n gian goi la ar cho AR(p). Cac chng trnh khac nh B34S, SHAZAM, PcGive, va Eviews cung cho phep c lng AR(p). V cac tieu chuan hoi tu gia cac chng trnh khac nhau nen ket qua cung co the co khac biet.





D Bao Va o Thch Hp Trong Cac Mo Hnh AR Phng trnh (9.4) mo ta mot bieu thc oi vi viec d bao Yt theo tng quan chuoi bac nhat trong ut. Tng t cho mo hnh AR tong quat la

tY

= 1 + 2 Xt2 + . . . + k

Xtk + 1

-1tu

+ 2

2-tu

+ . . . + p p-tu

(9.13)

Tai thi iem t, tat ca cac so hang u co hieu ng tre eu co the c lng va do o d bao cua

Yt co c theo cach nay se hieu qua hn nhieu so vi d bao theo OLS vi viec bo qua cac so

hang u (tat nhien vi gia nh la mo hnh c ac trng va qua trnh sai so la chnh xac).

Tng t can phai lu y la gia tr R2 tnh c t phng trnh (9.12) se la thc o s bien thien trong bien phu thuoc a c bien oi ch khong phai trong Y. Do vay se la phu hp hn

neu tnh R2 nh la bnh phng cua tng quan gia Yt thc va tY

d bao t phng trnh (9.13).

Trong phan 4.1, ta a mo ta cach tnh phng sai cua d bao tY

. Tuy nhien vi s hien dien cua tng quan chuoi, cach tnh nh vay khong the thc hien c v phng sai cua d

bao lien quan en nhieu so hang khac nh Var( 1

-1tu

) va Cov( 1 , 1

-1tu

).

} 9.6 Kiem nh Engels Arch Cac loai tng quan chuoi c trnh bay cho en nay ch xem xet en so hang sai so ut. Do o trong AR(p) chung ta xem nh ut phu thuoc tuyen tnh vao p sai so qua kh ut-1, ut-2, . . . ut-p. o mot loai tng quan chuoi thng gap trong d lieu theo thi gian, ac biet khi tao ra cac d bao. Mot so cac chuyen gia d bao nhan thay rang phng sai cua sai so d bao khong phai la mot hang so ma thay oi theo tng thi oan. V du, khi Cuc D Tr Lien Bang chuyen t kiem soat lai suat sang kiem soat tang trng tien te, nh a c thc hien trc kia, lai suat tr nen bien ong rat nhieu (o la, chung bat au thay oi nhieu xung quanh gia tr trung bnh). V vay, cac sai so d bao lien quan en d bao lai suat co tnh chat goi la phng sai cua sai so thay oi. Mac du co the ky vong ch la mot s thay oi ve cau truc trong phng sai, ngi ta lai nhan thay rang phng sai a thay oi eu an. S thay oi phng sai cua sai so tng t cung c nhan thay khi chnh sach ty gia hoi oai chuyen t co nh sang linh hoat. Trong trng hp linh hoat, ty gia hoi oai dao ong manh, lam cho phng sai d bao ln hn. Trong ly thuyet tien te va ly thuyet tai chnh, tap danh muc tai san tai chnh la ham cua trung bnh va phng sai ky vong cua suat thu li. S bien ong manh cua gia chng khoan hay suat thu li thng la bieu hien cua phng sai khong co nh theo thi gian. Engel (1982) a a ra mot phng phap tiep can mi e mo hnh hoa phng sai cua sai so thay oi oi vi d lieu theo thi gian. Tac gia at ten cho mo hnh la ARCH (autoregressive conditional heteroscedascity phng sai cua sai so thay oi co ieu kien t hoi qui). Qua trnh cac phng sai c tnh c gia nh nh sau





t2 = 0 + 1 u2t-1 + . . . + pu2t-p (9.14)

Phng trnh (9.14) c biet en nh la qua trnh ARCH bac p. Thuat ng t hoi qui c dung v phng sai sai so tai thi iem t c gia nh la phu thuoc vao bnh phng cac so hang sai so trc o. Tng t, phng sai tai thi iem t la co ieu kien theo phng sai cac giai oan trc va do o hnh thanh thuat ng phng sai cua sai so thay oi co ieu kien. Kiem nh ARCH co gia thiet ban au H0 : 1 = 2 = ... = p = 0. Cac bc kiem nh nh sau:

Bc 1 c lng phng trnh (9.10) theo OLS

Bc 2 Tnh phan d tu

= Yt 1

2

Xt2 3

Xt3 . . . k

Xtk, bnh phng cac phan

d va tnh 1-tu2

, 2-tu2

, . . ., p-tu2

Bc 3 Hoi qui tu2

theo mot hang so, 1-tu2

, 2-tu2

, . . ., p-tu2

. ay la hoi qui phu, vi n-p quan sat.

Bc 4 T R2 cua hoi qui phu, tnh (n-p)R2. Theo ieu kien gia thuyet H0, (n-p)R2 co phan bo chi-square vi bac t do p. Bac bo H0 neu (n-p)R2 > 2p (), iem nam tren 2p vi dien tch nam ve pha ben phai.

} V DU 9.9

Khi gii thieu mo hnh ARCH, Engel a ap dung vao mo hnh ty le lam phat Anh. Mo hnh c dung nh sau:

.p t = 1 .p t-1 + 2 .p t-4 + 3 .p t-5 + 4(pt-1 wt-1) + 5 + ut

Trong o .p t = sai phan th nhat cua logarith cua ch so gia tieu dung (Pt) o la, lnPt lnPt-1 , la ty le

thay oi tc thi cua Pt pt = lnPt wt = lnWt , Wt la ch so cua mc lng D lieu hang quy cho giai oan t 1958.2 en het 1977.2. Trc tien Engel kiem nh mo hnh oi vi tng quan chuoi bac sau trong cac phan d va khong thay co bang chng nao ve tng quan chuoi. Sau o ong thc hien kiem nh ARCH cho cac bac mot va bon. Tac ong ARCH bac mot khong y ngha, nhng tr thong ke Chi-square cua ARCH bac bon la 15,2. Bi v 24 (0,01) = 13,277, mo hnh ARCH bac bon co y ngha. Co the nhan thay la d lieu theo qu, nen tac ong ARCH bac bon nh vay la khong qua bat ng. Tuy nhien, khong co tac ong tng quan chuoi bac bon trong ban than cac phan d, ma ch la cac phng sai cua chung.





} V DU 9.10

Kiem nh va c lng that s oi vi mot mo hnh ARCH c minh hoa bang mot mo hnh n gian hoa ve lai suat. DATA9-2 co d lieu hang nam cua My trong giai oan 1960-1995 ve suat chiet khau cua Cuc D Tr Lien Bang (tnh theo phan tram), cung tien te (M2 tnh theo ty o la), va tham hut lien bang (D) tnh theo n v ty o la hien hanh. Mo hnh bieu dien quan he suat chiet khau (r) vi cung tien te (M) va tham hut ngan sach chnh phu (D) co hieu ng tre hai thi oan nh sau

rt = 1 + 2Mt-1 + 3Mt-2 + 4Dt-1 + 5Dt-2 + ut Phng sai sai so c gia nh ban au theo ARCH (3):

2t = 0 + 1u2t-1 + 2u2t-2 + 3u2t-3 Phan thc hanh may tnh 9.8 gom cac bc e at c cac ket qua thc nghiem cua v du nay va bang 9.2 la bang the hien mot phan ket qua. Phng trnh li tc c c lng au tien, sau o la bnh phng phan d c lng, va hoi qui phu oi vi phng sai c lng. R2 cua hoi qui nay la 0,126, nhng (n-p) R2 = 3,91 co tr thong ke p la 0,27, khong co y ngha. Do o, ARCH(3) khong c chap nhan. Tuy nhien, so hang ARCH(1) co y ngha mc 0,09 (xem bang 9.2), do o mot ac trng ARCH(1) c kiem nh tiep. Gia tr p cua kiem nh nay la 0,048, cho thay co y ngha mc 5 phan tram. Sau o chung ta dung hoi qui phu a c lng e tnh trong so va dung e thc hien c lng bnh phng toi thieu theo trong so (WLS) cua mo hnh. Bi v so hang tham hut D2 la khong co y ngha, no b loai ra khoi mo hnh e cai thien o chnh xac cua cac bien khac va e giam bat ky quan he a cong tuyen neu co hien dien. Mo hnh cuoi cung c a ra di ay, vi gia tr p trong ngoac:

tr

= 3,380 + 0,0283 Mt-1 0,0262 Mt-2 0,0347 Dt-1 (





Ve van e khao sat cac ng dung cua ARCH trong tai chnh, xem them Engle va Rothschild (1992). Ve ARCH tong quat (con goi la GARCH), xem them trong Bollerslev (1986), Greene (2000, chng 18.5), va cac trch dan co lien quan o. } Bang 9.2 Mot Phan Ket Qua Cua V Du 9.10 Vi Data9-2 [nh ngha cac bien co hieu ng tre sau ay]

M1 = M(-1) M2 = M(-2) D1 = D(-1) D2 = D(-2)

[Bo qua hai quan sat au tien, v M2 va D2 khong xac nh, va c lng mo hnh] Model 1: OLS estimates using 34 observations 1962-1995 Dependent variable: r

VARIABLE COEFFICIENT STDERROR T STAT 2Prob ( t > |T| )

0) Const 2,8622 0,8085 3,540 0,001371 *** 5) M1 0,0328 0,0064 5,130 0,000018 *** 6) M2 -0,0300 0,0064 -4,662 0,000065 *** 7) D1 -0,0378 0,0131 -2,884 0,007331 *** 8) D2 -0,0076 0,0131 -0,580 0,566637 } Bang 9.2 (tiep theo) [e thc hien kiem nh Arch(3), trc tien tao cac bien sau:

usq = 2

tu

trong o tu la phan d t mo hnh tren

usq1 = usq (-1) usq2 = usq (-2) usq3 = usq (-3) Bo qua ba quan sat ke tiep va c lng hoi qui phu ARCH(3) vi usq la bien phu thuoc.] Model 2 : OLS estimates using 31 observations 1963-1995 Dependent variable: usq


0) const 2,1770 1,2131 1,795 0,083923 * 10) usq1 0,3353 0,1915 1,751 0,091306 * 11) usq2 0,0597 0,2022 0,295 0,770149 12) usq3 -0,1039 0,1921 -0,541 0,593185

Unadjusted R-squares 0,126 Adjusted R-squares 0,029 Chi-square (3): area to the right of (LM)3,905795 = 0,271818





[ARCH(3) khong c chap thuan ngay ca mc 0,25, nhng ARCH(1) co y ngha mc 9,13 phan tram. Do o, can thiet phai kiem nh ARCH(1) bang cach hoi qui usq theo mot hang so va usql. Lu y la ay ban ch can bo qua mot quan sat.] Model 3 : OLS estimates using 33 observations 1963-1995 Dependent variable: usq


0) const 1,9308 0,9817 1,967 0,058206 * 10) usq1 0,3454 0,1691 2,043 0,049668 **

Unadjusted R-squares 0,119 Adjusted R-squares 0,090 Chi-square(1): area to the right of (LM) 3,914781 = 0,047863 [Gia tr p cho thay ARCH(1) co y ngha tai mc 5 phan tram. Tng t, du khong the hien ra ay, tat ca cac gia tr cua phng sai a c thch hp (ky hieu la usqhat) la dng. Ke tiep la tnh bien trong so wt=1/(can bac hai cua usqhat) va dung no e tnh c lng FGLS theo phng phap bnh phng toi thieu theo trong so.]

} Bang 9.2 (tiep theo)

Model 4: WLS estimates using 33 observations 1963-1995 Dependent variable: usq Variable used as weight: wt


0) const 3,3075 0,7569 4,370 0,000155 *** 5) M1 0,0278 0,0058 4,760 0,000053 *** 6) M2 -0,0255 0,0058 -4,393 0,000145 *** 7) D1 -0,0323 0,0124 -2,611 0,014355 ** 8) D2 -0,0046 0,0129 -0,358 0,723045

Unadjusted R-squares 0,520 Adjusted R-squares 0,451

MODEL SELECTION STATISTICS SGMASQ 3,61497 AIC 4,15292 FPE 4,16269 HQ 4,48215 SCHWARZ 5,20987 SHIBATA 3,99672 GCV 4,2605 RICE 4,40083

Excluding the constant, p-value was highest for variable 8 (D2) [Ke tiep, bo qua D2, vi he so khong co y ngha ngay ca mc 70 phan tram] Model 5: WLS estimates using 33 observations 1963-1995 Dependent variable: usq Variable used as weight: wt


0) const 3,3795 0,7186 4,703 0,000058 ***





5) M1 0,0283 0,0056 5,093 0,000020 *** 6) M2 -0,0262 0,0054 -4,898 0,000034 *** 7) D1 -0,0347 0,0103 -3,383 0,002070 ***

Unadjusted R-squares 0,515 Adjusted R-squares 0,464

MODEL SELECTION STATISTICS SGMASQ 3,52526 AIC 3,94783 FPE 3,95256 HQ 4,19629 SCHWARZ 4,73301 SHIBATA 3,84897 GCV 4,0115 RICE 4,0893 [So sanh gia mo hnh 4 va 5: 8 gia tr thong ke a c cai thien]

} 9.7 Ap Dung: Nhu Cau Ve ien Nang Ap dung c chon e xem xet cac van e khac nhau a trnh bay trong chng nay la vi d lieu theo quy nham mo hnh hoa viec tieu thu ien nang cua cac khach hang dan c cua cong ty Gas va ien San Diego. Bien c dung la ien nang tieu thu, n v kilowatt/gi (kwh), tren moi khach hang. Van e c quan tam chu yeu la c lng o co gian cua cau theo gia va theo thu nhap oi vi ien nang va sau o nghien cu xem co bat ky s thay oi ve cau truc nao khong. DATA9-3 c mo ta trong phu luc D the hien d lieu theo quy cho cac bien sau t quy hai 1972 en het quy bon 1993:

RESKWH = Doanh thu ien t cac khach hang dan c (trieu kilowatt - gi) NOCUST = Lng khach hang dan c (tnh theo hang ngan) PRICE = Gia trung bnh cho bieu gia oi vi ho ca the (xu/kwh) CPI = Ch so gia tieu dung San Diego (1982 1984 =100) INCOME = Tong thu nhap ca nhan cua hat San Diego theo quy (trieu o la hien tai) CDD = Ngay nhiet o lanh (giai thch ben di) HDD = Ngay nhiet o nong POP = Dan so hat San Diego (tnh theo hang ngan)

D lieu c bien oi phu hp trc khi s dung trong cong thc toan kinh te. ay chung ta dung mo hnh log-hai lan, phu hp khi tat ca cac co gian khong oi (xem phan 6.10). Bien phu thuoc (ky hieu la LKWH) do o se la logarit cua kilowatt gi doanh thu tren moi khach hang dan c. Chung ta co

LKWH = ln(RESKWH/NOCUST)





Cac Yeu To Quyet nh Nhu Cau ien Nang Mot trong nhng yeu to quyet nh chu yeu cho nhu cau oi vi bat ky san pham nao la thu nhap. V tieu dung c tnh theo tng khach hang, thu nhap cung phai c tnh theo au ngi. Hn na, cac thong so phai dang thc e hieu chnh nhng tac ong cua lam phat. Do o, bien thu nhap thch ang la tren moi au ngi theo gia tr o la khong oi. DATA9-3 co gia tr tong thu nhap ca nhan theo o la hien hanh. Do o, thu nhap tren au ngi theo gia tr hien hanh la INCOME/POP. e chuyen oi bien nay sang dang thc, chung ta can chia cho ch so gia CPI/100. Gia tr nay se o thu nhap tren au ngi cho giai oan c s (trong trng hp nay la 1982-1984). Bien thch ang se la

LY =

POP*CPI

INCOME*100ln

Mot yeu to quyet nh quan trong khac xac nh nhu cau la gia cua hang hoa. Do vay gia ien rat quan trong. Khong co mot mc gia ien duy nhat, ngay ca cho oi tng khach hang dan c. Gia tang dan theo mc tieu thu ien thc te. Ai o co the bien luan rang chi ph bien hay chi ph trung bnh cua ien nang co the dung nh mot bien giai thch. Tuy nhien chung ta se khong ban en cac van e o. oc gia co the xem them ve ket qua khao sat rat hay cua Lester Taylor (1975). ay chung ta dung gia trung bnh theo bieu gia oi vi ho ca the ai dien cho khach hang dan c. Gia c tnh bang xu tren moi kilowatt gi theo gia tr o la hien hanh. Nh a e cap la gia phai c tnh theo gia tr thc, no phai c chia cho CPI/100. Bien gia se la

LPRICE =

CPIPRICE*100ln

Co le yeu to quyet nh quan trong nhat oi vi viec tieu thu ien chnh la thi tiet. Khi

tri lanh vao mua ong, khach hang phai bat lo si, va trong nhng ngay he nong, ho lai bat may ieu hoa nhiet o hay quat ien. Do o chung ta co the ky vong rang nhiet o se co anh hng co y ngha en xu hng tieu thu. V d lieu theo moi thi oan ba thang, chung ta can co mot cach thc te nao o e biet c tac ong cua nhiet o. Mot phng phap pho bien thng dung bi hau het cac cong ty trong nc la tnh so ngay nhiet o. Trong mua he, o se la so ngay nhiet o lanh (CDD), va trong mua ong o la so ngay nhiet o nong (HDD). Cac bien nay c nh ngha nh sau:

CDD = ==

+Dd

d

dd

1

0 ,652

MINTEMPMAXTEMPmax

HDD = ==

+Dd

d

dd

1

0 ,2

MINTEMPMAXTEMP 65max





Trong o D la so ngay trong quy, MAXTEMP la nhiet o cao nhat, va MINTEMP la nhiet o thap nhat cua ngay d.

Mac du cong thc co ve phc tap, no lai rat de hieu theo y ngha thong thng. au tien chung ta tnh nhiet o trung bnh trong mot ngay theo trung bnh cua nhiet o cao nhat va thap nhat. Neu nhiet o trung bnh chnh xac la 650F, ta mac nh rang khach hang se khong bat lo si hay may ieu hoa. Trong mua he, neu nhiet o trung bnh nay vt qua 65 mot mc ang ke nao o, khach hang se dung ieu hoa nhiet o. Khoang gia tang nhiet o nay c o theo tr trung bnh tr i 65. Khi cong tat ca cac gia tr cua cac ngay trong quy, chung ta co so ngay nhiet o lanh. Neu trung bnh di 65 vao mua he, khong co bat ky ieu chnh nao, do o CDD bang khong. Nguyen tac tnh toan HDD trong mua ong cung tng t. Neu nhiet o tang qua 65 trong mua ong, khach hang se khong can dung en lo si, HDD bang khong. Khi trung bnh la di 65, chenh lech gia 65 va tr trung bnh se gop phan vao so ngay cua mua trong HDD. Cong tat ca cac ngay nong trong quy, ta co tong HDD.

Lu y rang trong d lieu co mot so quy HDD va CDD rat gan gia tr khong. ieu o co ngha la tac ong cua cac bien nay gan nh bang khong oi vi tng ngay cua quy. V ieu nay chung ta se khong lay logarit cua HDD va CDD, chung c a vao mo hnh theo tuyen tnh. Mo Hnh C Ban Mo hnh c ban c the hien qua phng trnh sau:

LKWH = 1 + 2LY + 3LPRICE + 4CDD + 5HDD + u (9.15) Thu nhap cang cao, nhu cau ve mot san pham thong thng cang ln. Do o co the ky vong 2 dng. Khi gia ien tang, nhu cau ve ien se giam. Do vay co the ky vong 3 se am. CDD tang cho thay co nhieu ngay co nhiet o trung bnh cao hn 65 o hn. ieu nay thng c ky vong se keo theo nhu cau dung may ieu hoa nhiet o, do o 4 se dng. Tng t neu HDD tang, nhu cau si se tang va 5 cung se dng. Dau ky vong cho cac (tr 1) nh sau 2 > 0, 3 < 0, 4 > 0, 5 > 0 Chung ta s dung 87 quan sat trong DATA9-3 e bien oi d lieu tho sang cac bien trong phng trnh (9.15). Ap dung qui trnh OLS, mo hnh c lng la (Phan Thc Hanh May Tnh 9.9 trnh bay chi tiet e thc hien lai tat ca cac ket qua thc nghiem trong ap dung nay)

LKWH = 0,398 0,036LY 0,094LPRICE + 0,0002676CDD + 0,0003607HDD (1,87) (-0,24) (-3,38) (7,78) (12,09)

2R = 0,651 d.f. = 82 DW d = 1,219





Gia tr trong ngoac la tr thong ke t, nhng neu co tng quan chuoi, cac gia tr nay (va cua 2R ) se khong con y ngha. Cung can lu y la LY co dau am, ngc vi anh gia theo trc

giac. Kiem nh Tng Quan Chuoi T bang A.5 cua phu luc A chung ta lu y rang n = 87 va k = 4 (so hang hang so khong a vao ay) cac bien cua tr thong ke Durbin-Watson (noi suy) la dL = 1,556 va dU = 1,749 oi vi kiem nh mot pha vi mc y ngha 5%. Gia tr d tnh c nho hn dL, va do vay co dau hieu co y ngha ve t hoi qui bac nhat. Tuy nhien v d lieu theo quy, nen se hp ly hn neu la tng quan chuoi bac bon. Phng trnh sai so bay gi se la

ut = 1ut-1 + 2ut-2 +3ut-3+4ut-4 + t

Gia thiet khong la 1 = 2 = 3 = 4 = 0. V chung ta ang s dung bon o tre, so quan sat hieu lc ch la 83. Tng t, R2 cha hieu chnh cho hoi qui phu la 0,0666, lam cho tr thong ke (n-p)R2 la 55,3, tng ng co gia tr p nho hn 0,0001. Nh vay chung ta a co mot chng c rat manh ve tng quan chuoi bac bon. Mo hnh sau o c c lng theo thu tuc Cochrane-Orcutt a trnh bay trong phan 9.5; ket qua nh sau vi gia tr trong ngoac kep la tr thong ke t.

LKWH = 0,237 + 0,102LY 0,098LPRICE + 0,0002756CDD + 0,0002288HDD (1,7) (0,9) (-3,5) (10,98) (9,4)

2R = 0,897 d.f. = 78 = 0,02547

Du cac he so la hp ly nhng mo hnh nay c ac trng sai mot cach nghiem trong bi

v khong hp ly khi ky vong rang cau truc nay se on nh trong suoi giai oan 1972-1993 trong khi a co en hai cuoc khung hoang nang lng. Do o chung ta se chuyen sang mot mo hnh vi cong thc va phan tch the hien ay u hn nhng thay oi ve cau truc. Mo Hnh Hoa Thay oi Ve Cau Truc Trong suot giai oan 1973 1974 va 1978 1979, gia dau tho a gia tang ot bien va tiet kiem la khau hieu e giam nhu cau. Ket qua la cac thiet b, may moc tiet kiem nang lng, o to tiet kiem xang. Do o co the ky vong quan he gia tieu thu ien nang va cac yeu to quyet nh cua no se thay oi. Tuy nhien, gia tang ot bien ve gia se khong xay ra lien tuc. Nh chung ta co the thay hnh 9.6, bat au t nam 1983, gia thc cua ien nang a giam. Do vay chung ta co the mong muon kiem nh xem lieu co mot s thay oi ve cau truc a dien ra t nam 1983 hay khong.

Neu co mot s thay oi ve cau truc, co ba bien gia c nh ngha nh sau

D74 = 1 t 1974.1 tr i; bang 0 neu ieu kien khac





D79 = 1 t 1979.1 tr i; bang 0 neu ieu kien khac D83 = 1 t 1983.3 tr i; bang 0 neu ieu kien khac

Tiep theo chung ta cho cac he so hoi quy phu thuoc vao cac bien gia nay. Chang han, trong Phng trnh (9.15) chung ta co:

2 = a0 + a1D74 + a2D79 + a3D83 Cac o co gian theo thu nhap trong 4 thi oan, bat au t 1972.2, se la a0, a0 + a1, a0 + a1 + a2, va a0 + a1 + a2 + a3. Do o, a1 la s thay oi ve o co gian theo thu nhap (tng ng vi giai oan t 1972.2 1973.4) co the c quy cho la do s thay oi ve cau truc nam 1974, va a2 la s thay oi bo sung do s thay oi ve cau truc nam 1979, va cung tng t cho cac gia tr khac. Ngoai s thay oi nay, o nhay cua cac so o thi tiet (4 va 5) co the cung phu thuoc vao gia ien. Neu, chang han, gia ien cao, khach hang se han che dung may ieu hoa nhiet o hoac lo si e tiet kiem tien. Tac ong nay co the c giai thch bang cach cho 4 = b0 + b1LPRICE + . V co rat nhieu so hang, chung toi khong trnh bay mo hnh hoan chnh, thay vao o se trnh bay danh sach bien Bang 9.3. } Hnh 9.6 Gia ien Thc (xu/kwh) cho SDG&E Viec lap mo hnh co xet en toan bo moi tng tac cua tat ca cac bien gia la tinh than cua phng phap Hendry/LSE, phng phap i t mo hnh tong quat en mo hnh n gian hn. Kiem nh nhan t Lagrange cung tr nen cong kenh hn neu ap dung trong trng hp nay v no oi hoi phai hoi quy cac phan d t mo hnh a bien oi Phng trnh (9.12) theo cac bien

Gia





a c bien oi tng t trong phng trnh tong quat. Thay v vay, au tien chung ta c lng mo hnh khong gii han trc va sau o co gang lam cho no n gian hn. Bang 9.4 cha cac tr c lng OLS cua mo hnh hoan toan tong quat (xem Phan thc hanh may tnh 9.9 e biet cac lenh chay lai cac ket qua nay). Tr thong ke Durbin-Watson cho mo hnh khong gii han nay la 1.931, cho thay rang khong ton tai s tng quan chuoi bac nhat. V vay chung ta co the ap dung phng phap OLS va thu c cac c lng vi cac tnh chat mong muon. That thu v khi biet rang trong khi ac trng mo hnh c ban b tac ong cua hien tng t tng quan, mo hnh hoan chnh hn se khong chu tac ong nay. Tuy nhien, nh co the thay Bang 9.4, hau het cac he so hoi quy co gia tr p-value cao, cho thay chung khong co y ngha. ieu nay khong co g ngac nhien v, vi rat nhieu bien oc lap dang cac tch cheo, chung ta co the ky vong hien tng a cong tuyen cao gia chung. e cai thien o chnh xac cua cac c lng, cac bien khong co y ngha vi cac gia tr p-value cao nhat se c loai bo mot hay hai bien mot lan va mo hnh c c lng lai. Cac ket qua cua mo hnh cuoi cung c trnh bay bang 9.5. Nh se thay rang mo hnh nay cung se khong chu tac ong cua s tng quan chuoi bac nhat. Hn na, tat ca he so hoi quy la co y ngha tai mc y ngha 5% hay thap hn, va cac tr thong ke la chon mo hnh tot hn nhieu so vi mo hnh tong quat. } Bang 9.3 nh Ngha Cac Bien c Bien oi

Ten nh ngha

LKWH ln(RESKWH/NOCUST LPRICE ln(100*PRICE/CPI) LY ln[100*INCOME/(CPI*POP)] LYD74 LY*D74 LYD79 LY*D79 LYD83 LY*D83 LPRD74 LPRICE*D74 LPRD79 LPRICE*D79 LPRD83 LPRICE*D83 D74CDD D74*CDD D79CDD D79*CDD D83CDD D83*CDD D74HDD D74*HDD D79HDD D79*HDD D83HDD D83*HDD LPRCDD LPRICE*CDD LPRHDD LPRICE*HDD





Dien Dch Cac Ket Qua Nhng he so c c lng cho 4 thi oan c trnh bay bang 9.6 (kiem tra lai). Nen lu y rang giai oan ieu khien t 1972.2-1973.4 ch co 7 gia tr quan sat va v vay cac ket qua cua mo hnh cho giai oan nay khong nen c xem xet qua chat che. Chang han, o co gian ve thu nhap la khong co y ngha ve mat thong ke trong giai oan nay. Trong suot giai oan hai cua gia ien tang (1974.1 1978.4), o co gian thu nhap gan nh bang 1. Trong giai oan th ba no giam xuong con 0,16, va trong giai oan cuoi, khi gia ien thc giam, o co gian theo thu nhap co gia tr am, cho thay rang nhu cau ve ien la mot hang hoa thap cap (thiet yeu) } Bang 9.4 c Lng OLS cua Mo Hnh Tong Quat Hoan Toan VARIABLE COEFFICIENT STDERROR T STAT 2Prob(t>|T|)

CONSTANT -0.796868 5.714984 -0.139435 0.889538 D74 -1.004434 5.730953 -0.175265 0.861416 D79 1.916922 0.706665 2.712631 0.008534***D83 0.024624 0.592544 0.041557 0.966979 LY -2.636002 6.672636 -0.395047 0.69410Q LYD74 3.586062 6.680982 0.536757 0.593268 LYD79 -0.7321 0.518463 -1.412058 0.162703 LYD83 -0.309173 0.444267 -0.695917 0.488962 LPRICE 2.240851 1.82873 1.225359 0.224862 LPRD74 -1.884615 1.831642 -1.028921 0.30733 LPRD79 -0.44734 0.136597 -3.274888 0.001697***LPRD83 0.133727 0.064403 2.076425 0.041813** CDD 0.001418 4.665718e-04 3.039785 0.003409***D74CDD -2.324821e-04 3.630704e-04 -0.640322 0.524214 D79CDD -3.897257e-05 9.707234e-05 -0.40148 0.689384 D83CDD 7.021266 e-05 6.488312e-05 1.082141 0.283188 LPRCDD -4.066302e-04 1.677691e-04 -2.42375 0.018153** HDD 9.496237e-04 4.176021e-04 2.273992 0.026276** D74HDD -2.830809e-04 3.169507e-04 -0.893139 0.375078 D79HDD -4.221766e-05 8.608874e-05 -0.490397 0.625504 D83HDD -3.228573e-05 6.658090e-05 -0.48491 0.629371 LPRHDD -1.095802e-04 1.558676e-04 -0.703034 0.484545 Mean of dep. var. 0.327332 S.D. of dep. variable 0.080775 Error Sum of Sq (ESS) 0.081511 Std Err of Resid. (sgmahat) 0.035412 Unadjusted R-squared 0.855 Adjusted R-squared 0.808 F-statistic (1, 32) 18.212322 p-value = Prob(F>18.212) is < 0.0001 Durbin-Watson stat. 1.930695 First-order autocorr. coeff 0.025

MODEL SELECTION STATISTICS





SGMASQ 0.001254 AIC 0.001554 FPE 0.001571 HQ 0.001997 SCHWARZ 0.002898 SHIBATA 0.001411 GCV 0.001678 RICE 0.001896 Lu y: ba dau * ch mc y ngha (hai pha) tai mc 1%, hai dau * ch mc y ngha gia 1 va 5%, va mot dau * ch mc y ngha gia 5 va 10%. } Bang 9.5 c Lng OLS cua Mo Hnh Cuoi Cung

VARIABLE COEFFICIENT STDERROR T STAT 2Prob(t>|T|) Constant -1.682911 0.395837 -4.251527





Ton tai s tng tac gia nhng ngay co nhiet o mat va gia ien. Nhng ngay co nhiet o mat thay oi t 0 en gan 1000. } Bang 9.6 Cac He So c Lng Cho Bon Giai oan Bien

CONSTANT LY LPRICE CDD HDD LPRICExCDD1972.2-1973.4

D74 = D79 = D83 = 0 -1.68291100 0.00000000 0.96591000 0.00103500 0.00055834 -0.00033167

1974.1-1978.4 D74 = 1, D79 = D83 = 0 -1.68291100 0.98080400 0.28108100 0.00103500 0.00043660 -0.00033167

1979.1-1983.2 D74 = D79 = 1, D83 = 0 0.26660700 0.16009600 -0.14114200 0.00103500 0.00043660 -0.00033167

1983.3-1990.4 D74 = D79 = D83 = 1 0.26660700 -0.10072400 -0.00654400 0.00103500 0.00034324 -0.00033167

Trong giai oan au nay, khi gia ien tang cham, o co gian ve gia co gia tr dng, ieu nay ngc vi cac ly thuyet kinh te chuan tac. Nguyen nhan cua ieu nay co the la do viec tieu thu ien tang dan theo s tang trng cua dan so va thu nhap, va xu hng noi bat nay co the c nhan dien c bang mo hnh hoi quy vi mot dau dng. Nen lu y rang khi gia bat au tang, tac ong dng b giam ang ke; va t nam 1979 khach hang a phan ng bang cach giam so lng cau, mac du hanh vi nay t c tuyen bo trc nam 1983 khi gia ien thc bat au giam. Nh a thao luan trc ay, chung ta lap luan rang tac ong thi tiet co the phu thuoc vao gia ien, va chung ta co nhng bang chng xac nhan ieu o. Tac ong can bien cua nhng ngay co nhiet o mat c trnh bay di ay va nh nhau cho tat ca cac thi oan

0,001035 0.00033167LPRICE Ro rang tac ong can bien cua thi tiet phu thuoc am vao gia ien. Noi cach khac, gia tang mot ngay co nhiet o mat se dan en mot s gia tang nho hn trong viec s dung ien neu gia ien cao. Nhng ngay nhiet o nong cung co tac ong ky vong dng, mac du khong co s tng tac co y ngha vi gia. Trong cac nam 1974 va 1983 co s sut giam ve tac ong HDD can bien. So Sanh Cac Gia Tr D Bao That thu v khi xem xet cac tr d bao t cac mo hnh se thay oi nh the nao khi chay tren d lieu that. Bang 9.7 cha cac sai so phan tram tuyet oi cua ba mo hnh. V cac bien phu thuoc dang logart, chung ta ap dung hieu chnh thien lech nh a mo ta chng 6 (xem cac bc tien hanh Phan Thc Hanh May Tnh 9.9). Phan tram sai so d bao tuyet oi t cac c lng OLS c ap dung vao Phng trnh (9.15) c gan ten la Mo Hnh A, cung mo hnh





nay nhng c c lng theo CORC tong quat cho AR(4) c gan ten la Mo Hnh B, va Mo Hnh C ch mo hnh cuoi cung trong bang 9.6. That thu v khi phat hien ra rang ve mat nang lc d bao, mo hnh cuoi cung, mo hnh xet en s thay oi ve cau truc nhng khong the hien s tng quan chuoi, khong phai la mo hnh tot nhat. Mo hnh B co ca hai gia tr sai so phan tram tuyet oi trung bnh (MAPE) va sai so bnh phng trung bnh (MSE) thap nhat. ong thi, cac gia tr sai so phan tram rieng le hau het thap hn 5%, ch co mot trng hp ngoai le mc 6,08%. } Bang 9.7 So Sanh cac Sai So Phan Tram D Bao Tuyet oi (%)

Thi oan Mo hnh A Mo hnh B Mo hnh C Thi oan Mo hnh A Mo hnh B Mo hnh C

1973.2 1973.3 1973.4 1974.1 1974.2 1974.3 1974.4 1975.1 1975.2 1975.3 1975.4 1976.1 1976.2 1976.3 1976.4 1977.1 1977.2 1977.3 1977.4 1978.1 1978.2 1978.3 1978.4 1979.1 1979.2 1979.3 1979.4 1980.1 1980.2 1980.3 1980.4 1981.1 1981.2 1981.3 1981.4 1982.1 1982.2 1982.3 1982.4

2.98 0.95 2.45 3.44 5.70 2.48 4.86 1.44 7.73 2.08 4.28 3.03 1.76 2.37 9.41 8.52 2.51 0.49 8.23

11.48 2.34 3.39 7.43 5.83 1.94 1.68 9.44 9.79 0.52 0.47 6.98 6.02 1.74 5.71 4.00 1.57 3.39 3.49 0.83

3.28 2.93 1.43 6.08 3.48 1.76 3.09 4.07 0.64 0.53 1.03 2.46 5.04 2.33 2.89 4.58 3.49 1.99 0.60 3.04 0.60 2.57 1.88 1.47 0.69 0.95 2.39 0.87 0.39 1.18 0.98 2.14 4.19 6.31 1.17 1.11 0.02 1.33 2.33

4.08 1.56 2.49 0.49 3.48 1.25 7.39 0.07 5.10 1.11 3.09 2.07 1.77 0.92 5.55 3.34 6.23 3.83 3.78 3.83 5.19 2.49 2.27 3.02 2.86 4.26 4.57 5.19 2.29 3.52 6.39 3.11 2.15 4.09 2.90 2.13 3.43 0.58 0.21

1983.4 1984.1 1984.2 1984.3 1984.4 1985.1 1985.2 1985.3 1985.4 1986.1 1986.2 1986.3 1986.4 1987.1 1987.2 1987.3 1987.4 1988.1 1988.2 1988.3 1988.4 1989.1 1989.2 1989.3 1989.4 1990.1 1990.2 1990.3 1990.4 1991.1 1991.2 1991.3 1991.4 1992.1 1992.2 1992.3 1992.4 1993.1 1993.2

0.33 1.40 2.54 6.99 2.42 3.59 6.14 0.92 0.08 0.12 5.78 0.64 2.63 4.27 5.72 0.12 1.05 3.63 6.17 1.60 0.61 6.62 7.26 0.61 0.05 3.52 6.70 2.21 0.29 4.88

13.51 1.80 1.34 3.01 3.42 3.55 0.16 2.78 5.47

1.02 2.39 3.58 4.32 3.89 1.54 2.17 4.35 2.20 0.26 1.68 1.21 0.80 0.32 1.12 0.63 1.39 0.73 1.32 1.54 1.90 0.32 3.27 0.56 1.11 2.71 1.00 2.11 0.68 0.48 4.94 2.07 1.73 1.16 3.18 4.26 1.60 2.49 2.78

1.90 0.26 1.51 4.01 3.91 1.87 5.04 1.56 1.54 2.15 3.97 1.92 4.42 1.28 3.63 1.11 2.92 0.00 3.49 1.95 1.92 1.55 3.90 0.11 2.61 1.91 3.02 0.36 1.75 0.04 9.04 1.43 2.92 1.50 1.61 0.68 1.86 2.07 2.55





1983.1 1983.2 1983.3

0.07 0.69 4.39

1.98 1.71 2.72

3.38 0.96 0.45

1993.3 1993.4

3.35 1.13

0.98 0.04

1.80 3.72

MAPE MSE

3.57 21.15

2.04 6.12

2.67 10.12

Tom Tat Trong chng nay, chung ta a tm hieu tng quan chuoi (hay con goi la t tng quan), co ngha la tng quan gia cac phan d cua mo hnh hoi quy. au tien, chung ta xem xet ket qua ma khong tnh en tng quan chuoi va tiep theo thao luan hai kiem nh oi vi s hien dien cua t tng quan. Gia s tng quan chuoi la bac nhat, chung ta thc hien hai thu tuc c lng. Cuoi cung, chung ta se thao luan trng hp cua tng quan chuoi bac cao hn, ca kiem nh va c lng.

Khi co s hien dien cua t tng quan, cac c lng OLS (bnh phng toi thieu thong thng) va cac d bao van khong thien lech va nhat quan, nhng khong phai la BLUE va v the khong hieu qua. Tuy nhien, ac tnh nhat quan se khong co neu bien phu thuoc c xem nh bien giai thch. Hn na, neu cac bien ngoai sinh luon tang theo thi gian va tng quan chuoi dng (thng xay ra trong trng hp nay) th phan d c lng se la mot c lng qua thap va gia tr R2 se la mot c lng qua cao. ieu nay co ngha la tnh chat thch hp tot nhat se c phong ai len va tr thong ke t se ln hn gia tr thc. Nghiem trong hn, neu tng quan chuoi b bo qua va thu tuc OLS c ap dung th cac kiem nh cua cac gia thuyet se khong con gia tr.

Hnh ve minh hoa phan d c lng la mot chu dan hu ch ch ra s hien dien cua tng quan chuoi. Neu tng quan chuoi ton tai, cac phan d lien tiep se co xu hng hoi tu.

Tng quan chuoi bac nhat co the c kiem nh bang kiem nh Durbin-Watson. Thu tuc nay c ap dung e c lng mo hnh bang OLS va tnh phan d c lng tu . Tr thong ke Durbin-Watson (d) c tnh tiep theo bang cach s dung phng trnh (9.6). Trong kiem nh mot pha oi vi tng quan chuoi dng, hai gia tr dL va dU c oc t Bang A.5 trong phan phu luc A.II. Neu Ldd , chung ta ket luan rang khong co tng quan chuoi. Neu Ldd , chung ta ket luan rang co t tng quan bac nhat co y ngha. Neu d nam gia dL va dU , kiem nh khong the ket luan. oi vi t tng quan am, 4-d c so sanh vi dL va dU.

Tuy nhien kiem nh DW co vai bat li va v the khong gii thieu ay: thng no cho ket qua khong the ket luan, no khong co gia tr neu co bien phu thuoc co hieu ng tre va khong the ap dung neu qua trnh t hoi quy bac cao hn co sai so.

Mot kiem nh khac co ket luan trong moi trng hp co the ap dung tong quat hn se da tren kiem nh nhan t Lagrange (LM) c mo ta chng 6. Kiem nh nay, goi la kiem nh Breusch-Godfrey, bao gom viec chay mot hoi quy phu tu da vao 1 -tu va tat ca cac bien giai thch trong mo hnh. Di gia thuyet khong ve t hoi qui co gia tr bang khong, gia tr cua (n 1)R2 co phan phoi chi-square vi mot bac t do. Neu gia tr nay vt qua gia tr ti han, th ket luan rang tng quan chuoi bac nhat co y ngha.





Kiem nh Breusch-Godfrey cung co the c ap dung e kiem nh cac tng quan chuoi bac cao hn. Thu tuc se hoi qui tu da vao 1 -tu , 2 -tu , , p-tu (thng da tren tnh chu ky cua tap d lieu), them vao cac bien ban au trong mo hnh. Gia tr (n p)R2 t hoi qui phu nay c so sanh vi gia tr ti han trong phan bo chi-square vi cac bac t do bang vi so phan d tre c s dung trong hoi qui phu ( ay la p). Kiem nh LM, tuy nhien, la mot kiem nh mau ln va oi hoi t nhat 30 bac t do e no co y ngha. Sargan, Hendry, va Mizon a ch ra rang tng quan chuoi quan sat c co the la mot trieu chng cua viec ac trng sai trong phan xac nh cua mo hnh va gi y bao ham nhieu hn cac phan ong, viec kiem nh lieu mot phien ban n gian hn vi cac cong thc tat nh va sai so t hoi qui co phu hp hay khong, va sau o s dung cac ky thuat c lng thch hp. Neu tng quan chuoi bac nhat c nhan biet, thu tuc tm kiem Hildreth-Lu (HILU) co the c s dung e ieu chnh no. Thu tuc se chon la mot gia tr , he so t tng quan bac nhat, nam gia 1 va +1. Sau o tnh cac bien a c bien oi, Yt Yt-1 va Xt Xt-1 cho moi X trong mo hnh. Bien phu thuoc a c bien oi c hoi qui da tren cac bien oc lap a c bien oi va t

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