Tt^ chi Khoa hgc TrudngDgi hgc Can Tha Phdn A: Khoa hgc Ttr nhien, Cdng nghe vd Mdi trudng: 33 (2014): 130-138
Tap chf Khoa hpc Trirdng Oai hpc Can Thd website: sj.ctu.edu.vn
D i r B A O D A N S O V I E T N A M B A N G C A C M O HINH T H O N G K E Vo Van Tai va Pham Minh Tryc^
' Khoa Khoa hgc Ty nhien. Trudng Dgi hgc Cdn Tha
^ Hgc vien Cao hgc, Khoa Khoa hgc Tir nhien, Trudng Dgi hgc Cdn Tha Thdng tin chung:
Ngdy nhgn: 19/03/2014 Ngdy chdp nhdn: 28/08/2014 Title:
Forecasting Vietnam's population by statistical models
ABSTRACT
This study uses different models of regression, time series and fuzzy time series to forecast Vietnam's population from
historical data. By using statistical criterions, the most appropriate model can be found for forecasting Vietnam's population to 2020.
Td khda:
Hoi quy, chuoi thai gian, chuoi thai gian md, du bdo. tieu chudn AIC Keywords:
Regression, time series, fuzzy time series, forecast, AIC criterion
Nghien cuu ndy su dung cdc mo hinh khdc nhau ciia hdi quy, chuoi thdi gian vd chuoi thai gian ma di du bdo ddn sd nuoc la difa tren cdc so lieu cua qud khu. Su dung cdc tieu chudn thong ke di tim mo hinh thich hgp nhdt cho moi trucmg hgp. tit do tiin hdnh du bdo ddn so nude ta den nam 2020.
1 GIOI THIEU
Ddn sd la mdt vdn de ldn md m§i chinh phii diu phai cd sy quan tdm d ^ biet bdi vi nd anh hudng true tilp din sy phdt ttiln krah tl xd hpi cda qudc gia minh. Dy bao dan sd la mot cdng viec phai thyc hiSn dau tien, khdng toe toilu dupe trudc khi bo^cb dinh cac chinh sach vT md ngin han cung nliu dai ban ciia rapt dia phuong, mot qudc gia.
Cac chinh sdch cbo tdt ca cac Imh vuc edn phdi dya Uen todng tin vl ddn so. Dy bao dan sd tot, khdng nhOng t|n dung dupe n ^ d n nhan lye hop ly ttoit Uong phdt ttiln ldnh tl xa hdi ma cdn tilt kiem cung nhu chu ddng Uoiig xay dung ca sd vat chit, dpi ngu can bp,... eiia tit cd cac liiih vuc.
Trong todng ke, hai md hinh ehinh dang duac sii dung rdng rai ttong dy bao Id md hinh bdi quy vd md hinli chudi tool gian. Trong hai rad hinh nay, chudi todi gian dupe xem cd itoieu im dilm hon. Chuoi tlidi gian dang dupe su dung phd bi6n vd hieu qua Uong nghien cuu khoa hpc bdi vi rdt
nhieu sd lieu cin dy bdo dupe tou todp tiieo todi gian. Cac md hinh chudi thdi gian nhu ty bdi qui (AR), ttung bmh ttupt (MA), ty hdi qui trung binh truot (ARMA), tu hdi qui tich hpp trung binh trupt (ARIMA),... da dupe dp dung rat ph6 biln Uong cdc dy bao ciia kinh t l xa hpi,... Tuy nhien, dy bdo bing md hinh ebuSi todi gian se khdng ed hi§u qud nlu chudi dtt lieu khdng dimg vd khdng tuyln ti'nh.
Vdi su kit hpp cua \^ touylt tdp md, nhiing so li?u tou dupe cua qua kbii cd sy lien kit xdc suit theo mpt quy tdc nhat dinh. Chudi todi gian md tan dung sy lien kit sd Heu ndy da dupe chijng minh c6 nhilu uu vi^t bon uong dy bdo so vdi chudi todi gian khdng md. Nhilu md hlnb chudi tiidi gian md da duac dl nghi nhu md hinli eua S M Chen (1996), K-Huamg (2001), A.M. Abasov et al (2002), S.R.Smgh (2009),... Theo tim bilu eiJa chung tdi, chudi tocri gian md chua dupe quan tdm diing miic d nude ta nen nbOng dy bao cy toi trone cac Imh vyc chua dupe xem xet nhilu.
Tgp chiKhoa hoc Trudng Dgi hgc Cdn Tha Phdn A: Khoa hgc Tu nhien. Cdng nghi vd Mdi trudng: 33 (2014): 130-138 Hi^n nay, nganh todng ke tten toi gidi, dac biet
la ITnh vyc dy bao da cd sy phdt trien vupt bac.
Trong ITnh vuc dy bdo dan sd, cd nhiing md hinh, cdng cy tirto toan va sy ddnh gia mdi troi^ nhiing n3m gin dSy. Vdi sd lieu da cd, md hinh todi^ ke da dupe n ^ ^ n ciiu, ciing vdi cae phin mem todng kS hi?n tai chung ta hodn todn ed thi xdy dyng dupe cdc md binh de dy bao tdt cho ddn sd nude ta.
Kit qua dy bao sg la thdng tin quan Upng dl hoach djito cae ehinh sach vT md Uong phat trien kinb te xa hdi ciia dat nude. Bai viSt ndy khao sat cac mo hinb hdi quy, chudi thdi gian md va khdng md de tim cac md hinh thich hpp nhdt uong dy bdo dan sd nude ta. Cacb 1dm ttong bdi viet nay cd the dupe ap dung de dy bao ddn sd cho cae tinh, huyen va nhieu ITnh vyc khdc d nude ta.
2 CAC MO HINH DU* BAO 2.1 Mdhmhh^iquy
Gpi t la nam iing vdi dan sd dy bao y^, cac md hinh hdi quy dupe sir dung ttong nghien cihi la
Tuyin tinh dan: y^ = a-hbl (1) ,~ , . b\n(t)+a
Liiyit\m:yt=e ^ •' (2) MS bien dang: y( = a-hbc (3) cdp sd cgng: y^ = ^-JQI i (1 "•" q ^ 0 (4) Cap so nlian: ^'^ ~ ^2011^^''"'2^ (5)
Trong md hinh (1), (2) va (3), a va A la cac he
- ! / • \
sd cua md hinh, t =—(/-20111 vdi t la todi 5
gian cdn dy bao; Uong md hinh (4) va (5), A/ la khoang tool gian tii nam dy bdo den nam dupe chpn lam gdc; /S,/^ Id tdc dp tang dan sd bang nam duac tinh bdi
ln(j'2)-In(j'i)
vdi t\, t2 la diem todi gian dau va cudi ttong day sd lieu dupe su dung de tinh tdc dp gia tang ddn so tuong ung vdi sd dan ^1 vaj^.
2.2 Md hiuh chuoi thdi gian
Mo hinh tu hdi gui bdc p {AR(p)):
>',-(»0 + .S«',>'f_,+u, (6) P
Uong do ™' la cdc he sd udc luong cua md hinh, Ui la sd hang dam bao tinh dn ttang.
Mo hinh trung binh di dgng bge q (MA(q)y.
ttong dd /J^ ciing la cdc he sd udc lupng cua md hinhva u- gidng nhu Uong (6).
Md hinh ty hdi qui vd tnmg binh di dpng (ARMA(p,q)):
yt ='PQ+'Piyt-i+^yi-2+-+^pyt-p+'^ •*-^"t^^^"t-^2'^ (8) Mpt qud ttinh ARMA(p,q) s6 ed qud Uinh ty hdi
quy bac/7 va qua triito Uung binh di ddng bdc q.
yt=S + ayy^^^ + a2>',_2 "^ •" + ^/J^r-/? + ^ Uong dd aj,i = \„2,...,p la toam sd ty hdi quy;
^(^j,J = ^-<^->1 '^ tham sd tnmg binh di dpng;
S = pi0^+ ^2'^-'^ fiq)' M la gid tri ttung bmh cua chudi todi gian; z, la sai sd dy bdo (^1 = p/ - J*^ = sd lieu dy bdo - sd lieu toye tl).
Md hinh tnmg binh di ddng tdng hc^ vdi ty hdi qui ARIMA(p,d,q):
£f_^+...+ fiq£t~q+^t ^^^
2.3 Md hmh hinh chudi thdi gian md Hien tai ed nhilu md hinh chudi thdi gian md khac nhau dupe dl nghi. Trong ung dung, ngudi ta toudng sur dung cac md hinh ciia Chen (1996), Smgh (2008), Huamg (2001), Abbasov - Mamedova (2003), va ciia Chen-Hsu (2004). Ngoai tru md hinh cua Abbasov -Mamedova, cac md hinh cdn lai diu dupe de nghi gdm 4 budc, trong dd ed 3 budc diu ^dng nhau chi khac nhau d budc cudi cimg: md hoa dir lieu. Ba budc chung eiia cdc md hinh dupe de nghi nhu sau:
Tgp chiKhoa hgc TrudngDgi hgc Can Tho Phdn A. Khoa hgc Tu nhien, Cdng nghi vd Mdi Irudng: 33 (2014): 130-138 Budc 1: Xdc dinh tap nln U Ujn cdc gid ^ f^ la dilm giOa cua doan U,).
tri hch su cua chuoi thdi •' ' •*
g i a n : t / - [ f l ^ - Z ) i ; D , ^ + i J 2 ] , t r o n g ddD„,„, Ngio;en tdc 2: ^iu 4 la gid tri md hda t?i tiidi D^ lin lupt la gid tri ldn nhit va nhd nhit cua ^ilm / va cd nhdm moi quan be md Id chudi dii li^u, A , Dili cac sd duang thich hpp A-^ Af,A.,A,,... toi gia ui dy bao tai todi diem dupe cbpn. J K I
t +1 Id trung binh cdng cua Bu&c 2: Chia tap U thdnh timg doan thich hpp ™ ™ ™
vd deu nhauf/,,t/j,...,t/„. Xac dinh cdc tap md ' (my,m^,m^,...la diem giiia eOa 4 tuong umg vdi C/j.Neu A, Id gia tri md hda tai doan U :,U,,U,,...).
todi dilm / vd A la gia tri md hda tai thdi dilm /
.. , . , Nguyen tSc 3: Neu A; la gia tri md hda tai todi + 1 toi ta CO moi quan he raa , - *
A -^ A ii i = } 2 ^ diem / va khdng tdn tai moi quan h? md nao tiii gid Ui dy bao tai thdi dilm / +1 la m^- ( mj la dilm Budc 3: Xac dinh eae nhdm quan he md.
giiia ciia do^n U^).
Budc cuoi cimg ciia timg md hinh dupe dl nghi
ey thi sau: 2.3.2 Mo hinh cua Singh
2.3.1 Mo hinh cua Chen ^^. ^ ^ —^ ^ . j ^^^ j , ^ ^^ ^-^ pj^x^ ^^^^^
Nguyinlac l:Neu A^ la gia tri mo hoa tai th6i k+ 1 Ik A - > ^ - , diSm t va chi CO moi quan he ma duy nhat la
y ( , - > 4 thi gia tri dvr bdo tai t h « diim <+l la V o l / ! = 0,5' = 0, tinh c4c gia tri sau:
D, a R+M{A,) Q = £+2xD,, QQ, = E,-lxD G, = E.+-i-,aG: = E,—^,fl,=£,+3xQ,Hff, = £ . - 3 x a ; F , . = 1-
' ' ' ' ' ' 6 ' ' 6 ' ' I I I I J ^ ^ j
Trong d6 £,-, £,_,, E._.^ lin lupt la gia trj tai diem ( + 1.
thoi diem (, r -1, r - 2; A,, A, ijn luot la gia tri mo ^^' "^ ^ ''° '^ "8"y=n <Sc mo h6a du lieu J • • nhir sau:
t?i thoi diim^r, r +1 ,- Fj la gid trj du bao tgi thoi
Xj!iUj^R = R + Xj,S = S + \;XX.sUj^R = R+XXj,S = S + \;Yi<iUj^R^R + Y^,S = S + l;
ry.eUj=>R = R+Yr^,S = S+l;PisUj=iR = R+Pi,S = S + l;PPieUj^R = R+PPj,S = S + i;
QlsUj=>R = R + Q^,S = S + l;QgjiEUj^R = R+QQj.S = S + \;GieUj=>R=R+Ci,S = S + l;
aG^eUj^R=R+<JG/,S = S+l;H^£Uj^R = R+Hj.S = S+l;HHisUj^R = R+HHi,S = S+l
2.3.3 Mo hinh Heuristic x = X(l)-X(l-l). Niu x>0 thi Ta c6 gia trj m6F(0c6 nh6m quan hS Pi>P2'—'Plc^J' ngirgc lai neu x < 0 thi i\\(lAj-¥ Ap,A^,A,.,As,...wk ham Heuristic p^.p^.-^Pi^^ j • Khi dd, niu x>D t y
hU;Ap.A^,A„A„...) = Ap^.Ap.^,...,Ap^^ vdd -^y^-^ppV V ™
Tgp chi Khoa hoc Trudng Dgi hgc Cdn Tiia Pl,P2'-'Pjc >y,ngux:<Otili
Phdn A: Khoa hgc Tu nhien, Cdng nghi vd Mdi Irudng: 33 (2014): 130-138 chudi de lieu.
Budc 2: Chia tap U toanh n doan todi gian ed
•Pk-J- Nguyen tac md hda du li?u tuang ty md hinh eiia Chen.
2.3.4 Mo hinh ciia Abbasov -Mamedova im 6 budc Md hinh chuoi todi gian rad nay nhu sau:
Budc 1: Xdc dinh tiip nen U chiia doan todi gian gi&a cac bien ddi nhd nhat va ldn nhat Uong
dp ddi bang nhau chiia cdc gia tri bien ddi tuong ling vdi ly le tang trudng khae nhau cua dan sd.
Ddng thdi tinh cac gid Uj trung bmh cua tiing doan
(w^,/-l,...,HJ.
Buac 3: Md ta chat luong ciia cac gia Ui bien ddi dan sd nhu la mpt biSn ngdn ngu, xac dinh cdc gia tti tuang iing ciia bien ngdn ngir hoac toiet lap cac tap md F{1):
"4 (u.)/u,yiSU,^^40,l], Mj.{ui)-
1Trong dd A' Id md hda cac bien cua nam /; C la hing sd ty chpn sao cho //< (w,) e [o, l ] ; U la cae biln ddi ciia timg nam, hoac la gid tri trung binh; w^^ '^ S'^ ^ri Uung binh cua timg d o ^ thii i.
Budc 4; Md hda eae dii li^u ddu vao hoac chuySn ddi cac gia tti sd vao cdc gia Ui md. Hoai ddng nay cho phep phan aito sy tuang iing gia trj dinh lupng hay dinh tinh cua ty le phat Uien ddn sd tifiu biSu ti-ong gid tt; ciia ham quan h^.
Budc 5: Lya chpn toam sd w(l < w< ny,n la sd nam ciia dii lieu ban dau tuong iing vdi doan
^{t) = \ max(^R^ ll'-"21'- ttong dd i = l,...,W,J-l,.
^(-^12'-^^2
Sucre 6: Giii md kit qua thu duoc hoac chuyen doi cdc gid tri md vdo cdc gia trj dinh tinh. Dy bao cho nam tdi Vif):
v(t). h"'^
lA"')
Ket qua dy bdo cho nSm thd t dupe tfnh theo cdng toiicA'(() = A^((-l) + K(;).Uong do N{l) la dan so ciia nam t, V{i) la sd ddn toay ddi tir nam t - 1 den nam t.
3 TONG QUAN VIIEC THlTC HIEN 3.1 NguSn so li^u
Bai vilt sii dung sd ligu cda qua khii tir Uang web cua T6ng eye toing kg 12/2012. Cu toi sd li§u dupe cho bdi cdc bdng sau:
{cx(l7-4)]
todi gian trudc khi sang nSm cd liSn quan, tinh toan cac mdi quan hfimd cda ma ttdn/'"'(r).
Hay
R{t) = 0'"{t)l>K(t)-
]nK{,)[j\
" 1 1 "-11
hi "21
" l y
•,Rn)-""-^[hj'hr-^ii)\
B a n g 1: D d n so ca nud'c giai d o a n 1975 - 2 0 1 1 Nam
1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
S6dSn 47.6 49.2 504 51.4 52.5 53.8 54.9 56.2 57.4 58.8 59.9 61.1
Nam 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
So din 62.5 63.7 64.8 66.2 67.8 69.4 71.0 72.5 74.0 73.2 74.3 75.5
Nam 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
So dan 76.6 77.9 78.9 79.7 80.9 82.0 83.1 84.1 84.221 85.122 86.024 86.928 87.840 (Sd liiu Bang 1, ciing nhu trong bdi hdo ndy dugc tinh dan vi Id trieu nguoi.)
Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tho Phdn A. Khoa hgc Tv nhiin. Cdng nghi vd Mdi Irudng: 33(2014): 130-138
3.2 Phmmg ph^p thuc hien
Su dung cdc md hirto hdi quy, cbu5i todi gian Uen dii Heu gdc va du lieu md boa dl dy bdo tdng sd ddn. Cu the:
i) Sii dung so li^u Bdng I, eae md hinh hdi quy ttong phin 2.1, xay dyng cac md hinh hdi quy cu toi. Diing cdc tieu chudn ddnh ^ a khdc nhau dl lua chpn md hinh hdi quy phu hpp nhat.
ii) Sii dung dO lieu goc, phuong phdp Box- Jenkins xdc djnh cae md hinh chudi thdi gian khdng md AR(p\ MAiq), ARIMA(p.d.q) cd thi cd.
Dya vdo tieu chuin AIC de lya chpn md hlnli chudi todi gian tdt nhat.
iii) Md hda dO lieu gdc bing eae md hinh ciia Chen, Singh, Huamg, Chen-Hsu. Sau khi lya chpn duac md hinh co chi sd MSE nhd nhit, chiing ta cung sir dung phuong phap nhu da 1dm Uong ii) de tim md hinh phd hpp nhdt.
iv) Sil dung md hinh chudi thdi gian rad Abbasov-Mamedova cho vigc dy bdo tir dii lieu gde.
v) Lya chpn mfl hinh cd chi sd AIC nhd nhat tir i), ii), iii) va iv) dl 1dm md hinh tdi uu nhat.
Vdi md hinh da chpn, tien hdnh dy bao dan so Viet Nam din nam 2020. Viec xii \j dupe toye hien bing phin mim todng ke R.
4 KET QUA DV" BAO TONG DAN SO CUA CA NUdC
4.1 Su" dung c^e md hinh hdi quy 4.1.1 Dudng hoi quy tim dugc
Til so li^u Bang 1, cdc rad hinh (1), (2), (3), (4)
SodSn
va (5) dupe thilt ldp cy toe nbu sau:
Hoi quy tuyin tinh dan:
yi - I . I 4 h - 2 2 0 4 . 6 7 4 . Hoi quy lOy thira:
>-, =exp(33.84hi/-252.85).
Cdp so cgng:
;', =87.84[1 + 0.01092(/-2011)].
Cdp so nhdn:
y, ^87.84(l + 0.0l0977)'"'^*'^' Hdm ma bien dang.
J', =97.53824-19.91821.(0.9397109)^
4.1.2 Lua chgn dirdng hoi quy
Tir cae rad hitto da dupe xiy dyng ttong rauc
^././, ta cd bdng tdm tit kit qui tinh eic tieu chudn ddnh nhu sau:
Bang 2: Cac tieu chuin dinh gid md hinh hoi quy da xay dung
(r-2000)
H^m dir bao S? AIC SIC MSE
Tuyln tinh dan Luy tolia Cap sd cdng Cdp sd nhin MG bien dgng
0.994 134.97 138.19 0.725 0.970 191.78 195.00 1.747 0.950 25.29 26.26 0.576 0.980 18.41 19.38 0.361 0.886 73.49 74.95 4.262 Chung ta eiing cd dd thi cho cac dudng hdi quy xiy dyng v i sd lieu toye t6 nhu sau:
Luy thira
Hinh 1: Dd thi cac md hinh dy bio giai doan 1975-2011 va s6 ii^u thyc tl 134
Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tho Phdn A: Khoa hgc Tu nhien, Cdng nghi vd Moi trudng: 33 (2014): 130-138 Nhdn xet:
i) He sd xdc djnh cua cic md hlnb hdi quy xay dyng ting din theo thii ty: Mil biln dai^ —• cip sd cpng —*• cap sd nhdn —• lily thiia —^ tuyln tinh dan.
Trong do, n^oai trii md hinh mu bien dai^ ed be so xac djnh toip, cdn lai cdc md hinh khac cd he sd xic djnh cao va khdng cd sy sai lech nhieu, chiing td cac md hinh hdi quy xdy dyng cd miic phu hop khd tdt.
ii) Chi s6 AIC vi SIC eua cdc md hinh xay dyng tang ddn theo toir ty: Cap sd itodn ~* cap sd cpng —* mu bien dgng —> tuySn tinh don —»• liiy thCra. Trong dd, md hinh cdp sd cdng ed chi sd AIC vi SIC nhd nhdt nen ddy la md hinh phii hpp hon nhiing md hinh cdn lai.
iii) Sai sd tuyet ddi tnmg binh MSE cua cae md hlnb xdy dyng tang din toeo toii ty: Cip sd nhdn
—» cip sd cdng —• tuySn tinh don —» luy toiia —•
mii biln d|uig. Nhu vdy, chi sd nay cung cho ta thdy md hinh cap sd nhan Id phii hpp nhat.
iv) D6 thi phdn tdn cho dii liSu toye t£, cic dudng hdi quy da thilt l§p tir Hlnb I cbo ta tody rad hinh cap s6 nlidn khd gdn vdi gid tti toye tl.
Tir eic nhdn x6t Ufin, ta thiy ring uong cdc md hinh hdi quy xdy dyng, md hinli cdp sd nhdn la phii hpp nhit.
4.2 Phuung phip chudi thdi gian vdi dir n|u khdng md
4.2 I Cdc mo hinh dye hdo theo day so thdi gian
Tir s6 li^u Bdng 1, kilm Ua tinh dimg, dd tiu ty tuong quan (ACF) va ty tuong quan rieng (PACF), ta cd cic md hinh dy bao ed toi nhu sau:
Md brah MA: Kit qui phdn tich cho ta toiy cd mdtMA(l).
Md binli AR: Su phan tich cho ta thay khdng ton t^i.
Md hinh ARIMA: Cdc md hinh cd toe cd la AR1MA(0,2,1);ARIMA(0,2,2);
AR1MA(0,2,3);ARIMA(1,2,0);ARIMA(2,2,0);
ARIMA(3,2,0);ARIMA(1,2,1);ARIMA(1,2,2);ARI
MA(1,2,3);ARIMA(2,2,I);ARIMA(3,2,1);ARIMA (2,2,2);ARIMA(2,2,3);ARIMA(3,2,2);
ARIMA(3,2,3).
4.2.2 Lua chgn mo hinh Dung chi sd AIC de tun md nhat tit cac md hinh ed toe tten, hop sau:
Bang 3: Chi so AIC cho cac md hinh chuoi thdi gian
hirto thich hpp ta ed bang tdng
Mo hinh AR1MA(0,2,1) ARIMA(0,2,2) ARIMA(0,2,3) AR1MA(1,2,0) ARIMA(2,2,0) ARIMA(3,2,0) ARIMA(1,2,1) ARJMA(1,2,2) ARIMA(1,2,3) AR1MA(2,2,1) ARIMA(3,2,1) ARIMA(2,2,2) ARIMA(2,2,3) ARIMA(3,2,2) AR1MA(3,2,3)
AIC 46.83 48.71 50.67 56.42 55.11 56.22 48.72 50.00 52.67 50.67 52.63 51.98 53.89 53.98 55.11 So sanh eae md hinh Bdng 3, ta toay md hinh ARIMA (0,2,1) (hay MA(1)) ed ehi sd AIC nlid nhdt. Dd toi Standardized Residuals co sai so chudn t^p trung gdn gii Ui 0, dd thi ACF of Residuals cho toiy tinh phu hpp cita rad hinh. Nhu vdy, md hinh ARIMA (0,2,1) phii hpp dy bao l i
= £, - 0.8750f,_ ~-X,-2X,_ t-\ t-2 4.3 Pbuxrag phip chudi thdi gian vdi du lieu md hda
4.3.1 Ma hoa dir lieu
Tir cac nguyen tdc md hda rad hinh Chen, Sin^, Huamg va Chen-Hsu da ttinh biy ttong phin 2.3, tinh todn cho dii lieu cua Bdi^ 1 ta cd kit qui sau:
Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tha Phdn A: Khoa hgc Tv nhiin. Cdng nghi vd Mdi trudng: 33(2014): 130-138
B a n g 4 : K i t q u a m d h d a d i r l i | u m d h i n h c u a C h e n , S i n g h , H u a n i g v a C h e n - H s u giai d o ? n 1989-2011 Singh H u a r n e
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
64.8 66.2 67.8 69.4 71.0 72.5 74.0 73.2 74.3 75.5 76-6 77.9 78.9 79.7 80.9 82.0 83.1 84.1 85.171 85.122 86.024 86.928 87.840
67
-
67 70 70 73 73 76 76 76 76 79 79 79 82 82 85 85 85 85 86.5 86.5 86.5
-
67.86
-
71.50 71.04 74.50 74.04 73.85 74.32 77.50 76.67 77.87 79.61 79.76 82.80 82.31 83.13 86.50 85.30 86.02 86.24 86.90
67
-
67 70 70 73 73 74.5 76 76 76 79 79 79 82 82 85 85 85 85 86.5 86.5 86.5
- -
67.75 69.25 71.50 71.50 74.50 73.50 74.25 75.25 76.75 78.25 78.25 80.50 80.50 82.75 82.75 84.25 84.25 85.38 86.13 86.69 87.63
MSE 1.214
4.3.2 Lira chon mo hinh tie so li^u ma hoa Trong cac mo hinh a tren, ra6 hinh Chen-Hsu c6 chi so M S E nho nhat. Lay dir lieu m o hoa theo mo hmh nay, thirc hien viec dir bao bang m o hinh chuoi thoi gian nhu di^ lieu khong m d cita 4.2, ta cd bdng tdm t i t chi so A I C nhtr sau:
B i n g 5: C a c m o h i n h A R I M A C H v d i dir liEu rati hoa theo C h e n - H s u
MS hinh AJC"
A K I M A C H ( 0 A 1 ) A R I M A C H ( 0 , 2 , 2 ) A R 1 M A C H ( 0 , 2 , 3 ) A R I M A C H ( 1 , 2 , 0 ) A R I M A C H ( 2 , 2 , 0 ) A R I M A C H ( 3 , 2 , 0 ) A S 1 M A C H ( 1 , 2 , 1 ) A R 1 M A C H ( 1 , 2 , 2 ) A R I M A C H ( 1,2,3) ASIMAcn(2,2,l) A R I M A C H ( 3 , 2 , 1 ) ARIMAcu(2,2,2) A R I M A C H ( 2 , 2 , 3 ) A R 1 M A C H ( 3 , 2 , 2 ) ARlMAca(3,2,3)
60.94 55.90 57.02 56.91 55.73 57.54 53.40 55.35 57.20 55.34 57.66 57.33 54.89 56.88 60.50 So sanh cac mo hinh tren ta thay mo hinh ARlMAcH (1,2,1) cd chi sd AIC nho nhdt. Vdy md hinh thich h(ip d i d u bao la A R I M A C H ( 1 , 2 , 1 ) :
-0.6388jr , + E - 0 . 8 4 6 6 £ ,
Phirong phap chuoi thoi gian m o Abbasov- Mamedova
Su" dung cac b u d c thirc hien cOa md hinh chuoi thai gian m o A b b a s o v - M a m e d o v a v d i dtt lieu Bang 1, ta c6 bdng tinh toan sau ciing n h u sau;
B a n g 6: K e t q u a d i r b a o d a n s ^ ca nud'c giai d o j n 1 9 9 7 - 2 0 1 1 j , -
T b i r c t I D g b d o Sd J t n B i f a doi Sd d a n Bi^n J 6 i
0.352 0.791 0.828 0.787 0.S63 0.749 0.615 0.828 0.787 0.787 0.740 0.436 0.690 0.690 _ 0.619 0.347 _2M3 1997
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
74.300 75.500 76.600 77.900 78.900 79.700 80.900 82.000 83.100 84.100 84.221 85.122 86.024 86.928 87.840
1.100 1.200 1.100 1.300 1.000 0.800 1.200 1.100 1.100 1.000 0.121 0.901 0.902 0.904 0.912
73.552 75.091 76.328 77.387 78.763 79.649 80.351 81.728 82.787 83.887 84.840 84.657 85.812 86.714 87.619 MSE
AIC
Tgp chi Khoa hgc Trudng Dgi hgc Can Tha Phdn A: Khoa hgc Tu nhien. Cdng nghi vd Mdi Irudng: 33 (2014). 130-138
90 - 80 75 -
S ( o c n o ^ N c o - * i f l ( O N ( O G O T - o i < r > - * i n ( D N f f l O ) 0 O i m O l O O O O O O O O O O T - T - t - T - r - T - T - T - i - T - O J 0 ) © 0 ) O O O O O O O O O O O O O O O O O O O O O T - T - T - f M ( M ( M r M r M ( M r ' J f M f M f M N C M C I f M ( M M M M M r M ( N
"•-Thi/ctl - * - O i r bao
Hinh 2: Dan sd thyc te va dy bao bang md hinh Abbasov-Mamedova giai do^n 1997-2020 Chi sd AIC v i hinh vS tryc quan (Hinh 2) cho
ta thdy md hinh Abbasov-Mamedova cd ket qud dy bdo rit tot dan sd Viet Nam.
4.4 Dy bao
Tir cac md hinh toi uu da lya chpn trong 4.1, 4.2, 4.3 vd 4.4, ti^n hinh dy bao din so nude ta din nam 2020, ta ed bing tdng hpp sau:
Bang 7: DSn so nude ta giai doain 2012-2020 tir cac md hinh dy bio
Nam 2012 2013 2014 2015 2016 2017 2018 2Q19 2020
Abbasov-Mamedova ARIMACH(1,2,1) ARIMA(0,2,1) c i p sd nhin
88.540 89.110 89.620 88.447 89.343 90.191 88.782 89.723 90.665 88.800 89.780 90.86
90.080 90.970 91.390 91.810 92.230 92.230 91.070 91.930 92.802 93.666 94.534 95.400 91.607 92.548 93.490 94.431 95.373 96.315 91.760 93.790 94.82 95.860 96.910 96.910 Trong cdc dy bao ciia Bing 7, dya vdo ehi sd
AIC, ta thiy md hinh Abbasov-Mamedova cho mpt kit qua dy bdo tot nhdt dan sd Viet Nam.
5 KETLU4.N
Bai bao dd khio sit eic rad hlnb khac ttoau cua hdi quy, chudi todi gian md va khdng md ttong dy bdo dan sd nude ta, dua vao tieu chudn todng ke, kit ludn dupe md hinh hoan toin dua tten sy md hda dii liiu Abbasov-Mamedova cho mdt ket qud dy bdo rit tot. Ddy la-rapt ket qud dy bio tdt ma toye te iing dung khdng nhieu bd sd lifiu cd dupe.
Mdc dil, sy phdt Ui€n dan sd ciia nude ta phu toupc vdo cdc chinh sdch ve dan sd eiia nha nude trong tuong lai, phu toudc vdo sy phit triln kiito tl xd cua ddt nude, tuy nhien vdi die diem ddi tupng dy bdo khdng ddi hdi qui chinh xac, toeo chiing tdi kit qui dy bdo Uen cd to^ dupe sii dung Uong hoach dinh chinh sdch kinh tl xa hdi vT md cho eic cdp qudn li.
Cic md hinh va cdch lam nhu dS thyc hifn cho dy bdo ddn sd ca nude ttong bdi vilt niy, cd toi dupe thyc hi?n tucmg tu cho dy bao dan sd cua mot huyen, tinh hoac toanh phd cung nhu cho nhilu ung dyng khic ciia thyc te.
TAI LIEU THAM KHAO
1. A.M. Abbasov et al, 2002. F u z ^ relational model for knowledge processing and decision making. Advances in Mathematics.
1: 1991-223.
2. A.M. Abbasov and M.H. Mamedova, 2003.
Application of fiizzy time series to population forecasting, Vienna University of Technology. 12: 545-552.
3. H. Bozdogan, 2000. Akaike's information criterion and recent developments in information complexity. Joumai of matiiematical psychology. 44: 62-91.
4. K. Huamg, 2001. Huamg models of fiizzy time series for forecasting. Fuzsy Sets and Systems. 123:369-386.
5. Q. Song and B.S. Chisom, 1993. Forecasting emolhnents with fiizzy tune series (Part 1), F u z ^ Sets and Systems. 54: 1-9.
6. 6. Q. Song and B.S. Chisom, 1994.
Forecastmg enrollments with fiizzy time series (Part II), Fuzzy Sets and Systems.
62: l-8.orecasting enrollments wi.
7. S.M.Chen, 1996. Forecasting enrollments based on fiizzy time series. Fuzzy Sets and Systeras. 81: 311-319.
Tgp chi Khoa hgc Trudng Dgi hgc Can Tha Phdn A: Khoa hgc Tv nhien, Cdng nghi vd Mdi Iruang: 33 (2014). 130-138 8. S.M.ChenandC.C.Hsu,2004. ANew lO. Matoematics and Computers in
metood to forecast enrolhnents usmg fiizzy Simulation. 79: 539-554.
time series. Intemational Jomnal of Applied ^ j , 0 5 ^ g j ^ ^ ^ ^^^^ ^ computational Science and Engmeermg, 12: 234-244. ^^^^ of forecasting based on high-order 9. S.R. Singh, 2008. A computational method fuzzy time series. Expert Systems with
of forecasting based on fiizzy time series. Apphcations. 36:10551-10559.
