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7/28/2019 Sims and Zha 1999 Error Bands for Impulse Responses (Vietnam)
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Mis. Qunh Anh
Econometrica, Vol. 67, No. 5 (September, 1999), 11131155
VNG SAI S CHO SPHN HI CC TN HIU U VO
(ERROR BANDS FOR IMPULSE RESPONSES)
BY CHRISTOPHER A. SIMS AND TAO ZHA(1)
(1)Htrcho nghin cu ny c cung cp mt phn bi qukhoa hc quc gia sSES91-22355. Quan
im thhin trong quan im ny khng nht thit phn nh quan im ca Ngn hng DtrLin
bang Atlanta hoc H thng DtrLin bang
Chng ti ch ra vic mrng nhng phng php bit to ra vng sai s trong hnh thc
gim ca phng sai n cc m hnh nhn dng hon chnh chnh xc n mc no. Chng ti
chng t rng vng theo im truyn thng ph bin ti liu cn c b sung nhng bin
php ca s khng chc chn v hnh thc, v chng ti cng ch ra cch to ra cc bin php y.
Chng ti tp trung vo cc vng m m t hnh thc ca s hp l. Nhng vng y khng phi
l nhng vng tin cy cin. Chng ti gii thch rng nhng vng tin cy cin kt hp vi
thng tin v v tr tham s vi thng tin v m hnh ph hp, v do c th gy hiu lm l tm
tt nhng n ca d liu cho v tr ca cc thng s. Bi v nhng vng tin cy cin cng
trnh by cc vn khi nim v tnh ton trong m hnh chui thi gian a bin, chng ti xut rng vng da trn khnng, ch khng phi vng tin cy xp x da trn l thuyt tim
cn, l tiu chun bo co cc kt qu cho loi m hnh ny.
Tkha: s t hi quy vc t, vng tin cy, phng php Bayesian, s phn hi cc tn hiu
u vo.
1. GII THIU gii thch m hnh tuyn tnh a bin ng lc, chc nng ca ng c trng xung lc
l mi quan tm trung tm. Trnh by cc bin php ca tin cy thng k ca cc phn
hi cc tn hiu u vo c tnh do l quan trng. Chng ti s tho lun v cc phn
mrng ca cc phng php hin c xy dng cc vng sai s m gii quyt mt s
vn thc tin quan trng.
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Thng thng cc ti liu c p dng xy dng khong xc sut 1 ring bit timi im ca mt chn tri phn ng, sau m mu phn ng chnh n vi gii hn trn
v di ca khong thi gian xc sut l ba dng. Vng kt qu ni chung khng phi l
vng cha phn hi cc tn hiu u vo vi xc sut 1 v khng trc tip a nhiu
thng tin v cc hnh thc ca lch tc tnh im ca chc nng phn ng c kh
nng nht. Trong mc 6 chng ti xut cch cung cp thng tin ny.
Trong khi c 1 thut ton chnh xc(2)v thng c s dng to ra vng sai s chophn hi cc tn hiu u vo trong m hnh phng sai hnh thc gim, khng d dng thy
c cch mrng n thnh phng sai cu trc nhn dng hon chnh, v mt s n lc
nhm vo phn mrng xut hin trong cc ti liu. Trong mc 8 chng ti s trnh by
vic mrng ny chnh xc n mc no v cch s dng phng php s hc thc
hin iu ny.
(2)Phn phi trong hng dn RATS ktphin bn u tin ca chng trnh
Nhng trc khi chng ti trnh by cc chi tit ca phng php xut ca chng ti gii
quyt nhng vn ny, chng ta cn phi thc hin mt s vn khi nim. Vng sai s
chng ta ang bn n l m t hnh thc ca chc nng khnng, hoc l hnh thc ca chc
nng khnng nhn vi loi ti liu tham kho c s dng rng ri trc trong bo co
kt qucho c gi khoa hc. Tm quan trng ca vic m t hnh thc ca khnng khng nn
gy tranh ci, v vai tr quan trng ca khnng trong s s dng ra quyt nh ca m hnh
thng k. Nhng bi ph bnh chnh i vi s suy lun da trn khnng (v d Love (1988))
lp lun chng li cc nguyn tc ca khnng, lun iu rng duy nhtkhnng cn phi c
bo co, khng chng li tm quan trng ca bo co hnh thc ca khnng. Tnh ton v bo
co cc khong miu t khnng l mt thch thc ng k, v xng ng c ch hn trong
cng tc ng dng.
C nhng lun c hp l cho vic bo co nhiu hn l khnng, v khong tin cy cin c
thc coi nh xy dng t khnng cng vi thng tin b sung v s ph hp ca m hnh
tng th m cn thit cho m hnh ph bnh. Tuy nhin, cc khong tin cy kt hp vi thng tin
v khnng v thng tin v s ph hp m hnh theo 1 cch kh hiu: vng tin cy cin hp
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c th l du hiu ca thng tin mu chnh xc v v tr ca tham s hoc ca thng tin mu chc
chn rng thng tin ny khng hp l. Tt hn ht nn gi hai loi thng tin ny ring bit.
Phn 2 a ra chi tit hn v l lun chung cho bo co hnh thc ca khnng v cc tiuchun ph hp mt cch ring bit, hn l bo co khong tin cy.
Phn 3 nh ngha phn hi cc tn hiu u vo v loi ca cc m hnh chng ta angxem xt.
Phn 4 tho lun v nhng vn c nu ln bi mt thc t rng chng ti ang to racc tiu chun ca s chnh xc ca suy lun ca chng ti v chc nng gi tr vector ca
mt vector ca cc thng s, vi bc ca chiu cao hai vect. Cho vng sai s m t kh
nng, vn ch l s la chn cc chi tit thc t ca vic thc hin. Vic th nghim
nhng vng tin cy thay th tr thnh cc vn v khi nim nghim trng trong trng
hp ny.
Thm ch trong nguyn tc, m hnh chui thi gian m chng ta quan tm cng khng th xy
dng khong tin cy cin cho phn ng xung lc vi l l mu nh chnh xc. C rt nhiu
cch tip cn t c khong tin cy c lng m schnh xc cng tng ln khi kch
thc mu tng. Nhiu cch tip cn trong s c dng trong thc tin c cng mc
bin minh trong l thuyt tim cn cin bc nht nh thc tin ca vic s dng khong xc
sut hu nghim Bayesian nh th l nhng khong tin cy. C nhiu phng php khi ngc bit (t c s dng trong nghin cu chui thi gian ng dng) m ci thin c tnh tim
cn th hai trong l thuyt, mc d khng phi trong thc t theo cc nghin cu ca Monte
Carlo.
Phn 5 tho lun vcc phng php ny v cc vn trong vic thc hin chng.V d trong mc 7 v 8B minh ha vic thc hin cc phng php ngh ca chng ti v
cung cp mt s so snh vi cc phng php khc.
2. HNH THC HP L VS. XC SUT BAO PH(LIKELIHOOD SHAPE VS. COVERAGE PROBABILITY)
Di mt siu kin chnh quy, l thuyt quyt nh hnh thc dn n kt lun rng quy tc
kt lun hp l c hnh thc ca quy tc Bayesian.(3) Theo Hildreth (1963), chng ti c thngh
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n bo co khoa hc nh l vn ca vic chuyn cc kt qu ca sphn tch n c gi m
c nim tin a dng ttrc v tham s v chc nng hao ht a dng nhng li chp nhn mt
m hnh thng k chung. Bo co khng phi l quyt nh, v do khng th dng nim tin
ch quan trc y c. Thay vo n da vo nguyn tc ca kh nng: (4) tt c bng
chng ca mu v tham s ca m hnh c cha trong khnng, p.d.f. bnh thng cho mu
vi d liu c t chc cnh v cc thng sc cho php thay i. Khi y bo co khoa
hc ch l vn ca vic chuyn ti hnh thc ca khnng n ngi s dng tim nng ca
bi phn tch.
(3) Kt qunh vy gi l mt lp nh l hon chnh, Xem Ferguson (1967)(4)Xem Berger and Wolpert (1988)
Tuy nhin, c v khng hp l khi cho rng ng o c gi rt thng xuyn chp nhn m
hnh thng k l hin nhin ng, hn l 1 gi thuyt l th hay mt php xp x hp l. Nhng
c giquan tm n m hnh v tham s ca n, nhng c thng thi mun quan tm n
cc m hnh khc, s cn nhiu hn l chc nng ca khnng. so snh s ph hp ca mt
m hnh tham s vi mt m hnh khc cho cng mt d liu, mt m hnh cn xy dng chc
nng khnng cho m hnh quan trng c xy dng t c hai m hnh, vi tham s ring m
chn gia hai m hnh. xy dng khnng tng th, chng ta cn s dng c hai khnng
m hnh ring bit v mc tng i ca chng. Nu mt ti liu tham kho Bayesian (5)
chnh xc c s dng, vic ny c thc thc hin bng cch trnh by p.d.fs sau cho hai
m hnh ring bit, m thng s gn vi khnng ca chng trong hnh thc, v xc sut hu
nghim ca hai m hnh. V dnh Geweke (1995) xut bo co thng tin . Nhng tc
dng ca tin nghim l khng cn thit bo co thng tin ny. Cng mt thng tin c cha
trong hai khnng ring bit, cng vi cc s liu thng k xc nh chiu cao tng i ca
chng, v d t l gi tr p.d.f. ti mt sim c bit trong khng gian mu. Tt nhin, nu tp
hp cc m hnh c xem xt khng c bit trc, th mc ca gi tr pdf l cn thit chott ccc m hnh c bo co.
(5)Ngha l mt phn phi xc sut, chkhng phi l mt hm mt , iu khng thlng ghp
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Chc nng khnng cha cc thng tin mu v cc tham s ca m hnh, trong khi cc thng tin
b sung v mc ca pdf cha thng tin v s ph hp ca m hnh ny ty theo cc m hnh
i th c th. Mt khong tin cy cin, cng vi khnng ph ca n, khng ch ph thuc
duy nht vo khnng. V vy, trong vic ra quyt nh vi mt m hnh ng tin cy, vic s
dng mt khong tin cy cin v khnng ph ni chung phi dn n quyt nh ti u. Tuy
nhin, trong bo co khoa hc, nh chng ta va tranh lun, vic truyn t thng tin xa hn th
trong khnng c th l quan trng. Do khng th lp lun rng vi khnng c sn, cc
khong tin cy l d tha. Mc d vy, c th ni rng vi khnng v bin php ca s ph
hp tng th c sn, cc khong tin cy l d tha.
BNG 1:
B TIN CY KHNG NG K HOC RNG
X
LR 100% conf set Simple 99% conf set Flat prior odds rati
1 0.99 1.00 0 0.00 (A) (A)
2 0.01 1.00 0.01 1.00 (A, B) ( ) 1
3 0 0.00 0.99 1.00 (B) (B) 0
A. V dn ginXem xt 1 tnh hung n gin, mt n bin ngu nhin X c quan st ch nhn 3 gi tr
nguyn 1, 2 hoc 3. N c phn phi hoc theo m hnh A hoc m hnh B trong Bng I. Ch
X = 2 l ph hp vi c 2 m hnh, mc d n l 1 quan st him gp cho mi m hnh. ngha
ca m hnh n kt lun l r rng v trc gic: nu X = 1, m hnh A chc chn ng; nu X =
3, m hnh B chc chn ng; v nu X = 2, quan st X khng cho chng ta bit phn phi ng
l A hay B. Cc t l lct cui cng ca bng nm bt c ngha ca d liu mt cch
chnh xc. ngha ca quan st X cng c th hin r bng mt khong tin cy 100%, da
trn t l khnng, trong ch cha A nu X = 1, ch cha B nu X = 3, c A v B nu X = 2.
y cng l khong xc sut hu nghim Bayesian 100% di bt k phn phi tin nghim no
m c trng s khc 0 c 2 m hnh. V t l khnng (t l v khnng ti mt gi tr tham s
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c bit n khnng ti a ca n) lun lun l 0 hoc 1 trong v d ny, khong 100% ny l
t l khnng duy nht da trn khong tin cy c gi tr cho v d ny.
Cc khong tin cy da trn t l khnng c li thl chng c xu hng c hnh thc gn nh
ging nhau nh l khong tin cy hu nghim c chiu di ti thiu (hoc h tch ti thiu, trongbi cnh a thng s) di mt tin nghim phng. Chng cng c thc chng minh l c
mt sc tnh ti u cin. Nhng bt k tp hp th nghim no ti mt mc ngha 1
chnh xc cho trc, c ch r bng tt ccc im trong khng gian tham s, ng mt vng
tin cy chnh xc. Trong v d ny vic th nghim m hnh A v m hnh B c th l hp dn,
bc b A nu X = 3 v bc b B nu X = 1. iu ny dn n vng tin cy chnh xc 99% c
lit k trong ct th 7 trong bng I. Khong ny ph hp vi khong 100% tr khi X = 2, khong
99% l rng thay v cha ton b khng gian tham s.
Lm th no chng ta c th lm sng t mt nhn nh, khi thy X = 2, rng vi tin cy
99% m hnh khng th l A hay B. Nu chng ta tht s tin rng c th khng m hnh no
ng, loi nhn nh ny c thc ngha. Khong tin cy c xy dng t t l khnng gia
mi m hnh A v B v mt m hnh n th ba - m trong t xc sut bng nhau trn tt c
ba gi tr ca X. y ch l mt cch m t nhng g c thc hin y - cho mi gi tr
tham s (A hoc B) thu thp cc im trong khng gian mu vi mt xc sut thp nht (so
vi mt thc o xc sut trng s cn bng trong vng ba quan st c th) to thnh vng
bc b. Khong tin cy rng khi X = 2 c quan st xut rng, nu chng ta xem m hnh n
thba ny nh mt khnng tht s, th vic loi b c m hnh A v B c thc chng minh
l ng.
BNG II:
B TIN CY THNG TIN SAI
X LR 99% conf set Flat prior odds ratio1 0.979 1.00 0.979 1.00 (A,B) 1.00
2 0.01 0.91 0.011 1.00 (B) 0.91
3 0.011 1.00 0.01 0.91 (A) 1.10
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Nu ai mun thng tin v khnng ca vic khng c gi tr tham s trong m hnh hoc cc
m hnh ang c xem xt thc hin tt, vic vng tin cy c th cung cp iu ny, v khng
c vng da trm khnng (nh l vng khnng hu nghim Bayesian) c th lm vy, c thl mt li th ca vng tin cy. Tuy nhin, gn nh ph bin trong cng tc ng dng khi khong
tin cy ch yu c th hin l s thng bo cho chng ti v v tr ca gi tr tham s, ch
khng phi v tnh hp l ca m hnh. Mt khong tin cy rng ch l mt trng hp cc bin
ca mt khong tin cy hp. Cc khong tin cy c th trnn sai lm nh l cc ch s ca
chnh xc ca kin thc ca chng ti v v tr tham s do chng nhm ln thng tin vi thng
tin v s ph hp m hnh tng th.
Xem xt v d ca Bng II, trong mt ln na quan st n bin ngu nhin X nhn gi trnguyn, v c 2 m hnh c khnng cho X l A v B. Ln ny, hai m hnh rt ging nhau, vi
xc sut ca mi gi tr trong 3 gi tr c th c ca X khc nhau khng qu 0,001. Mt tp hp
tin cy da trn t l khnng, c hin th trong ct 6 ca bng, to ra mt hn hp thng tin
kh gii thch v s ph hp v v v tr tham s. N khng bao girng, nhng n ch cha m
hnh B khi X l 2 v ch cha m hnh A khi X l 3. Vi quan st X = 3, mt nhn nh rng vi
tin cy 99% th m hnh l A khng c ngha nh mt tuyn b v chnh xc ca kh
nng ca chng ti phn bit gia cc m hnh A v B da trn quan st. Khong l ngn
do s km ph hp v tng th ca m hnh, ch khng phi do chnh xc ca nhng du hiu
ca d liu v vic chn gia A v B. Khnng trong cc trng hp hai m hnh n gin nh
vy l thng tin tng ng vi t l t lcc phng trc trong ct cui cng ca bng. Cho
d quan st gi tr no ca X, vic bo co n s th hin chnh xc cho trng hp bng II rng
vic xem xt X cung cp rt t thng tin xc nh A hay B l m hnh ng. Nhng nu chng
ta xem xt X = 3 v trch dn 1 cch n gin t schnh l 1.1 c li cho A, chng ta s
khng th truyn t c s tht rng X = 3 l khng th xy ra m hnh A hay m hnh B.
Tt hn l bo co hai gi tr p.d.f. ring bit .011 v .01, hay t s chnh 1.1 v khnng bin
(tng gi tr p.d.f. ca 2 m hnh, .021). Cc khong tin cy trong nhng v d ny cho thng tin
sai lch v hnh thc ca khnng ch c trong cc mu xc sut thp. iu ny phn nh mt
mnh tng qut, rng mt khong tin cy chnh xc phi c xc sut hu nghim Bayesian ln
hn 1 n trn mt tp hp cc gi tr mu vi xc sut, theo phn phi bin so vi cc quan st
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hm n bi phn phi tin nghim v m hnh ng thi, t nht l (n-1)/n, cho bt k n> 1. Ni
cch khc, mt khong ngu nhin vi tin cy cao trong hu ht cc mu phi c xc sut hu
nghim cao. Mnh l i xng: mt khong ngu nhin m c xc sut hu nghim 1
trong mi mu phi c xc sut phcao hn hoc bng 1n cho tp hp gi tr tham s m c
xc sut tin nghim t nht l (n-1)/n.(6)
(6)Vic chng minh nhng nh ny theo nhng quan st hai vic sau l nh nhau: (i) Smong i
trn phn phi u tin ca xc sut (cin) iu kin bao ph c cho bi cc gi tr tham s, v (ii)
smong i trn sphn phi bin ca dliu (vi cc tham stch hp ngoi sdng su tin) ca
nhng xc sut sau l tham strong b dliu cho trc. y l hai cch tnh ton xc sut, di s
tnh ton xc sut chung trn cc tham sv dliu, ca skin cc tham snm trong tp ngu nhin.
V vy, nu cc khong tin cy hoc cc vng c tin cy gn 1 l ddng tnh ton c,
chng c thc chng minh l c khnng c xp x tt iu khin nhng c im ca
hnh thc khnng vi xc sut cao. Nhng ch no m nhng c im trc tip ca hnh
thc khnng ddng hn tnh ton, nh trong cc m hnh chng ta xem xt, dng nh c
t l do thc hin cc n lc c bit tnh ton vng tin cy hn l bin php trc tip ca
hnh thc khnng. Ngoi ra, i vi hnh thc khnng c trng, vng tng ng vi xc sut
hu nghim 50% hay 68% thng hu ch hn vng 95% hay 99%, v cc khong tin cy vi
xc sut ph thp nh vy nhn chung khng c xc sut hu nghim gn vi xc sut ph ca
chng.
B. V d chui thi gian
hin th nhng im ny p dng trong m hnh chui thi gian nh th no chng ta xem xt
m hnh n gin
(1) (t) = (t -1) + (t) (t = 1,,T)
Chng ti cho rng l c lp v c phn phi chun N(0,1), c lp vi ngy trc . Gi
s mu to ra = .95 v = .046, c hai gi tr c th khi = .95. Mt khong tin (7) cy 68%mu hu hn chnh xc cho , da trn phn phi ca ( )2/ (t l khnng log), l (0.907,0.998). Vng xc sut 68% hu nghim trc phng Bayesian l (.904, .996). y vng tin cy
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khng d gy hiu nhm lm. N c xc sut hu nghim trc phng .67 thay v .68, m khng
phi l 1 li ln, v c chuyn ln bng 0,003 gii hn di v 0,002 gii hn trn, l
mt s thay i ch c khong 5% chiu di ca n. Cc mc khnng gii hn trn v
di ca khong khc nhau ch khong 6%.
(7)Tkhi mu phn phi cin nhc tnh ton bi phng php Monte Carlo trn mt li vi
khng gian 0.001 trn trc v vi 2000 s trng lp, tnh chnh xc nn t trong ngoc y,nhng schnh xc l tt cho cc v dny. Phng php c xy dng, vi mi , 2000 munhn to vi mi y c to bi (1) vi T=60, phng sai ca bng 1 v y(0)=0 (Cc chui tng tca s c dng cho tt cs trn mi draw ca mt chui ). Vi mi , mt phn phi thc nghimca bn ghi nhtn sut khnng xy ra c xy dng v 16% v 84% nhngquantile ca phn phi thc nghim tnh ton. Ri mt khong tin cy cin 68% c thc xy
dng trong mt mu xc nh nh l mt tp tt cc vi mi sliu thng k tn sut khnng xy ranm gia 16% v 84% quantile thch hp cho . Phng php tng tc chp thun trong cc vd tnh ton khc trong phn ny lun.
S khc bit gia cc khong tin cy v cc khong khnng - tch hp trnn ln hn nu
chng ta xem xt cc khong 95%. i vi mc xc sut ny, khong Bayesian l (0.860,1.040),
trong khi khong tin cy chnh xc da trn LR l (0.865,1.052). Khong ny cho thy s bin
dng ng ch gii hn trn. Khnng gii hn di ca khong gp i so vi gii hn
trn. Do , khong l i din ca cc hnh thc ca s tin tng hu nghim ch cho tin
nghim vi pdf tng dn qua khong = 1,052 l c khnng gp i = 0,865. Tuy nhin,khong c xc sut hu nghim trong tin nghim phng .95 (chnh xc n 2 ch s).
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Khong tin cy chnh xc da trn LR chng ti xem xt y l trc quan hp dn v c mt s
l gii trong l thuyt cin, nhng nh thng l khng c khong tin cy cin duy nht.
N thng c xut (xem Rothenberg v Stock (1997), v d) l cc khong nn thay v cn
c vo t l khnng du hiu (s khc bit du hiu trong khnng log). Cc khong c xu
hng bt i xng r rt hn trong m hnh ny so vi khong LR bnh thng. Trong trng
hp n gin ny cc khong tin cy da trn LR l (0.917,1.013) cho tin cy 68% v
(0.869,1.064) cho tin cy 95%. Mc d nhng khong ny c thin vhn nhiu hng ln
nh cc m t khnng so vi khong da trn LR, chng c khnng hu nghim phng trc
0,68 v 0,95.
Cc trng hp khong tin cy rng hoc khong tin cy sai lc ngn hn c th pht sinh khi
khng gian tham sc gii hn
(0,1). Nu khong tin cy da trn phn phi ca s khc
bit du hiu gia khnng log v khnng log MLE khng gii hn (c th tin ti 1, ttnhin), v c xy dng t cc th nghim c ui tng ng, cc khong tin cy rng 68%
c khnng 16% v cc khong tin cy rng 95% c khnng 2.5% khi = 1. (8) . Nu thay vs phn phi tn sut khnng ti ti khnng ti cc i ca n trn on [0, 1] c dng to ra khong thi gian, phn ny s khng bao gitrng nhng n s ngn hn l c th hp
l bi cc hnh thc khnng trong nhng mu ny ni m nhng MLE khng gii hn nm
trn 1, l do nhng hin tng tng tny hin th trong bng II. V dnh khi l 1, thmt quan st cao ca c1.0387 c khong 1% khnng xy ra, v mt kt hp c trng l0.0394. Vi nhng mu nh vy, chnh xc 68% khong tin cy cin da trn vic k LR,
tnh ton s hc trn mt li vi khong dao ng ca l 0.001, ch bao gm 3 im, nhngha khong thi gian (0.998, 1), v khong thi gian 95% mrng chn (0.996, 1).Nhng
khnng xy ra c form c trnh by nh hnh 1, r rng l khng tp trung r nt v1 nh l
khong tin cy s ngh. V dnh khng ging nh mi trn khong [0, 1] nhng khngnhiu nh ca phn 0.97 so vi ca phn 1 nh l khong tin cy s ngh. Mt u tin
phng pha sau 68% khong thi gian cho l (0.975, 1) v xc xut cho khong thi gian 95%l (0,944, 1).
(8)y l mt kt qu chnh xc, bng cch khi to nn. Khong tin cy nm hon ton bn trn trong cc mu l m v bn di phn ui ca s phn phi c iu kin
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trn . Nhng bng cch khi to ny xy ra ch trong ca cc mu trong khi thc ra l ti .
Kt lun ca nhng v d ny dng minh ha cho vic u tin phng khong xc sut
Bayesian 1, da trn khnng xy ra, thng rt gn ti khong tin cy chnh xc (1)%,v v vy nhng mu khc, khong tin cy c thhi sai khc nh cc thng tin c m t
trong cc mu v tham sa im.
Hnh 1: khnng xy ra trn on (0, 1) vi = 1.0387, = 0.0394.
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3. M HNH A BIN NG LC(MULTIVARIATE DYNAMIC MODELS)
Cho mt m hnh ca form
(2)
Trong
(3) | |
Theo , cng thc nh ngha nh l mt hm ca , .
Gi sl c lp ca , vi s>0 v c p.d.f.
Cc iu kin (3) cho ta vit mt p.d.f cho ph thuc iu kin trn , m ta s nh nhn:
(4) , ,
iu ny thng gp nhng khng ph bin thc hnh xem (4) nh l mt hm tim nng.
N ch thc s l mt hm tim nng ch khi s phn phi khng ph
thuc trn cc tham s khng xc nh, hoc ch ph thuc trn cc tham s khng xc nh
khng lin quan tiv .
Nu (2) tha vi y c ergodic(t ny khng dch c), mt cch tnhin thc hin phn
phi bin ergodic ca tt nhin l ph thuc hon ton vo v , nh phn
phi
iu ny kt hp vi (4) to nn mt p.d.f cho vec-t gim st y
. C 3 l do vic ny khng thng lm c: n thng lm cc tnh ton khhn; n yu cu hoc l khng theo lut, hoc l xem nh l mt trng hp tch bit, phin bn
bt bin ca m hnh; v n c th khng c chnh ng rng c ch ng c m t(2)
c thc thi di, trong mt form khng i, cho phn phi ergodic.Hai im cui c lin quan. Mt m hnh bt bin khng c phn phi ergodic. Mt m hnhgn
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bt binc th c phn phi ergodic, v th c th hiu l thi gian cn t c phn phi
ergodic t iu kin khi to ty l qu di n mc vic p t phn phi ergodic
l khng cn l do.
Suy din Bayesian s dng phn phi ergodic cho iu kin khi to ti tham s c gi tr tt bntrong vng khng bt bin ca khng gian tham s, ri chuyn dch nh nhng qua phn phi t
kt ni ti v nh vng bt bin c chm ti. M hnh ny nh l mt ng dng c lp,tuy nhin phn cn li ca bi bo ny ta xem (4) nh l mt kh nng. Chng ta cng gi nhng
iu kin khi to cnh trong vic to ra mu MonteCarlo ca khi chng ta nhgi xc sut hi t c in (9)
(9) Vquan im ny, chng ti khc vi Kilian (1998a). Quy nh trn dliu ban u trong vic hnh
thnh khnng hoc trn xy dng c lng (m thc tth quan im ca Kilian ph hp vi chngti) b qua mt sthng tin trn nhng quan st ban u. Quy nh trong vic m phng Monte Carlo
ca dliu thh mi nhn ra skhc bit gia iu kin ban u v mi to ra nhiu thng tin hn
vmu. Nu ys ban u cho thy lch ln bt thng tcc gi tr trong trng thi n nh, mu c
khnng to ra thng tin mnh bt thng vcc thng s. N khng c ngha tnh cc xc sut bao
ph m trung bnh tc c cc mu thng tin khi n ddng ly c tthc tm chng ti may mn
(khng may mn) trong cc iu kin ban u ca mu c thtrong tay
Mr.Chin
Nhiu phn tch ca chng ti s tp trung vo trng hp trong g l tuyn tnh trong tham s
u tin ca y vi mt ma trn h snh danh, v b cng tuyn tnh, v h l Gauss. Di nhng
iu kinbnh phng ca b, trong cc mu nh v ln, cho cc m hnh tuyn tnh cnh.
i vi m hnh tng qut t cng thc 2, c sm h vcch thc y s phn hi phi
c xc nh. y, tuy nhin, chng ta ch xem xt m hnh vi g l tuyn tnh trong tham s
y ca n, tnh phn hi cij(s) ca yi(t+s) ti j(t) c ddng xc nh. Bng cch gii quyt
quy (2) (recursively) chng ta c th gii quyt cho y(t+s) nh l mt hm ca (t+s), (t+s-
1),.., (t) v y(t-1),.., y(t-k)
Sau
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(5) cij(s) =
ch ph thuc vo , ch khng phi l y hoc l , v c th tnh ton bi ma trn s cp. Lu
rng, mc d cc xung lc phn hi c nh ngha y trng vi cc h s ca cc i din
trung bnh di ng (MAR) cnh, cho m hnh tuyn tnh cnh v n cng c xc nh
cho m hnh khng cnh, ni m MAR khng tn ti.
Nu chng ta vit cc m hnh tuyn tnh trong iu kin mt ton tc tr (the lag operator),
nh l
(6) A(L) y(t) = (t)
Sau tnh xung lc phn hi l cc h strong a thc v trt t (infinite-order) trong ton t
tr C(L) = A-1
(L), ni m nghch o gin hn lin quan n sc mnh dng ca L v cxem nh l mt ton t trong cc phn ca a thc v trt t ca ton t tr. Mt nghch o nh
vy tn ti cho bt k cho v trt t no t A vi A0c cp y , khng ph thuc vo
ngun gc c trng ca A, mc d tc nhin n c th hm h s ma trn Cs tht bi trong
vic hi t v 0 khi s. Cc nh x t h s trong A l mt dng t hi qui ca m hnh, ti
nhng phn t trong C, l cch mtmt. Bi v A c bc hu hn (trong m hnh chng ta xem
xt) v C th khng, iu c ngha l A c c tnh kinh thn C, Mt khc, bi v cc yu
t cij(t) ca ma trn Ctc khuynh hng vn hnh, ging nh chc nng ca t, nh cc d liu
ang c m hnh ha, cc thuc tnh ca m hnh thng d dng nm bt bng trc gic bng
cch xem cij(t)s hn l xem nguyn bng ca aij(t)s.
Mc d cc nh x t cc ton t A ti ton t C theo nguyn tc mt- mt, cc nh x ca aij ti
cc thnh phn cij(t) trnn phc tp. Ni chung, cc nh x khng phi l mt mt, thm ch
chng ta xem xt mt tp hp cij(t), t=1,.,H, trong H nh l s chiu ca tham s t do
trong A (10). iu ny sinh ra mt s rc ri trong vic xc nh vng sai sv (t bit) trong
vic xc nh khon tin cy cho cij(t).
(10)xem xt im ny, hy xem xt mt m hnh bc 1 vi A=IA1L v A1 m*m. Nu A1phn ra
Jordan A1=PP-1, vi l ng cho, sau cij () ph thuc vo dng thi ca P, v ct thj ca P
-
1, v tc c cc thnh phn ca ng cho ca , nhng khng phi l cc kha cnh khc ca A1. R
rng, iu ny ri b nhiu A1s ti phn phi chnh xc nh cij()
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4. HNG BC (DIMENSIONALITY)
Bi v tnh thc y phn hi l mt i tng khng gian a chiu, do , vic m t vng sai
s l mt thch thc. Cc tip cn tt nht m t chng s khc nhau mt mc no ,
nhng chng ti m t mt phng php c p dng rng ri trong di y trong Mc 6.Trong phn ny, chng ti s tho lun v nhng kh khn c to ra bi m hnh chui thi
gian a bin vi vi khng gian a chiu.
Mt c tnh hon chnh ca mt tp hp con ca mt m hnh chui thi gian vi khng gian
150 chiu (khng ln bt thng cho mt m hnh a bin) c cho l qu phc tp nghin
cu c ch. Thay vo , chng ti c gng nm bt nhng c im c bn v quan trng ca
mt vng sai s c s liu v chiu thp hn. V d, chng ta c th tp trung s ch vo mt
vi sthc y s phn hi rt quan trng cho phn ng ca mt chnh sch trong nn kinh t.
Vi mt phn phi Bayes cnh, m t xc sut, a ra cc d liu, ca mt tp hp cc gi tr
c th cho mt sthc y phn hi, v d, xc sut m cij(t) [a,b], t=1,.,4 l mt bi tp n
gin: Mt tch hp hu nghim p.d.f vi tt cc cc thng s ca m hnh trn tp hp cc gi tr
tham s cung cp cijs tha mn c cc hn ch.
i vi cc khong tin cy, s chiu cao trong khng gian tham s lm ny sinh mt vn
khc. Tng t chc nng thc y s phn hi ca cij c th pht sinh thm t 2 ton t khc
nhau ca A(L). Xc sut bao ph (coverage probability) ca bt k thit lp ngu nhin trong
khng gian ca cijs, bt kc to ra nh th no, s khng ch ph thuc vo chnh cij v do
s khc nhau gia A(L)s tng xng vi cij. Do , tin cy khng chnh xc thit lp cho
cij l c th.
Ti im ny, xc xut bao ph thng ph thuc vo cc thng s gy nhiu (nuisance
parameters) v iu ny gy ra mt s vn , v vn l vn c. Mt s tc gi xc nh
mc tin cy ca khon cch ngu nhin l ti thiu trong khng gian tham s ca xc xut bao
ph. (11)
(11) Jack (1971) l mt v dxc nh mc tin cy theo cch ny, trong khi Wilks (1962) dng nh
xem xt trong cc mu nh chc trng hp xc sut bao ph chung vi ton b khng gian tham s
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iu ny tng ng (v tnh 2 mt gia vng tin cy v kim tra gi thuyt vnh ngha chun
ca kch thc ca mt thng k th nghim) l ti a trong khng gian tham s ca xc xut b
bc bdi gi tr. Tuy nhin, cc vn ny c cp trong cc nghin cu ca Dufour
(1997), Faust (1996) v Horowitz v Savin (1998),phng php ny l khng tha mn yu cu
v n thng dn n 1 tnh hung l khng c khong tin cy khng quan trng , thm ch l
tim cn. Trong thc t, cc nh nghin cu s dng mt khong tin cy hoc mt ku vc hp l
ca l thuyt tim cn, iu c ngha l xc sut bao ph hi tn mc danh ngha nh tng
kch thc mu, theo tng im ti mi im trong khng gian mu. Thng th iu ny c th
c thc hin bng cch n gin l tnh ton xc sut bao ph ti cc gi trc tnh theo cc
thng s gy nhiu (nuisance parameters).
Tuy nhin, trong cc mu nh, cch tip cn ny c th dn n mt bin dng nghim trng ca
s hp l. V d, c th c mt lot cc gi tr ca mt tham s gy nhiu v, tc cu c kh
nng cao, vi nhng tc ng khc nhau cho xc sut bao ph ca vng tin cy. Nu chng ta
thay th v bi mt gi trc tnh n gin, chng ta c thc c mt gi trkhng i din
cho xc sut bao ph.Trong tnh hnh , khong xc xut hu nghim Bayes slin qua n v
hn, ch khng phi l s la chn ca mt v duy nht, m tt hn i din cho nhng tc ng
thc t ca d liu.
Vi khnng tri u trn vs vi nh hng khc nhau, kt qu ca Bayes c th nhy cm hn.
Nhng mt m t k lng v khnng, k c nu cn xem xt nhiu hn cc nghin cu
trc, lm r tnh hung ny. Hn na, thng l kh nng chim u th trc , trong
phm vi ca vs c quan tm nhiu hu ht ngi c s ng rng giai on trc kh
phng.
5. TIM CN , TKHI NG
(ASYMPTOTICS APPROXIMATION, THE BOOTSTRAP)
Chng ti trch dn thc t l khong cch hu nghim trong m hnh xc sut Bayes chngminh cho khong tin cy trong cc m hnh chng ti xem xt. Kt qu ny, nhiu khong tin
cy ca ca cc m hnh ny lm cn c, trn thc t ch p dng cho nhng trng hp m m
hnh c bit n nh l cnh. Kt qu d nht l xem xt trng hp c bit ca mt m
hnh khng b rng buc gim t VAR, tc l m hnh vi A0=I.
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Trong trng hp iu kin likelihood trn nhng quan st ban u l Bnh thngo ngc-
Gamma trong hnh dng, xoy vo c lng OLS, vi mt ma trn hip phng sai m thm
ch mu hu hn l ma trn hip phng sai ca phn phi tim cn ca c lng. Phn phi
bin ca Ajs l sau d dng nhn thy hi t vi hnh dng ca cc hn ch cng phn phithng thng m ly mu phn phi ca OLS c lng hi t. Tt nhin iu ny sau c
ngha l tt c cc hm vi phn ca cc h s ca A, bao gm ca Cjs, c phn phi hu nghim
l tim cn thng thng, v ph hp vi cc bn phn phi ly mu ca cc chc nng tng
t ca c lng OLS ca A.
i vi m hnh tuyn tnh cnh tng qut hn l mt c lng ti a khnng ca cc h s
ti A, hoc mt c lng khnng gi ti a da trn khnng Gaussian khi cc xo trn l
khng Gaussian, hoc mt c lng GMM, mi bn s hi t, trong iu kin nh dn u,
mt joint thng thn phn phi.Phn phi hu nghim ca cc thng s, c iu kin trn cchm c lng ca chnh mnh v ma trn hip bin tim cn c tnh (khng c iu kin trn
cc mu y , ngoi cc trng hp Gaussian), ti mu ln cng nn c tnh xp x bng
cch ly sn phm ca p.d.f trc vi p.d.f. thng thng tim cn nh mt joint p.d.f. gn ng
t xy dng hu nghim. Nhng k t khi mu ln ti khnng chi phi trc , chng
ti c th x l trc nh hng s ti xp x ny. Vic tnh ton cc khon hu nghim n
nh c lng v ma trn hip phng sai c lng ca n, sau x l p.d.f tim cn ca
mu nh mt hm ca cc h s ti A trong xy dng p.d.f hu nghim cho A. iu ny s lm
cho phn phi hu nghim c hnh dng ging nh phn phi ly mu tim cn ca cc c
lng.Bi v phn phi tim cn l i xng v bnh hng bi cc thng s ch thng quamt sthay i v tr thun ty, vng tin cy sau trng vi cc khong xc sut. Bng chng
ca nhng kt qu ny, vi c t k thut cn thn cc quy lut iu kin, l trong Kwan
(1998).
Cc nh x t h sAj n h s Cj c thc phn tch khc bit, phn phi tim cn bnh
thng i vi cc h s A c thc dch sang phn phi tim cn bnh thng i vi cc h
s C. Chi tit c cung cp, v d nh, trong Lutkepohl (1990) v Mittnik v Zadrozny
(1993) (12) Tuy nhin cc th tA n Cj ngy cng tng ln phi tuyn khi j tng do lng
ca xp xc cung cp bi loi l thuyt tim cn b suy gim u n vi sgia tng j trong
bt k mu no. Cui cng l j tng (v iu ny xy ra cho j l kh thp trong thc t) ch tiu
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phng sai ca Cj bt u l -j , ni l ngun gc ca |A(L)| = 0 l nh nht trong gi tr
tuyt i. iu ny c ngha rng khi c lng im ca vt qu mt, cc vng li thu nh
ti -j t l cho j ln, ngay c khi c trong thc t khng chc chn ng k v ln ca .
y l mt ngun quan trng ca s thiu chnh xc, v kt quhnh vi km trong nghin cu
Monte Carlo ca cc vng sai sc to ra theo cch ny. (See Kilian (1998b).)
(12)Cch tip cn ny c sdng, nhPoterba, Rotemberg, and Summers (1986)
Mt cch khc to ra khong tin cy vi cng th tu tin xc nh tim cn l s dng
cc khong Bayesian l khong tin cy cn s dng th tc n gin bootstrap. C l v Bose
(1998) ch ra rng tnh ton bootstrap cung cp mt bc cao hn xp x tim cn trong vic
phn phi cc c lng trong mt hu hn trt t m hnh t hi quy mt s nh nghin cu ccm gic rng phng php n gin chuyn mt c tnh ca s phn b ca cc c lng
gi tr tham s thc s vo mt khong tin cy phi ci thin tnh chnh xc ca khong tin cy,
nhng y khng phi l trng hp. Mt s nghin cu ng dng (13) s dng nhng g
c gi l'' bootstrap ngy ng'', nhng m Hall (1992) v chng ti trong phn cn li ca bi
vit ny s gi''phn trm khc'' khong bootstrap. Mt c tnh ph hp ban u c to ra,
v Monte Carlo rt ra c lm t cc m hnh vi A=, to ra mt phn phi c lng
v . to ra mt di tin cy cho cij(t), ca sc nh x vo mt phn phi
ij(t)s, v (1-
)% khong tin cy'' c hnh thnh bng cch tm cn trn v cn di (/2)% ui ca phn
phi ca ij(t)s. Phng php ny r rng khuch i bt k thin v hin din trong quy trnh
lp dton. n gin trong chui thi gian v d ca chng ta v mc 2B, quy trnh s to ra cc
khong chuyn xung so vi cc khong Bayesian, thay v sthay i tng nh do cc khong
chnh xc cin.
(13)Cc tip cn ny c s dng bi Runkle (1987), Blanchard and Quah (1989) v
Lastrapes v Selgin (1994) sdng sthay i vi nhng iu chnh ngn chn cc vng tnh
ton khi cc sai, bao gm cc c lng im.
Trong mt vn v tr thun ty, khi chng ti quan st X f(X-) v p.d.fkhng i xng,
phng php tiu chun to ra mt khong tin cy l phi tm cn trn v cn di (/2)% ui
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ca p.d.f f bit a v b, sau s dng thc t l, vi cnh v X khc nhau mt cch ngu
nhin th:
(7) P [a < X- < b] = P[X-b< < X-a] = 1- .
Nu chng ta s dng bootstrap khc-phn trm v lm y Monte Carlo rt ra xc nh
hnh dng ca f chnh xc, chng ta s khng s dng (X- b, X-a) khong hm bi (7), nhng
thay vo l (X+a, X+b), khong trong (7) m xung quanh im quan st X. N c v hin
nhin rng, sau khi bin bootstrap ca chng ti chy theo m hnh Monte Carlo theo chng ta
nn s dng khong trong (7), khng phi l khong bootstrap khc-phn trm. Tht vy,
khong (X- b, X-a) ng bi (7) c gi l phn trm khong bi Hall (1992) v x l bi
ng nh khong bootstrap t nhin nht. Trong bi cnh v tr dch chuyn thun ty, n to ra
mt khong thi gian vi phng trc khi Bayesian xc sut tng ng vi xc sut bao phdanh ngha ca n, v do l mt m t hu ch ca hm khnng.
Nhng chng ta cng c thtng tng mt thit lp m chng ta khng c vn vthay i
v tr vi phn phi phi Gaussian, trong thay v c mt Gaussian (hoc c bn nu khng phi
phn phi i xng) vn v tr, trnn phi Gaussian qua mt phi tuyn chuyn i. cha
bit c ngha l, chng ta quan st X v mun to thnh mt khong tin cy cho , nh trc
y, nhng by giX = g(Z) v =g(), trong ZN(, 2), g l n iu, v chng ta khng
nht thit phi bit g. N c th c ch ra rng trong tnh hung ny khong phn trmbootstrap khc- s cung cp cho cu tr li chnh xc, theo ngha l n s to ra mt khong thi
gian vi flat trc khi Bayesian xc sut ph hp vi xc sut bao phdanh ngha ca n.
Trong vn chui thi gian, cho cc thng s c ng d liu tnh, c tnh cc h s trong
A(L) l tim cn thng thng, nhng thin v trong cc mu nh. Cc h s trong Cj l chc
nng ca cc h s trong A(L), vi mc phi tuyn trong vic nh xngy cng tng vi j.
Ngi ta c th k vng sau xem xt thin v c th thng tr trong j gn bng khng, lm
cho khong phn trm theo Hall chy tt nht, trong khi nhng tc ng ca bin i phi tuyns thng tr trong j ln, lm cho cc khongphn trm khc-chy tt nht. Nhng khng c hin
nhin, phng php chung ca vic s dng m phng phn trm bootstrap to ra khong tin
cy c di v c lch phn nh chnh xc s bt i xng thng tin v mu ca Cjs.
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Kilian mt s nghin cu Kilian (1998a, 1998b)) lp lun cho vic s dng khong phn
trm bootstrap khc- vi iu chnh sai lch (14).. Trong khi khng c lp lun c sn m khong
thi gian l chnh xc hn trong kh nng bao ph tim cn hn phng php phn trm
bootstrap khc hoc hn khong thi gian xc sut Bayes, s thin v hiu chnh khng c xu
hng loi b cc quan trng nht ngun gc ca hnh vi xu ca cc khong thi gian khc-
trong cc m hnh chui thi gian.
(14)Nhng xin lu rng, Kilian ch yu chiu chnh cc c tnh ban u cho chnh lch.
Xem Hall (1992) trang 129 cho mt scch xy dng nhng im c gi l chnh lch
hiu chnh trong cc ti liu vkhong tin cy bootstrapp khng phi l siu chnh ca cc
c lng thin lch.
C nhiu cch xy dng cc khong tin tng ti v khi ng m lm cho chng tim cn
chnh xc t hng th nh, thay v ch th tu tin. Mt trong nhng phng php c
nghin cu bi Hall (1992) l'' i xng phn trm-t''. Khc na l nghin cu ca Efrom v
Tibshirani(1993) l BC''(15). Khong ca Hall u nm i xng vcc c tnh im, v vy
h khng th cung cp thng tin v s bt i xng trong khnng. Efron v Tsibshirani c
tnh c gnh nng mt s tnh ton. Chai c x xu trong nghin cu Monte Carlo ca
multivari-chim chui thi gian m hnh Kilian (1998b).
(15) khon thi gian ny l 1 trong nhng nhm thi gian c iu chnh cho xu hng v gia
tc.
Cng nn r rng rng, chng ti tin nhng vng sai s m m t c khnng c a chung
hn, trong bo co khoa hc, quan im nim tin cin c bit n xc sut phm vi bao
ph, ngay c khi sau ny c thc xc lp. Tuy vy chng ti vn trnh by trong cc v d
di y mt s bin php v hnh vi ca ti v khi ng da trn khong tin cy gn ng.Chng ti s dng thin v ca Kilian -phng php bootstrap iu chnh (Kilian (1998a) v p
dng ph bin khc -phng php phn trm. Nh chng ta lu , c hai c thc bin
minh nh gn ng tt khong Bayesian theo cc ginh c th v cch thc phn phi cc
s liu thng k quan st ph thuc vo cc tham s. Chai u l tng i n gin tnh
ton.
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Mis Bo H
6. NHNG PHNG PHP O LNG TT HN SAI S V HNH DNG CA
NHNG PHN HI
(BETTER MEASURES OF UNCERTAINTY ABOUT SHAPE OF RESPONSES)
Phng thc thng thng l a ra dy sai s 1 chiu ij(t) ij(t) vi t= 0,, H, sau v trn
biu mt tp hp cc im trn h quy chiu 3 trc ca hm s thi gian ij(t) - ij(t), ij(t),
ij(t) + ij(t), c gng cho ngi c ng thi c lng phn hi v du hiu dy sai s ca
hnh thc s phn hi. iu ny hon ton khng ging trong nhng ng dng kinh t v s
khng chc chn v cij(t) c lp vi t, thc ra iu ny c vng. Ngi c c khuynh hng
ngh v nhng im nm trn hoc di ng xc nh biu th cho cij () trong ranh gii ca
mc bin i trong cij. Nu s khng chn chn v c thc tc lp vi t trong tng thi k,nhng im ny nm pha trn hay pha di ng tin cy, m t nhng lch ca cij vi ij.
Nhng trong nhng m hnh ph hp cc cp c trng tng k, c tng quan vi nhng
chui thi gian trong kinh t, s khng chc chn vc th thng r rng c tng quan tng k,
th nn c gng xem xt nhng im ij(t) ij(t) nh nhng phn b ca c th khng hp l .
D sao th nhng m hnh thnh thong thch hp vi d liu d khng hon ton sun s, hay
khc vi d liu, v thm ch d liu trong mc chui lin kt cc im c thi hng
khc i. m t tt hn sai s, c mt cch l biu din nhng im cij () trong h thng phihp th tt hn so vi biu din theo vector ca nhng gi tr ti t=0,, H. Nu vector {cij(t)}
t=0; H cng chun tc vi ma trn hip phng sai , h thng phi hp r rng c th thit lp
bi s don nhng thnh phn ch yu, v ngi ta c th s dng h thng phi hp ny d
cho bin c khng chun tc.
thc hin tng ny, mt tnh ton mt mu ngu nhin gi t s phn b ca cij, s dng
n tnh moment ma trn th nht v th hai. T, tnh ton ny c lng ma trn hip
phng sai ca H-dimensional ma trn cij v tnh ton vector tuyn tnh phn tch ca n
(8) WW =
Vi theo ng cho v W W=I. Bt k cij c thc biu din thng qua
(9) cij = ij +
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Chng ta xem cijnh H-dimensional vector ct, ijl c lng c ngha ca cij, v Wk l ct
th k (vd: vector tuyn tnh th k) ca W. Thay i ngu nhin trong cij, th hin s khng chc
chn ca cijc cung cpthng qua s quan st d liu, pht ra ngu nhin vi nhng h s
{yk}. Bng th, dao ng ca yk l ng cho th k ca ma trn trong phng trnh (8),
vd: ng th k l gi tr ring ca .
Trong cc m hnh d liu kinh t, c vnh phn ln mt vi gi tr ring ca c cho l
nguyn nhn ca hu ht sai s trong cij. Chng ta c th, trong trng hp ny, cung cp nhiu
s m ty sai s ca cijhn trng hp chui sai slin kt cc im c sn thng qua
trnh by vi im, hay hin th; cng thc ij(t) Wk(t). c th biu th xp x 68% xc sutxy ra vi gi tr sai s thnh phn th k, hay cng thc ij (t) Wk (t).1.96 xp x 95%.Khc vi hm s ca t c vtrn th dy sai s lin kt cc im, cc im ny th hin
hm s cijm khng ng vi gii hn ca phn khng gian hu hn th hin s tin chc trong
phn phi chun, khi s phn b ca cij l phn phi chun.
Phng php ny, hu dng trong thc tnh cch tit kim thi gian,vn khng tha mn, nh
chng ta bit cijth thng khng chnh xc nh phi hp thng thng, c bit khi t cng
ln. Cc chiu di ca chui vector tuyn tnh chng ta m tlun lun i xng vi ij , v d,
trong khi s phn bpha sau th khng i xng. iu ny quan trng bit khi no pha sau
khng i xng.
V vy, chng ta c th ci thin vi phng php trn bng cch tin hnh m phng Monte
Carlo, hay, trong vng u, s dng cng thc , c lu li, bng cch chuyn qua vic lu
tr khc. Thi im ny, chng ta trnh by theo bng 16%, 84%, 2.5% v 97.5% im vi phn
ca yk tng ng vi gi tr ring ln nht ca . Hm s Yk ring bit rt ra ca cij d dng
c lng c nh Wk.cij, vi Wk l hng th k ca W. Hai hm s ca t, ij + yk,.16 v ij +
yk,.84 , nu k l gi tr ring ln nht, mi gi tr th hin trc tip mc bin i trong cij, v
nhng ln ring bit ca s lch hng tij s cho bit du hiu ca skhng i xng
trong khnng hay hu nghim p.d.f.
Bc k tip a ra s liu tinh thn na c th thc hin c. iu ny thng quan trng
s dng hay lm sng t kt qu khc nhau ca cij, vi i khc j, th c lin hnh th no vi
nhau.V d, thng thng, ngi ta thng cho rng, phn hi hp l ca nn kinh t vi s xo
trn ca chnh sch tin t c th ko theo li sut tng, thtrng chng khon gim, sn lng
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gim, v ng tin b mt gi/ lm pht. Khi chng ta xem xt chui sai s cho phn hi thng
tin u ra ca c sc tin t v thy: trng c vchnh ng rng s st gim sn lng c th
nhiu hn c tnh, chng ta tht s cn bit khi no c gi v s st gim sn lng mnh bt
k vi phm du hiu m hnh m ng c sc th c xem nh l mt c sc chnh sch.
Kiu m hnh ny c thc gii p thng qua o lng vi bin cij biu din qua mt vector
ring bit, sau p dng phng php phn tch gi tr ring c a ra trn. N c th
khng c li ch rng ri trong vic p dng phng php ni cijnh p dng chng cho cij
ring l, bi v khng chc chn suy on tng quan cao ca gi tr cij(t) t i ti j, v ti t. Tuy
nhin, khi khm ph ra mt vi gi tr ring chim u th ma tn hip phng sai ca tp hp
tng quan trng yu ca cij, loi p dng ny c th rt hu dng.
Trc khi i n v d, chng ta nn lu rng tng ca phn ny khng b gii hn trong
ng dng thc y phn hi. Chng p dng bt k ch no cn m t sai s vc lng
hm s ca ch s t v khi c s tin cy ln theo t trong sai s v cc gi tr hm s. Chn chc
trong trng hp khi chng ta cn m t sai s vng dn thi gian tng lai ca bin kinh t
v dng dng trong dbo. N cng c thc p dng trong vi trng hp nh c tnh
ht nhn phi tham s ca hm hi quy, p.d..f., hay ging nh m t.
7. P DNG VO MT VI M HNH HAI BIN S
(APPLICATION TO SOME BIVARIATE MODELS)Chng ta xem 2 v d ca m hnh 2 bin trong chui s liu kinh t theo thi gian. Mc d n l
v d khng thc t, n to tnh khthi thc hin mt lot cc kim tra phng php, nhm
a ra mt n tng r rng hn v tnh kh thi ca phng php m chng ta ngh, nhng
gi tr ca chng trong truyn ti thng tin, v mc m n cho kt qu ging hoc khc vi
nhng phng php hin c cho vic to ra dy sai s.
Trc tin chng ta xem xt mt dng hnh tam gic mang tnh trc giao n gin ha VAR vi
4 trc trang b cho d liu hng qu v GNP thc v cung tin M1 trong khong qu 1nm 1948 n qu 3 nm 1989. Hnh 2 ch ra theo tng im phng sau c th xy ra trong
khong thi gian ca m hnh thc y hng ng ny. (16) i vi c shng ng ca Y vi
c sc ca n, pha trn bn tri, v phn ng ca M1 trc nhng c sc ca mnh, pha
di bn phi, ng ch c si xng trong cc chui, vi 95% dy c bit mrng xa hn
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ln pha trn so vi pha di. Hnh 3 cho thy 68% nhng nhm khc trong khon thi gian ,
nm ngoi xu hng ng.
(16)vi c 2 m hnh, chng ta sdng 1000 sMonte Carlo rt ra trong vic to ra m phng Bayesian
hoc ly mu khng hon li cho mt tp dliu nht nh, v 600 sb dliu trong xy dng mc
xc sut.
Ch rng i vi nhng phn hi ca GNP v M1 n nhng i mi ca mnh, nhng chui
phn trm khc th hon ton bt i xng, thay i gim dn v 0. iu ny phn nh xu hng
c lng, v n khng c ngha iu chnh nhng khong thi gian, m phn nh chnh xc
hnh dng ca phn bc lng tht s, nh m t nim tin hp l. Vi xu hng iu chnh,
nh hin th trong hnh 4, khon phn trm cc khon thi gian phng php ly mu c hon li
cho thy m hnh cht lng tng tnh cc khong Bayesian, nhng c nhiu sai lch, v c
xu hng rng ra vi phm vi thi gian rng hn.(17)
(17)lu rng vic thc hin ca chng ta vkhong thi gian phn trm khc iu chnh sai lch khng
theo Kilian trong v d mu vsiu chnh hiu qu ca n nhm loi b nhng yu tbt nh. Mc
tiu ca chng ta l nhng c lng bt nh c thl thc t, v thn thng khng thch hp b
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nhng khng gian hm sti hoc bn trong ranh gii ca khu vc cnh. Chng ta cng quy nh trn
nhng quan st ban u i vi bn vca phng php ly mu hon li, ci m Kilian khng lm.
Bng 3, tnh ton cho hu nghim m bao hm d liu thc, ch ra rng nhng khong thi gianca phng php ly mu hon li trn phn trm khc c hiu chnh sai lch c xc sut hu
nghim m c bn vt ng k. 68. iu ny c kt qu xut pht t chiu di ln hn n
nhng khong thi gian, nh c ch ra bi Bng IV. Vic x l nhng im c lng ca m
hnh ny nh l nhng gi tr tham s thc, chng ta c th kim tra nhng xc sut m bo.
Nh c th thy Bng V, khong thi gian Bayesian .68 c xc sut ph sng cin mt
cch h thng thp hn 0.68, thm ch thp hn 0.50. khong thi gian ca phng php ly mu
hon li c xc sut thp hn 0.68 cho ngn hn, trn 0.68 cho di hn, nhng s chnh lch th
nhhn cho khong thi gian Bayesian trong hu ht cc trng hp.
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Cho m hnh ny, dy khng lin tc cha gn nh tt c hnh dng ca thng tin, bi v thnh
phn u tin ca ma trn hip phng sai ca mi phn hi thc y chi phi mnh m. Ta c
th thy trong Hnh 5, th hin dy sai s cho thnh phn u tin ca bin trong mi phn hi
thc y. Nhng dy trong hnh ny rt ging vi dy khng lin tc c trnh by trong Hnh
2. S khc bit chnh l xu hng ca cc dy thnh phn l st hn khi t tin v0. i vi mi
bn chc nng phn hi trong th ny, gi trc trng ln nht tng trng cho hn 90%
tng ca cc gi trc trng. Gi trc trng th hai gii thch cho khong gia 2,3% v 32%,
v gi tr th ba cho khng qu 1,1%. Hnh 6 trnh by thnh phn thhai, trong trng hp ny
dng nh tha mn cho s bt nh v mc phn ng, thnh phn ny l hnh bu (hump-
shaped). Ta khng biu din thnh phn th ba bi v n tht s kh nh. Trong m hnh ny,
vic s dng dy khng lin tc, cng vi nhng g m chng ta don th l trc gic thng
thng th s bt n v mc ca nhng phn hi chim u th, ch khng phi hnh dng caphn hi, nhng suy on ny dn n s kt lun chnh xc.
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Gita trli vi vi song bin VAR vi 8 trc chn ra bi Blanchard v Quah (1989) t
s liu hng qu trn s pht trin thc t ca GNP v t l tht nghip ca nam gii t 20 tr
ln, tqu 1 nm 1948 n qu 4 nm 1987. Chng ti xy dng dy sai s cho cu trc phn
hi thc y di nh ngha Blanchard-Quah, nh ngha m da trn nhng hn ch di hn.
Bi vit gc trnh by nhng g c dnh c khong thi gian phn trm khc, vi siu
chnh c bit ngn chn nhng phn hi ca n, nhng phn hi nm ton b mt bn ca
phn hi c lng.(18)Chng ti c th lp li nhng kt quny, nhng chng ti nhn
ra trong qu trnh rng c nhng sai st trong nhng trang thc thi ca phng php ly mu
c hon li. S bt i xng rt mnh m trong nhng khong thi gian c biu din trong bi
vit l kt qu hu ht t nhng sai st. (19) Hnh 7 cho thy phn phng trc ca khong thi
gian. N th chkhng i xng mt cht, nhng n tng i rng cho nhng phn hi v c
sc v cung. Khong thi gian phn trm ngoi khng chnh xc trong hnh 8 th ging vikhong thi gian Bayesian, ngoi tr nhng h s bt i xng mnh cho bin t thp trong nhng
phn hi v c sc v cu. Mt vi giai on u tin cho thy 68% dy nm hon ton bn di
im c lng, v chng ta bit t Hnh 7 rng iu ny khng phn nh hnh dng ca cc kh
nng xy ra. Hiu chnh sai lch c tc dng mt t ln nhng dy ny, c th thy trong Hnh 9,
c bit l s sai lch ln khi tin ti 0 trong nhng dy dnh cho s phn hi ca cung gi tr t
thp vn cn hin din sau khi hiu chnh sai lch.
(18)
Qu trnh ging nhau chung ny cng c thc hin bi Lastrapes v Selgin 1994. i vi m hnhBlanchard-Quah, Koop (1992) tnh ton dy sai sBayesian v lu rng kh nh thno tdy gc
bsai st c trnh by.
(19) Xem nhng tho lun chi tit hn trong bn tho gn y nht ca bi vit ny, Cowles Foundation
Discussion Paper Number 1085.
Tri ngc vi nhng tc ng ca bng III i vi m hnh Y-M, bng VI ch ra rng khong
thi gian hiu chnh xu hng i ln l khng xu cho m hnh B-Q nh cc ch s xc sut hunghim, ngoi tr mt chiu hng l vic gi li mt xc sut qu thp ti thi im t thp
trong nhng phn hi p ng nhng chn ng (shocks). iu ny phn nh mt h s bt
i xng gi c ghi nhn cho nhng phn hi v gi tr ca bin t. Trong m hnh ny,
trong si lp vi m hnh Y-M1, khong thi gian Bayesian v khong thi gian hiu chnh
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xu hng i ln gn nh c di trung bnh bng nhau, nh c th thy trong bng VII. Xc
sut hu nghim thp hn, dnh cho cho nhng khong thi gian hiu chnh ti gi tr t thp cho
nhng phn hi ca cung, xut pht t nhng khong thi gian c t khng ng v tr, ch
khng phi do bn thn n qu ngn.
Nu chng ta ly ng h sc lng ca m hnh Blanchard-Quah, chng ta c th kim tra
nhng xc sut trung bnh ca khong thi gian hiu chnh v khong thi gian Bayesian. Bng
VIII chra hnh vi tng t ca khong thi gian hiu chnh v khong thi gian Bayesian theo
cc tiu ch cin. C 2 khong thi gian c xu hng che khut cho nhng phn hi nhu-cu-ca-GNP trong ngn hn, mc d s che khut ny c xem nh l ti thn cho khong thi
gian hiu chnh. Chai c khuynh hng hin ra trong di hn, vi xu hng ti thn cho cc
khong thi gian Bayesian.
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Mis Nh:
Hnh 7.Theo tng im: xc xut giao im ca sau .68 v .95, m hnh B-Q.
Bng VI
MIU T KHONG CCH HP L THEO TNG IM
(M HNH CA BLANCHARDQUAH)
Bin tXc xut xy ra theo khong cch tng im
Y n S U n S Y n D U n D1 .710 .696 .452 .6442 .706 .715 .583 .616
3 .701 .717 .655 .6114 .688 .712 .700 .661
6 .693 .696 .712 .673
8 .703 .698 .705 .731
12 .687 .718 .700 .692
16 .693 .713 .689 .68424 .668 .714 .670 .67632 .655 .721 .707 .718
Ch : Sai s chun Monte Carlo .68 tn s xut hin 1000 ln rt ra l .015. Khong cch theo
tng im c mc bao ph cc nh vi xc xut l .68. Cc v dc ngu nhin v ra ban
u t 1 ca Y.
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Hnh 8.68% v 95% cc giao im theo tng im s phn trm khc, m hnh B-Q
Bng VII
SO SNH CC CHIU DI KHONG CCH, M HNH CA BLANCHARDQUAH
Bin t T s trung bnh cc chiu di: on/Tng imY n S U n S Y n D U n D
1 1.009 1.004 .996 1.0082 1.005 1.001 .985 1.0063 .997 .999 .979 .9934 .990 .992 .979 .9846 .972 .981 .997 .9848 .962 .975 .991 .99412 .972 .985 .995 .999
16 .979 .983 1.005 1.01624 .976 .942 .984 1.00132 .963 .886 .958 .969
Ch : Sai s chun ca cc bin trong hnh Monte Carlo, nhngkhng vt qu 0.06.
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Hnh 9.68% v 95% giao im cc dc iu chnh, m hnh B-Q.
Bng VIIIKHONG CCH TNG ON V TNG IM NH L KHU VC TIN CY,
BLANCHARDQUAH MODEL
Bint
Xc xut bao ph ca tng imBin t
Xc xut bao ph ca tng onY n
SU n
SY n D U n D Y n
SU n
SY n D U n D
1 .657 .650 .050 .632 1 .653 .662 .273 .6722 .648 .653 .108 .425 2 .658 .655 .270 .6183 .647 .642 .225 .295 3 .650 .668 .372 .4624 .657 .642 .337 .297 4 .658 .660 .445 .4486 .678 .647 .550 .452 6 .642 .637 .615 .5058 .670 .672 .593 .525 8 .647 .623 .652 .60012 .687 .705 .630 .635 12 .690 .705 .658 .63216 .728 .775 .645 .707 16 .752 .792 .693 .72524 .747 .845 .783 .780 24 .768 .860 .845 .85332 .737 .910 .928 .865 32 .760 .923 .952 .920
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Ch : Sai s chun Monte Carlo ca .68 tn s xut hin 600 ln rt ra l .019. Khong cchtheo tng im c mc bao ph cc nh vi xc xut l .68. Khong cch theo tng on ltrn mt phng, gn on cui, .68 xc xut cc khong cch pha sau.
i vi m hnh ny, cc thnh phn u tin ca ma trn hip phng sai chim t hn nhiu
bin tng th, c bit l nhy ca cu, nh l: sh hin trong Bng IX. Giao im trn ccthnh phn u tin c th hin trong Hnh 10. Cc giao im c hnh dng chung nh ccim trong Hnh 7, nhng c cho bi cc phn hp hn, phn nh thc t rng h miu t chc mt, khng hon ton chim u th, thnh phn ca cc bin. iu th v l Y cung cp sphn ng c mt giao im rng hn v thnh phn u tin cho t ln hn, ngi ta thy iuny trong cc giao im ca hnh 7. iu ny ch c th xy ra do khng Gaussianity trong huphn phi.
T Hnh 11 cho thy thnh phn ca bin th hai. Chng ta thy rng khng chc chn v hnhdng ca cc phn ng trong m hnh l kh cao. c bit l phn ng do Y cung cp. Ngi ta
c th c n tng tng cc giao im s khng chc chn v mc , khng thy hnh dngphn ng ca Y cung cp, s khng chc chn nhiu hn mc ban u so vi mc sau.
Bng IX
PHN TCH SKHC BIT CHO CC CU TR LI CA M HNH B-Q
0.7147 0.2029 0.4092 Y thuc Cung
0.7487 0.1319 0.0654 U thuc Cung
0.6165 0.2002 0.0984 Y thuc Cu
0.4555 0.2117 0.1835 U thuc Cu
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Hnh 10.Thnh phn u tin: xc xut cc giao im .68 v .95, m hnh B-Q
Hnh 11.Thnh phn th hai: xc xut cc giao im .68 v .95, m hnh B-Q.
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Hnh 11 cho thy mt cch r rng rng cc cu tr li ban u rt tiu cc l t khnng c
kt hp vi cc cu tr li c mc tin cy mnh trong thi gian di. Chng ta th hin thnh
phn th 3 ca bin trong cc cu tr li Hnh 12. Cc thnh phn ny chim t5% n 20%
du hiu ca Ma trn hip phng sai, theo s liu ct 3 Bng IX. Kt hp th ba thnh phn
ny vi nhau cho thy hnh dng ca cc cu tr li l t c chc chn. Mc d, mrng cc
giao im bng cch thu hp hn cc yu t trong m hnh Y-M1. Mc d mc tng t ca
s thng sut trong cc giao im ca th. Cc d liu c thng qua trin khai cc biu
n bao gm nhiu thng tin r rng v hnh dng ca cc cu tr li trong m hnh Y-M1 hn l
d liu ca m hnh B-Q. Chng ta c th nghi ngs khc bit ny t thc t ca m hnh B-Q
l th d liu vo tng trng Y, trong khi m hnh Y-M1 s dng cc mc Y. iu ny lm
cho d liu Y-M1 c thng sut, c ngha l n thc y cc cu tr li c thng sut hn.
Tuy nhin, trong mt m hnh a chiu, n th nguy him tha nhn rng sthc y cc cutr li lun lun c k tha mc thng sut m chng ta thy trong d liu ca th. V
cng khng c phng cch no thy, tim ca cu tr li n c no trn th, rng c
mt loi khc nhau trong thng tin ca d liu em li vthc y cc cu tr li trong hai m
hnh.
Hnh 12.Thnh phn th ba xc xut cc giao im .68 v .95, m hnh B-Q.
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Vi nhng m hnh n gin, chng ta hy vng lm cho cc trng hp ca chng ta biu th
hp l sai scc giao im c xy dng nh l xc sut hp l cc biu sau l kh thi v c
th l mt ci tin to ln trn tng im da trn khong tin cy hp l nh m t hnh dng hp
l. Chng ta cng hy vng chng minh c rng thng tin v hnh dng vt ra xa giao im
l hu ch v khng t c tin cy bng cc phng php c thu thp tc lng bng
mt v trc gic.
By gichng ta tr li xem xt mt m hnh gn gi hn vi phm vi hin ti ang s dng
trong chnh sch phn tch kinh tv m. i vi m hnh ln hn ny,chng ta c nhiu gii
hn trn cc tham s. N ch ra rng, iu ny lm cho i hi nhiu hn trong vic tnh ton sai
scc giao im, trong cch m khng c cng nhn trong cc ti liu ang tn ti.
8. PHNG PHP MONTE CARLO CHO XC XUT SAU
TRONG CC M HNH HON CHNH
MONTE CARLO METHODS FOR POSTERIOR PROBABILITIES IN
OVERIDENTIFIED MODELS
A L thuyt (Theory)
Chng ta xem xt ng thi cc m hnh phng trnh tuyn tnh ca mu:
(10) (L) y (t) = (t)
Chng ta c:
(11) (t)\ y(s, s
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(13) = o-1 o-1
Chng ta ginh h thng l s t hi quy hu hn, iu c ngha l c mt k < nh vy
j = B j = 0 cho tt c j>k.
Cc p.d.f cho d liu y(1), ., y(T), iu kin trn nhng quan st ban u y(-k+1), , y(0), l
t l thun vi q theo quy nh ca
(14) q(B,) = | |-T/2exp[- trace (S (B) -1 )],
(15) (t;B) = B (L) y(t),
(16) S(B) =
i vi mt mu nht nh, (14) c x l nh mt chc nng cc thng s B v l chcnng hp l. Hnh thc ca n th chnh xc rng s hp l cho mt s gim st (hi quy) vi s
xo trn ca Gaussian bin ngoi sinh hi quy cht ch, mt m hnh cin m cc tnh ton
ca u c tho lun trong cc ti liu(20). Chng trnh RATS bao gm cc thi quen thc
hin bn v ca Monte Carlo s phn b chung ca im B v v s dng nhng iu c rt
ra to ra hnh dng tcc im phn phi sau ca cu tr li thc y.(21)
(20)Xem Box v Tiao (1973), chng 8 cho l thuyt ny
(21)Box v Tiao (1973) khuyn bn sdng mt Jeffreys tin nghim trn , m thc ra t l thun vi
. Quy trnh Gi RATS sdng thay th , ni m v l sc lng cho miphng trnh. Phillips (1992) ngh sdng cc Jeffreys tin nghim trn B v , m trong m hnh
chui thi gian (khng ging nh cc m hnh vi bin hi quy ngoi sinh) l khng bng phng trong B.
ngh ca Phillips c nhc im l cc Jeffreys tin nghim tnh ton kh bt tin v c thay i ng
kcng vi kch thc mu, lm kh cho ngi c khi so snh kt qu trn ton b d liu. Do ,
chng ti a thch cc gi nguyn tc ca Box v Tiao c chra trong trang 44, m ngay c trong
cc m hnh vi bin hi quy ngoi sinh sdng Jeffreys tin nghim c thdn n cc tnh hung d
thng. Trong nghin cu ny, gikt qu ca chng ti c tnh tng ng tt p dng cc ti
liu hin c, chng ti theo cch la chn quy trnh tin nghim ca RATS.
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Cu tr li thc y cho cc m hnh, c xc nh bi phng trnh s (5) trn, trong trng
hp ny h s ca
(17) B-1(L) o-1,
ni m yu t cn cu trc ri lon c mt n vkhng ng, hoc chuyn i cc cu
tr li tng ng h c cn ca cu tr li vi mt s xo trn kch tht tiu biu (mt
lch chun). Phng trnh (13) cho chng ta mt mi lin h gia , v . V l i xng,
o v c h s khng hn chhn . Mt m hnh VAR chnh xc l mt m hnh trong
chng ta c nhng hn ch c th lm phng trnh (13) biu din tn v . Trong
trng hp ny, ly mu t cu tr li thc y xc nh bi phng trnh (17) l khng kh
khn: ly mu t phn phi im ca B v bi m hnh chun, sau s dng biu c
xc nh bi phng trnh (13) v han ch chuyn i rt ra t phn phi cc cu tr li thc y.Vic s dng ph bin nht cch thc ny thu hp o thnh hnh tam gic, gii quyt cho o-1
bis tham gia phn tch ca Choleski.
Khi m m hnh khng c xc nh chnh xc, mc d, phng php v phng trnh m to
ra tcc im phn b chung ca hnh thc gim cc tham s l khng cn c th. Mt cch
thc khng i km vi mt v d nh ca mi quan h m khng s dng m hnh chun to
ra sc lp vi con s ca cc nh nghin cu (bao gm cchng ti) v c s dng t nht
trong hai ln xut bn (Gordon and Leeper (1994), Canova (1991)). Chng ti s gi n l cchthc Bayes ngngch. Bi v phng php ny c sc li cun trc quan gy hiu lm v i
khi c thc ddng hn thc hin hn so vi phng php chnh xc, chng ti m t
di y, chng ti bt u bng vic m t n v gii thch l do ti sao n to ra khng phi l
Bayes sau cng khng phi l phn phi ly mu cin.
Trong mt m hnh nhn dng hon chnh, phng trnh (13) hn ch cc hnh vi gim hnh thc
i mi khng ng trong ma trn hip phng sai . N vn ng, mc d, OLS c tnh cho
v l thng k, iu ny c ngha l hp l ch ph thuc vo d liu xuyn sut chng.Nh vy c tnh khnng ti a ca B, o v ng mt thut ton cho hnh thc gim biu
thit lp cu trc d ton (B*, o*, *) p ng cc hn ch. Thng th khng c gii hn
nh hng n B, v vy = B*. Phng php Bayes ngngch tip tc vng t gim hnhthc phn sau khng hn ch t p.d.f cho (B, ), sau lp bng ny da vo gi tr ca (B,
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o, ) thng qua ti a cc cch thc hp l. Nu gi tr cc tham sc rt ra t phn sau
khng hn ch trn (B, ) gim thay v c lng tham s. Phn phi kt qu ca bi hc l
tp trung vo mt phn ca khng gian tham s tha mn cc hn chnhng khng phi l tham
s phn phi cin cho cc c lng tham s, v phn phi phn sau cho (B, ) th khng phi
l mt mu phn phi cho ( v ).N th khng ng cho phn phi phn sau v phn phiphn sau khng hn ch cho (B, ) khng phi l phn phi phn sau b hn ch, v t lp bn
vo trong khng gian tham s hn ch thng qua cc cch thc lp d ton khng chuyn i n
thnh mt phn phi phn sau b hn ch.
Cch thc khng c cng mt loi chng minh tim cn m lm gn nh tt c cc im v
phng php Bayes to ra giao im li thi tng ng t mt quan im cin ca m hnh
n nh, v n c l l tim cn hp l t mt quan im Bayes nh mt bnh thng xp x bnh
thng ngay c m hnh khng n nh. thy iu ny, hy xem xt mt vn c tnh
tuyn tnh n gin, ni chng ti c mt tham s thc s, mt c lng phn phi khng
hn chnh N (, ), v mt gii hn R = vi Rk = m. Hn ch ti a cc c lng hp l
l sau hnh thnh trn R = a dng ca c lng khng hn ch ML theo cc s liuc xc nh bi: ,
(18) * = (-1)-1 -1 + M (M -1 M)-1,
Ni m M= R v c chn cho ct y c hng m-k v tin cy R = 0. Ly phnphi mu ca *th sau ln lt bnh thng, sau l bin i bnh thng tuyn tnh ca .Trong phn phi i xng, tha mn vn i xng qua trc, phn sau khng hn ch trn c
cng p.d.f bnh thng, tp trung ti , nh ly mu p.d.f ca v. Chng ta c th lm choMonte Carlo rt ra t mu phn phi ca * bng cch v mt ng t mu phn phi ca c lng khng hn ch, v a ra nhng c lng khng hn ch ny da trn s dng cng
thc (18) tham s khng gian hn ch. Nhng v trong trng hp ny phn phi phn sau ca v phn phi mu ca n l nh nhau, rt ra t phn phi phn sau trongbc u tin s cho
kt quchnh xc nh nhau. V v trong trng hp ny, hn ch phn sau c hnh dng bnh
thng nh vy v* rng phn b mu ca * c khong , s phn b m phng ph hp viphn sau cng nh phn phi mu ca c lng hn ch.
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Phng php Bayes ngnghch ly mu t cc phn phi ca cu tr li thc y da trn s
kh hiu khi ly phn phi mu vi phn phi phn sau, nhng trong trng hp ca cc khon
trn y s khng gy hi, bi v hai loi phn phi c hnh dng ging nhau. Cho cc m hnh
n nh, l thuyt phn phi cho( v ) l tim cn bnh thng, v hn ch ch sc timcn nh th chng l tuyn tnh. V vy, cc trng hp c xem xt trong on trc trthnh
mt xp x tt trong mu ln. Cho cc m hnh n inh hoc khng n nh, phn sau trn l
tim cn bnh thng, v vy phng php Bayes ngnghch ang tim cn hp l t mt quan
im im Bayes.
Nhng trong bi bo ny, chng ti ang tp trung vo phng php a ra sai sgiao im m
bt i xng c thc gii thch chnh ng nh thng tin v s bt i xng trong phn phi
phn sau ca cc cu tr li thc u. Bt i xng xut hin trong giao im c to ra bng
phng php Bayes ngnghc ch c th bt ra c bng chng cho thy xp x tim cn m c
th bin minh cho phng php ny khng c t chc trong mt phn mu.
Mr.Tm
iu quan trng cn lu rng, mc d cc phng php Bayes gin n cu i cng s lm vic
tt hn trong cc mu ln, c ngha l trong cc tnh hung thc t m mu xc nh c tnh
chnh xc, n c th cho kt qu xu ngu nhin ty trong tnh hung c bit l mu nh. V
d, trong mt m hnh 3-bin l c xc nh chnh xc bi cc iu kin thng qua ba hn
ch 0 trn trong m hnh hin th trong bng X (trong x ch ra h s khng b rng buc).N cho bit rng cc hm tp trung hocphn tn, nh hm , c 2 nh cao bng nhau. XemBekker v Pollock (1986) v Waggoner v Zha (1998)
Bng X
V D NHN DNG TABLE X (EXAMPLE IDENTIFICATION)
Lu : x l h s khng b gii hn
1 0 xx 1 0
0 x 1
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M hnh ny c lcng gip ta bit rng nu mt m hnh ba bin p dng c hnh thnh
ny, m hnh sc cng nhn l khng xc nh trn ton cu. Nhng thc t l vic n khng
xc nh trn ton cu khng c ngha l cc d liu khng thng tin v m hnh. Mt mu
chnh xc hp l, bng cch s dng phng php chng ta c d kin s kt hp thng tin t c
hai nh. Nu cc nh gn nhau trong khng gian p ng xung, s a dng ca n c th khng
l mt vn . Nu chng xa nhau, nhng p ng xung trung bnh s c li rng, vic truy tm
ra mt cch chnh xc bng cch tch hp khnng hp l. Tuy nhin trong cc thut ton Bayes
gin n, ch cn chn mt trong cc nh cho mi hnh v ty , vi nh ca thut ton hi t
gii quyt phng trnh. iu ny s d dng nu bt ra c nhng nh cng hng, hoc gn
nh tt c, do s khng chc chn sc nh gi thp ng k. (22)
(22)Trong khi v d ny c thxut hin c bit, nhng n c thddng nhng vo trong mt
m hnh ln hn. Nu m hnh ln hn c mt khi 3= 3 vi dng 0 hn chgc trn bn
tri ca n, nhng khng phi l chn hnh tam gic, n c thc xc nh trn ton cc. Tuy
nhin, nu h sma trn thc sl gn ngn chn diagonality, rt c thsc hai nh
trong cc phn khc nhau, nhng chiu cao tng t. iu ny sto ra khnng tng tnh
trong v dn gin 3 = 3 cho cc hm Bayes n gin phn nh khnng cc hnh chgn
mt trong nhng nh.
M hnh ny xc nh nhng hn chcng to ra mt kh khn cho cc thut ton Bayes gin
n. Mc d c rt nhiu h s khng b gii hn l yu t khc bit trong , cc iu kinnhn dng c tha mn, ma trn ca mu ny khng theo di trong ton b khng gian camin xc nh dng . iu ny c ngha l ca (13) khng c gii php cho nhnghng s ny. Vic v nhng nghim sau khng b rng buc phn phi bi , thut ton Bayesgin n i khi s to ra cc m khng c phng php gii. Nu gii quyt phng trnhbnh thng theo cch tip cn cho ph hp vi v , trong mt m hnh va xc nhc p dng y th s tht bi.
Chng ti nng cao mu 3 x 3 trong trng hp ny ch cho thy rng cc m hnh to ra vn
cho phng php Bayes gin n l c tn ti. Ni chung, trong cc m hnh hp l ny c
nhiu nh lm pht sinh ra m hnh nhn dng hon chnh, v chng to ra kh khn trong vic
tip cn phng php Bayes gin n. Nhng kh khn l c hai s - trong vic lin tc ti a
ha khnng qua hng ngn hnh vc rt ra t n l khng thc t theo di cn thn m
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nh cao cc thut ton c hi t - v phn tch khi c nhiu nh xp x tim cn m n c th
bin minh cho phng php Bayes gin n th r rng l khng chnh xc trong cc mu hin
ti.
m t mt hm chnh xc c to ra t hnh v Monte Carlo theo Bayes cho cc tham s
trong (10), chng ta bt u bng cch thc hin li vic tham s ha. Thay v (10), chng ti s
dng
(19)
Khi
and
v () . Khng c gim slng cc tham s t do,bi v ng cho ca th lun c chun ha vi 1 vector khng c rng buc c cngs tham snh mt ng cho cng vi 1 c chun ha. C mt sl do thch thamsny. N n gin ha lin kt vi (17) trong vic gim dng thc v cc thng s cu trc.
Thng thng tham s c th cung cp cho mt n tng sai lch v s thiu chnh xc trong d
ton ca 1 hng , nu s chun ha xy ra trong vic thit lp ti 1 h sc xc nh cbit trong cc hng tng ng ca . Nhng l do chnh gii thiu tham s ny y l s hpl khi vit l mt hm kh tch
, i hi phi c mt siu chnh trc cho php
hnh thnh mt phn phi sau, trong khi n l khtch nh mt hm ca (23)
(23)Nhn chung, khnng, vi B v c tch hp, l O(1) . trong cc yu tc nhn ca ti
tt c cc kch cmu. iu ny khng c ngha l n khng c tim cn bnh thng m kh
nng thc hin tr thnh nh bn ngoi mt khu vc xung quanh cc gi tr tham s thc s.
Ngoi ra cn c khnng l trng hp c bit kh tch, v d l bnh thng vi nhngng cho v hn chc hnh tam gic. bit chi tit, xem bn tho ca bi bo ny, Cowles
Foundation Discussion S1085. Tt nhin, chng ta c thsdng cc tham stiu chun v
gili kh tch nu chng ta thc hin A0, sau chuyn li cho khng gian tham s( . baogm c Jacobian thch hp . Nhng cch dnht gii thch sxut hin ca thutngny sl ly c n ttham sA0.
Chng ta c th vit li (14) cho hp l nh sau
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(20) * () (
( ) )+
Ly tin nghim phng trong B v A0, chng ta c th tch hp trn B c c hu nghim
bin trn A0
(21) [ (() )]
y vi m hnh gim dng m hnh chng ti s dng m RATS c dng rng ri
gim bc tdo iu chnh '' v trong (21). iu ny c thc coi l c hiu qu khi s dng
trc tin khng ng, hoc l kt qu ca cc h s ca A(L), sau chuyn thnh mttham s v dng v B(L). C thc nhn thy bng cch so snh (20) vi (21), iu ny ctc dng lm cho bin trn ca t l vi t l tp trung v do loi b s khc bit c th c
gia cc m hnh sau v c lng hp l cc i.
Biu thc (21) khng phi l dng ca bt k tiu chun p.d.f. sinh ra mu Monte Carlo t n,
trc tin chng ta phi dng Taylor m rng dng hai-a n v nh, trong cc hm
Gaussian xp x phn phi tim cn ca cc yu t ca Bi v y khng phi l hnh thcthc s ca p.d.f, chng ti khng th s dng trc tip cho hm Monte Carlo mu ca chng
ti. Mt cch tip cn l ly mu quan trng, trong chng ta rt ra t xp x Gaussian, hoc t
mt a bin t, vi cng ma trn, nhng c rt ra bi t l ca (21) m chng ta v. Mu trng
c.d.f. sau xp x vi c.d.f. tng ng vi (21).
(24)
Trng lng trong thc t khc nhau chkhng phi rng ri, do mt mc nht nh li trong p ng xung ly t mu Monte Carlo
tnh cch ny thng i hi nhiu thi gian nh nhiu m hnh Monte. Chng ti tm thy th
tc ly mu quan trng n gin ny khng lm vic tt cho cng vic ca chng ti.
(24) tng ny, ly mu quan trng, nhn thy sdng rng ri ktkhi c gii thiu bi
Kloek v Van Dijk (1978).
Chng ti thay v s dng mt phin bn ca b thut ton Metropolis ngu nhin cho chui
Markov ca Monte Carlo (MMCMC) c ly mu t p.d.f. Thng tin chi tit ca phng phpc quy nh trong Waggoner v Zha (1997). (25) c nn kt qu m phng chng ti trnh
by, bi mt s bin php rt chnh xc, nhng chim thi gian tnh ton ng k 11 gitrn
mt my tnh xch tay Pentium II 233 MHz. Chng ti hy vng rng nhiu ci tin trong thut
ton ly mu c th gim c thi gian ny.
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(25)Cc thut ton c sdng ba im bt u rt ra ngu nhin ring bit v a bin t c
phn phi vi 6 bc tdo phn phi cho nhy vo nhng thay i trong A0. V phn phi ca
cc thng scn li c iu kin trn A0 l Gaussian, chng ti cn cc thut ton MMCMC ch
cho cc tham sA0. Ma trn hip phng sai ca phn phi t c thit lp ti Hessian v
khnng ng nhp nh, thu nh li vi t l -.25. Chng ti sdng 480.000 thch hp cho
mi im khi u, loi b na u ca mi ln chy, do kt qu cui cng c da trn
720.000 thch hp. Cc'' tim nng gim quy m'' ca Gelman, Carlin, Stern v Rubin (1995).
L t1 n 1,0085 cho mi trong s20 tham stdo trong A0, v hn mt na trong scc
thng sn l t1 n 1.001. Tn sca bc nhy c tha nhn v0,49 trong mi mt
trong ba chui. Mt bin php hiu qu l dng cmu Monte Carlo, cung cp mt shng
dn nh tin cy ca im phn v lp bng, n l Monte Carlo ln kch thc mu t l''
trong chui'' n '' gia nhng c tnh'' chui cc sthay i ca mt tham s. i vi tng s
cmu ca chng ti 720.000, cc dao ng o c t176, cho cc phn tca A0 vi gi tr
ti t nht ca vic gim tim nng quy m, vi 772 gi tr trung bnh vquy m gim tim nng
trn tt c cc thng s.
Lu rng n cng c th tnh ton cc li. y li l mt v d v mt phng php cho cc li
ca vic tnh ton l tim cn hp l, nhng tha nhn khng c l do gii thch bt i
xng ca n nh cung cp thng tin v lch nh t mu bnh thng. N l thm ch nhiu
khnng hn so vi cc hm Bayes gin n tnh ton khng thc t h thng cht ch trongs hin din ca nhiu cc b cc i.
Mc d trong chuyn i sang cc tham schng ti loi b s cn thit phi chn mttiu chun theo ngha thng thng, vn cn l mt s tha ri rc trong cc tham s: l du hiu
ca mt hng c thc o ngc m khng cn thay i chc nng hm. N c v l mts la chn tiu chun c th khng nh hng nhiu ng kn kt qu, nhng iu ny l
khng ng s tht. Trong cc tham s thng thng, vi cc yu tng cho ca c
chun ha n 1, n c hiu rng ri l mt phng trnh vi h s thng k cng c xcnh trn hu ht cc bin ca n c thc chuyn i sang mt trong tt c cc h s
dng nh c xc nh bi chun ha cc phng trnh trn mt bin c h sl khng ng
k khc nhau t s0. iu ny l do mt s chun ha nh vy lm cho cc du hiu ca tt c
cc h strong phng trnh gn nh khng xc nh. Mt hin tng tng t pht sinh nhng
phn ng xung. S la chn ngu nhin chun ha c th dn n cc c tnh rng tt c cc
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cu tr li, khi mt chun tt hn s lm cho n r rng rng cc cu tr li thc sc xc
nh chnh xc. y chng ti theo Waggoner v Zha (1997) trong vic la chn mt cch
chun ha cho mi hnh v l gim thiu cc khong cch ca tc lng ML ca . Kinhnghim ca chng ti xc nhn ngh ca h rng phng php ny sc xu hng ging
k chuyn i cc phn ng xung v do cung cp kt qu sc nt hn.(26)
(26)Phng php chng ti sdng ti thiu khong cch Euclide gia ML v im cnh
bnh thng. iu ny lm cho phng php nhy cm vi quy m ca cc bin. Tt c cc bin
ca chng ti c chnh lch t ltng t, v vy y khng phi l mt vn ca ring mnh,
nhng n sl tt hn nu c h thng cho php iu chnh t l trong cc sliu. iu ny
c thc thc hin bng cch, sdng nghch o Hessian vkhnng ng nhp ti a
xc nh khong cch sliu. Khi chng ta sdng cch khc, dng nh hp l, quy tc chun
ha, tc ng n cc h thng li c tnh trong mi trng hp r rng, thng l theo hng
mrng chng.
B. Kt qu ca m hnh 6 bin
Mt bi bo trc ca mt trong chng ti (Sims (1986)) cha mt v d v mt nhn dng
hon chnh m hnh VAR vi mt gii thch th v.
N xc nh mt c sc trong cung tin to ra c 2 nh hng thanh khon n s suy gim u
tin trong li sut v nh hng n gi c hay lm pht sau mt giai on m rng tin t.
Nghin cu c xc nh nhng hn chv chng ti cho thy tnh ton xc nh c gn
nhn trong phin bn 2 ca bi gc.
Hnh 13 cho thy phn ng xung ca m hnh ny, vi 0,68 v 0,95 phng trc xc sut. Ct
u tin cho thy rng chnh sch tin tc xc nh nhng c sc c mt m hnh d kin
ca cc hiu ng, tng li sut t nht ban u, h thp cc c phiu, lm gim sn lng t nht
l mt nm hoc lu hn, gim t l lm pht, mc d c l khng nhiu, nng cao t l thtnghip, v nht l bc u ct gim u t. Ct thhai c ngha l gii thch nh nh hng
ca nhu cu sc tin. Rng v mnh mkhng i xng cho thy nhng nh hng ca ri lon
ny c xc nh. Skhng i xng mnh cho thy khnng c th c nhiu nh, vi cht
lng khc nhau ct MD trn cc nh. Ct Y v I hin th nhng c sc khu vc t nhn m
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gy ra bi Fed tng li sut. Ct Y l mt c sc lm tng sn lng, nhng khng phi l gi,
trong khi ct I gy sc tng sn lng v t l lm pht v mnh hn xc nh, mc d c th
khng mnh hn p ng li sut.
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Phn tch cc phn ng thnh cc thnh phn cung cp ci nhn su sc hu ch. Chng u
ging nh cc phn hi ca Blanchard-Quah hn phn hi Y-M1 trong t l kh thp ca cc
du vt ca cc ma trn hip phng sai cho cc phn hc chim bi nhng gi trring utin. Phm vi l 0,49-0,97, vi ngha l 0,75. K t khi tp trung ca chng ti y khng
phi l mt nh gi ni dung chi tit ca m hnh ny, chng ti b qua s hin th ca s phn
tch cho phn hi n l. Nhng n l ng gi hin th s hu ch ca s phn tch gia cc
bin. Chng ti xp chng ln nhau nhng phn hi vi c sc chnh sch tin t ca R, M1, P
v Y v cng phn r chng vi nhau. i vi phn r ny l 6 gi tr ring theo t l ca ma trn
bin thin: 0.52, 0.25, 0.06, 0.05, 0.05, 0.02. Hnh 14 cho thy bin xc sut 0,95 cho su
thnh phn.
Cc kha cnh th v nht ca th ny xut hin ch vi s ch trng n cc loi ng chm
chm khc nhau.(27) i vi thnh phn u tin, trong ct 1, dng u trong ca M v Y ph
hp vi dng di cng ca R v P. p ng dng ca R v P c lin kt vi p ng m
ca M v Y. Ba bin u tin l ph hp trong vic xut cc thnh phn chnh ca s khng
chc chn chn gin l s khng chc chn v mnh ca hiu ng ca c scl s gia
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tng R, st gim M, v s suy gim ln u ca Y ln hay nh? Nhng thnh phn P trnh by
trong m hnh i lpphn hi caR,M v Y th c lin kt yu vi phn hi P v ngc li.
M hnh ny c thc lin quan n vic gii thch cc kt qu ca m hnh, v s rt quan trng
bao gm trong c trng ca s khng chc chn viu kin d bo tm hnh c s
dng trong phn tch chnh sch.
(27)Phin bn lm vic ring ca chng ti trong tt ccc th sdng mu sc cho php
mt sphn bit chi tit hn gia cc dng hin th. Cc th mu sc c sn, cng vi trc
, hon ton khc bit v khng hon ton li thi, cc phin bn c ti
http://www.princeton.edu/~sim.
Ct th hai nng nht trn M v P, thc s l quan trng hni vi M hn l thnh phn u
tin. y l M v P di chuyn vi nhau. Thnh phn ny cho thy rng c mt s khng chc
chn ng k v hiu lc chung trn cc bin danh ngha ca s co tin t, c lp vi s khng
chc chn co tin t mnh nh hng n li sut v u ra. Thnh phn th ba nh hng n
hu ht cc phn ng u ra, tht ch yu l cc phn ng M, v thnm ch yu l phn ng
R, nhng tt cu khim tn vkch thc.
M hnh ny ch hin thng thi va phi, do s khc bit gia nhng tnh ton mt cch
chnh xc v tnh bng Bayes gin n hoc bng cch s dng trng s rt ra t xp x chunha tim cn p.d.f. cho do khim tn. Cc nhiu lon xung quanh phn hi vi ri lonchnh sch tin tc bit tng tcc phng php, c l v nhng phn hi tng i xc nh
mnh. Khc bit r rng hn trong cc phn hi t MD v c sc Y, trong c nhiu bnh
c xc nh. Trong hnh 15 chng ta so snh cc nhiu lon c xy dng mt cch chnh
xc bi chui Metropolis, theo phng php Bayes gin n, v rt ra trng s t xp x
Gaussian da trn Hessian v khnng ghi vo MLE. C sc Y l ngun chnh ca sthay i
v sn lng, v mt phn ng tch cc ca sc R ny cho thy chnh sch tin tc xu hng
tht cht khi u ra mrng. Nhng lu rng trong Hnh 13 95% nhiu ko di nhiu tiu
cc cho cc phn hi R-Y ban u, cho thy s khng chc chn ng k v sc mnh ca phn
hi ny. Hai phng php khc, hin th 95% nhiu trong mi trng hp l hon ton tch cc.
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Hnh 14: Thnh phn 1 - 6 ca phn ng chung ca R, M, P, Y n chnh sch tin t, 0.95 vng,
m hnh su bin.
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Hnh 15: M hnh 6 bin, phn hi cu tin v Y, so snh chnh xc, ngy th v trng s ca
vng Bayes
Cc phn hi MD c quan tm t hn ng k, k t khi kt qudng nh chng minh
rng tp hp cc phn hi l rt xu c xc nh rng gii thch l khng r rng. Tuy nhin,
c th thy rng c mt xu hng chung ca cc ct th ba v th nm, bng cch s dng
phng php n gin, cung cp cho cc nhiu hp hn so vi ct u tin. Cui cng, cc
nhiu ca phn hi ca gi n MD trong ct thba, tng ng vi cc hm Bayes gin n, cho
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thy hu nh khng c lch, trong khi khnng xy ra trong thc t cho thy lch rt
mnh, vi nhiu 68% nm gn nh hon ton di im c lng. (28)
(28) Chng ti tin tng rng skhc bit ca tho lun y khng phi l hin vt ca Monte
Carlo ly mu li. 8000 mu c lp c sdng cho cc Bayes n gin v khng trng sBayesian, cho php c tnh kh chnh xc vv tr ca cc giao thao. Cho chui Metropolis c
tnh trong hai ct u tin, chng ti so snh kt qu cho gp mu Monte Carlo vi nhng ngi
cho ba chui c lp ring bit. S khc bit gia cc giao thoa t ba dy chuyn hu nh
khng c thpht hin bng mt, do , mi mu chng ti tho lun trong vn bn c xc
nh r rt.
Chng ti cng kim tra cc phng php t khi ng cho m hnh ny. Cc phng php
phn trm khc, m khng c siu chnh sai lch ng ngc nhin. Trong trng hp hp l
cho lch, phn trm cha c sa cha c xu hng phng i lch, c lv xu hng
thin v khuch i ca h. Nhng nhiu ny hin thc tnh gn nh hon ton bn ngoi mt
vng nhiu 68% trong nm trng hp v gn nh hon ton bn ngoi mt vng nhiu 95%
trong mt trng hp (P nghing n p ng MD), nhng hnh nh cht lng c trnh by
bi nhng vng nhiu ny l nu khng ph hp vi vng nhiu hp l trn. Cc phng phpphn trm khc, vi siu chnh xu hng thc hin nng. Trong mt m hnh tng i ln
nh th ny, c th s l mt vi nghim ti hoc ngoi ranh gii ca trng thi dng. Chnh sai
lch ca phn phi bootstrap ca A(L) c xu hng y cc nghim khng thc t vo khu vc
khng n nh. Kt qu l vng nhiu t bootstrap thin v hiu chnh xu hng le ra nhanh
chng vi sgia tng t. Cc vng nhiu c xu hng rng hn so vi cc vng nhiu hp l
ngay ci vi t nh, v cho cc phn hi quan trng ca P n MS, bootstrap thin v hiu
chnh bao gm 0% trong 68% ca mnh, trong khi cc phng php hp l v tt c nhng ci
khc l tt, 0 cng trn di tn 68%. Kt lun v vic liu cc m hnh cho thy mt vn v
gi do c th b bp mo bng cch s dng khong thi gian bootstrap thin v hiu chnh.
9. KT LUN
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Chng ti gii thch l do cho vic tnh ton cc c im c th xy ra ca nhiu trong cc
m hnh ng, th hin nh thno vt qua tng im tiu chun hin th thng tin ca
dng, ch ra rng cc phng php chng ti a ra l tnh ton kh thi, v ch ra rng cc
phng php c c thri vo vic m t khnng xy ra thc t khng chnh xc, mc d h
bit rng cung cp xp x chnh xc trong cc mu ln. Chng ti hy vng s c cc nh
nghin cu p dng c th thuyt phc rng cc c im c kh nng xy ra ca nhiu l
phng php tt nht cung cp cc li trong cc m hnh chui thi gian. Chng ti hy vng
thuyt phc cc nh nghin cu l thuyt rng vic ci thin khnng tip cn da trn l mt
s dng hiu quhn cc n lc tr tuhn n lc hn na cung cp cho cc vng sai s vi
s bin minh tim cn.