Tap chi Khoa hoc 2012.23b 125-134 Trircmg Dai bgc Cdn Tha
Dir BAO SAN LlTONG LUA VIET NAM BANG CAC MO HINH TOAN HOC
Vd Van Tdi'
A B S T R A C T
The article uses different models of regression and time series to forecast Vietnam's paddy output based on past data. Using statistical eriterions in making model lofiiid the most appropriate model, from there forcasting paddy output for the next five years by this model.
Keywords: Regression, time series, forecast, AIC criterion, paddy output Title: Forecasting Vietnam's paddy output by mathematical models
T O M TAT
Bdi bdo sir dung cdc md hinh khde nhau cua hdi quy vd chudi thai gian de dir bdo sdn lutmg Itia cua Viet Xam dua tren ede sd lieu cua qud khir. Sir dung ede lieu chudn eiia thdng ke trong lya chgn mo hinh de tim md hinh thich hgp nhdt. lir do tiin hdnh dir hdo sdn lirgng Ida cho 5 nam tiep theo bang md hinh ndy.
Tir khoa: Hdi quy, chudi thai gian, dur bdo, tiiu chuan AIC, san lirgng lua 1 TONGQL.AN
1.1 T i n b hinh va y nghfa cua viec du* bao san lircmg lua ciia nvcrc ta Trong xu hudng hgi nhap qudc te hien nay. nhu ciu ve thdng tin thi trudng tai mot thdi diem nao dd frong tuang Iai la rat can thiet. N h i nudc ta da thiy rd y nghta to Idn cua du bao ddi vdi su phit frien kinh x€ x i hdi ciia dat nudc, do dd da cd nhieu quan tam den cdng tic nay frong nhinig nam gin di\'. Nhieu c a quan chuyen frach va ban chu\"en trach ve du bao d i dugc thanh lap d cip Bd. tinh va thanh phd. Tuy nhien, theo danh gia cdng tac du bao cua nudc ta cdn rat non kem \'a ban che nhieu m i t , chua dap ung dugc nhu ciu ciia sy phat trien kinh te ciia dit nudc hien nay.
Ngu\ en nhan ciia thuc frang nay thi nhidu. nhung cd the chi ra mdt sd nguyen nhin chinh sau: Su thieu hut nghiem frgng nhin lyc frong Iinh vyc du bao; cac sd lieu tdng hgp cho d y bio khdng day dii \ a khdng chinh xac; cac co quan don vi d dia phuang cdn xem nhe cdng tac dy bao; thieu phuang tien ky thuat. kinh phi cho dy bao: ...
Dy bao san Iugng liia la mdt frong nhiing \ iec cin thiet cho viec phat frien nganh kinh t l ndng nghiep hing diu ciia nudc ta. Khi chiing ta dy doan dugc san Iugng Ilia d tuang Iai tang hay giam so vdi hien tai, khi dd chiing ta se cd cac chinh sich tac ddng mdt each kip thdi va diing liic den cac bd phan Hen quan. Dd la cac chinh sach lien quan d i n dit frdng Iiia. thiiy lgi. ndng din. tu dd inh hudng den viec quy hoach cum cdng nghiep, d i n cu va nhieu v i n de kinh te x i hgi khac. Dy bio dugc san Iugng liia se giiip cho hiep hdi luang thyc (VFA) tham muu cho nha nudc frong viec dam bao an ninh lucmg thuc frong nudc. dieu hinh ke hoach xuit khau mang lai Iai ich cao nhit cho ngudi ndng dan va doanh nghiep. Hien nay Bd ndng ' Khoa KJioa hpc Ty nhieu. Tnitmg Dgi hoc Can Tha
Tap chi Kboa hoc 20I2-23b 125-134 Tru&ng Dgi hgc Cdn Tha
nghiep & Phat triln Ndng thdn dang chi dao cac ca quan chuyen trach lap k l hoach tdng thi phit friln cic loai cay trong chinh ciia nudc ta, frong do Iiia dugc xem la ciy quan frgng nhit. D I lap dugc k l hoach niy, dieu cin thiet la phai cd dugc dy bio cho san Iugng Iiia. Dy bio sin Iugng Iiia cang cd y nghia quan frgng frong dilu kien nudc ta nim trong vung chiu inh hudng nghiem frgng cua bien ddi khi hiu.
1.2 Ngu^n s6 lieu
Dk dy bao sin Iugng lua ciia nudc ta, chiing tdi su dung dfl- lieu cua qui khu tir nim 1990 den nam 2010 (21 nim). Sd lieu nay dugc Iiy tir trang web cua Tdng cue Thdng kS va Bd ndng nghiep Phat frien Ndng thdn ngay I/1/20I2. Cu the sd lieu dugc cho bdi bing sau:
Bang ]: Th6ng kS san lirang lua ca Nam
1990 I99I 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Ca oSm 19225.1 19621.9 21590.4 22836.5 23528.2 24963.7 26396.7 27523.9 29145.5 31393.8 32529.5 32108.4 34447.2 34568.8 36148.9 35832.9 35849.5 35942.7 38729.8 38950.2 39988.9
niro^c tir nam 1990-2010 San lirong Dong xuan
7865.6 6788.3 9156.3 9035.6 10508.5 10736.6 12209.5 13310.3 13559.5 14103.0 15571.2 15474.4 16719.6 16822.7 17078.0 17331.6 17588.2 17024.1 18326.9 18695.8 19218.1 So lieu cua bang 1 dugc ve thanh bilu d6 cpt nhu
axcno
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Hi thu 4090.5 4715.8 4907.2 5633.1 5679.4 6500.8 6878.5 6637.8 7522.6 8758.3 8625.0 8328.4 9188.7 9400.8 10430.9 10436.2 9693.9 10140.8 11395.7 11212.2 11595.7 sau:
1 1 1 1
I I LL
i^Llhlihlii, iFiiiniiiiiiitiiiii
|QCSn*nnUsffingxi^DLj^r>fetlajDLijam:B|
Liia mua 7269.0 8117.8 7526.9 8167.8 7340.3 7726.3 7308.7 7575.8 8063.4 8532.5 8333.3 8305.6 8538.9 8345.3 8640.0 8065.1 8567.4 8777.8 9007.2 9042.2 9175.1
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Tap chi Khoa hgc 2012-23b 125-134 Trudng Dgi hgc Cdn Tha
1 3 Phu-cmg phap thvc bien
Su dung sd lieu tir bang I, chiing tdi tien hinh dy bao san Iugng Iiia nudc ta b i n g hai phucmg phip: Md hinh hdi quy va chudi thdi gian.
Mo hinh hdi quy: Su dung cic md hinh hdi quy d i biet cho viec dy bao nhu: da thuc (vdi nhieu bic khic nhau). c i p sd cdng. c i p sd nhan va ham mii bien dang.
D y bao sin Iugng Iiia cho vu miia, ddng xuin, he thu va ca nam vdi tat ca cic md hinh nay, sau dd dya vao mgt sd tieu chuin cua thdng ke nhu he sd xac dinh P^, thdng tin Akaiken (AIC), thdng tin Schwarzn {SIC), sai sd trung binh {ME), do thi phan tan de dinh gia sy phu hgp ciia md hinh, tu dd lya chpn dudng hdi quy phu hgp nhat. Md hinh hdi quy da thuc dugc khao sat, nhung vdi du lieu thu dugc cac md hinh nay khdng phii hgp. do dd chiing tdi khdng trinh bay frong bii viet nay.
Mo hinh chudi thai gian: Sir dung cac md hinh dy bao frong chudi thdi gian nhu:
Md hinh ty hdi qui {AR), md hinh trung binh di ddng {Mi), md hinh ty hdi qui va trung binh di ddng {ARMA). md hinh trung binh di ddng tdng hgp vdi tu hdi qui {ARIMA). Dy bao san Iugng Iiia cho cic vu va ca nam. sau dd ta diing tieu chuin {AIC) de danh gia md hinh nio phii hgp nhit.
Sau khi lua chgn dugc 2 md hinh phii hgp nhat tu hai phuang phap fren, chiing ta tiep tuc sir dung tieu chuin AIC de cd dugc md hinh phii hgp han. Sir dung md hinh n i y de dy bao cho sin Iugng liia timg nam tir 2011 - 2 0 1 5 .
Viec phin tich va xa\ dyng cic md hinh hdi quy va chudi thdi gian dugc thyc hien tren phin mem thdng kd R.
2 CAC MO HINH DlTBAO SAN LUONG LUA 2.1 Mo hinh hoi quy
Ggi / la nam ung vdi san lugng Ilia dy bao jv, cac md hinh hdi quy dugc sir dung trong nghien cuu nay la
Hdi qu>' tuyen tinh:
y,^a + bt ( 1 ) Hdi quy da thiic bac n:
Him c i p sd cdng:
Ham cap sd nhin:
!•, =Oo -ha^l-¥a.J- +.... +a„t" ( 2 )
.''2010 (l+r,)-" (4)
Trong mo hinh (3) va (4) thi M la Ichoang thoi gian til nam dir bao den nam dupe chon lam gdc (2010); r,. r2 ISn lugt la t6c do tang san lupng liia hSng nam cua mo h i n h ( 3 ) v a ( 4 ) . C u t h e
^ hi(v.„i„)-lnCv,^) ^ ^ ij-;„i.
' 2010-1990 ' = \yi^
Tgp chi Kboa hoc 2012.23b 125-134 '^"'^ '"'' ^'^ ^ « ' ' ^'"^
Ham mubiendang: y, = a + 6c', ^ ' c la cac tham sd dugc udc lugng tir cac ;
( ( - 2010) vdi t la thdi gian can du bao.
Trong dd _ . . . . - u - ^ , a. b, c la cac tham sd dugc udc lugng tu cac so heu da biet
5
2.2 Mo hinh chuoi thoi gian
a) Mo hmh lir hdi qui bgep (AR(p)) dang:
Trong dd ^, la cic he sd udc lugng ciia md hinh, u, la sd hang dam b i o tinh nhilu tring.
b) Md hinh trung binh di dgng hge q {MA{q)) dang:
Trong dd p, cung la cac he sd udc lugng ciia md hinh va u, gidng nhu trong (6).
c) Mo hinh tu hdi qui vd trung binh di dong {ARMA{p,q))
Ket hgp md hinh ARip) vdi md hinh MA{q) ta cd md hinh ARMA{p,q). Md hinh nay cd dang nhu sau:
y, =$^^^^y,.^-^^.y,_.^...^^py,^p^u,+ p,u,_^ ^p2"<-2 ^ - + A,"i-,- (8) Mdt qua trinh ARMA(p,q) se cd qui frinh ty hdi quy bac p va qua frinh trung binh di dgng bac q.
d) Mo hmh trung binh di dgng long hop vai tu hoi qui ARIMA(p,d,q) Phuang frinh khai quat ciia md \i\nh ARIMA{p.d,q) dugc trinh bay dudi dang sau:
y, =d + a,y,_, +a.y,^. ^ ...^a^y,_^-v ^ +e,_, -r...^/3^e,_^ +e, (9) Trong do a Ii tham sd ty hdi quy; E la tham sd trung binh di ddng;
S = p{f3y + P-S+... + Pg); /4 la gii tri frung binh cCia chudi thdi gian; e, la sai sd dy bao {e, = y, -y, = s6 Heu dy bio - sd lieu thyc te).
2.3 Tieu chuan danh gia mo hinh
Hien nay cd rit nhieu tieu chuin khac nhau de dinh g i i miic do phu hgp ciia cic md hinh hdi quy va chuoi thdi gian da xiy dyng. Cd nhieu nghien cuu vl van de nay. nhung khdng the khing dinh dugc tieu chuin nao tot han. Trong bai vilt nay chiing tdi su dung cic tieu chuin sau de so sanh cac md hinh vdi nhau. Day Ii nhung tieu chuan phd bien, dugc tinh frong h i u h i t trong cac phin mim thdng ke.
a) He sd xde dinh:
f^iy.-y,y-
R'^^^ , (10)
Tiy.-yy-
Tap chi Khoa hoc 2012:23b 125-134 Tnr&ng Dgi hgc Cdn Tha
frong do 1, va y, lin lugt la gia fri thyc te va gia tri dy bao ciia md hinh hdi quy
•thi bien x nhin gia fri x,; y la trung binh ciia cic y,, i - 1,2,..., u.
Ic Ii mgt tham sd do su phu hgp cua md hinh hdi quy. Ta co 0<R' <:\, R'cang lon thi md hinh hdi quy d i xiy dyng dugc xem l i cang phii hgp. cang cd y nghta frong viec giai thich sy biln thien ciia y thdng qua sy biln thien cua x.
b) Tieu chudn thong tin Akaiken {AIC):
AIC=e-"- — , ( I I ) n
Trong dd k l i sd bien udc lugng (bao gdm ca he sd chin), n la sd m i u quan sat, 5'S£' = ^ ( y ^ - j ) ) - v d i y, v a y , gidng frong cdng thuc (10).
'=1
AIC la cdng cu phat hien sai sdt khit khe hem R- khi ting them biln ddc lip. Khi so sanh hai hay nhilu md hinh. md hinh nao cd AIC thip nhit thi md hinh dd sg tdt han.
c) Tieu chudn thong tin Schwann {SIC):
SIC=n.\n(^]-i-k. (12)
Trong do 55ft = ^ (i, - y)" vdi y va y, gidng frong cdng thiJc (10). Gia tn SIC cang nhd thi md hinh cing tdt.
d) Do thj phdn ldn:
Dd thi phan tin chi dugc ap dung frong trudng hgp hai bien. Tir sd lieu thyc te chiing ta v6 dd thi phan tan, tir sd lieu dy bao chiing ta ve dugc cic dudng dy bio.
Cac cham dai dien cho cic cap quan sit dugc phin tan ngau nhien, neu cac chim gan nhu t i p trung quanh dudng thing tuc mdi Hen he niy gin nhu tuyen tinh. Nhin vao dd thi. quan sat thay dudng dy bao nao gin vdi sd lieu thyc td thi chiing ta cd the chgn md hinh dd 6i dy bao.
e) Sai so ti-ung binh:
.\lE = -±\y,~y,. (13)
U 1=1
Trong dd.v,vi y, dugc xac dinh gidng nhu (10). ME cing nhd thi md hinh xay dyng cang phii hgp.
3 K E T Q U A D i r BAO T 6 N G SAN LlTONG LUA CUA CA NAM 3.1 S v d u n ^ cac mo binh hoi quy
a) Dirang hoi quy tim dtrgc
Tir sd lieu bing 1, chiing ta tinh dugc cac dudng hdi quy dy bao theo (1), (2), (3), (4) v i (5) cho sin Iugng Iiia ca nam cu the nhu sau:
Hdi quy tuyln tinh: y, = -2073842 + 1052.20/.
Trong do / la nam cin dy bao.
Ham c i p sd cdng:y, = 39988.9[(1 + 0.036619(/ - 2010)].
Tap chi Khoa hgc 2012236 125-134 Trudng Dgi hoc Cdn Tho
Ham cip sd nhin; v, = 39988.9(1 + 0.037298)'-'°"'. „ Ham mu biln dang: y, = 34788.92837 + 154.89497(1.598242;
Trong dd / = - ( / - 2 0 1 0 ) vdi Ma nam can dy bao.
b) Lira chgn duang hdi quy
i) Do thi phan tin ciia sd lieu va dd thi cua cic md hinh hdi quy dy bao dugc xac dinh bdi cac ham tren, dugc ve nhu sau:
T990 1995 2000 200S 2010 Nam
Hinh 2: fta thj phSn tan gia trj thirc te va 4 mo hinh hoi quy dir bao san lirong lua Hinh 2 cho ta thiy md hinh hdi quy tuyln tinh cd cic gia tri dy b i o g i n dung vdi gia tri thyc te nhit.
ii) Chiing ta ciing cd cac tieu chuin danh gii md hinh hdi quy da xay dyng cu the nhu sau:
Bang 2: Tong h ^ p cac tieu chuan danh gia mo binh cfao san lirgng Ilia ca n M6 hinh
Tuyen tinh CSp so cong Cap so nhan Ham mu bien dang
AIC 371.9016 391.9792 373.5087 399.0357
SIC 369.9016 389.9792 372.5087 397.0357
ME 899.2762 5193.9059 2155.9093 5707.8057 Bing 2 cho ta thay tit cic chi sd danh gii sy phu hgp ciia md hinh hdi quy tuyen tinh tdt han cac md hinh cdn Iai.
Tu cac phin tich fren ta thay frong cac md hinh hdi quy dy bao san Iugng liia c i nim. hdi quy tuyen tinh la pbii hgp nhit.
3.2 Phironag phap chuoi thoi gian
Vdi sd lieu bing 1. kiem fra tinh dimg ta thiy nd dugc thi hien rd nhit d sai phin bic 2.
Tqp cbi Khoa hoc 2012.23b 125-134 Tru&ng Dgi hgc Cdn Thcr
Hinh 3: Sai phau bSc 2 ciia san Iinjmg liia
Ta ciing cd ham ty tucmg quan {ACF) va ty tuang quan rieng {PACF) dugc cho bdi cac hinh ve sau:
-XVT-
Hinfa 4: Ham ACF sai p h a n bac 2 cua s i n lircrng lua ca niro'c
_ L 1
I ' l l !
Hinh 5: Ham P.4CFsai phan bac 2 ciia san lirffng iiia ca nirdc a) Cde md hinh du bdo theo day so thdi gian
Qua phin tich tir sd lieu. Idem tra tinh dimg. dd thi ACF v i PACF. ta cd cac md hinh dy bao cd the nhu sau:
Dir bdo bang mo hinh binh qudn di dgng {Mi): Ket qua phin tich cho ta thay cd mgt 3Z^ cap 1. hay tdn t a i M 4 ( l ) .
• Dir bdo vai md hinh tu hdi quy {AR): Sy phin tich ciing cho ta thiy tdn tai md hinh c i p 1 cua md hinh nay {AR{ I)).
Dtr bdo vai mo hinh ARIMA bang phuang phdp Box-Jenkins:
Cac md hinh cd thi cd la: ARBU{\.2.\). ARIMA{2.2.\),AR1MA{\.2.2).
ARIMA{ 1.2,3), ARIMA{2.2.2). ARIMA{223). ARIMA{3.2,1). ARIMA{3.2.2).
131
Tap chi Khoa hpc 2012:23b 125-134 Trucmg Dal hpc Can Tho
b) Lua chon mo hinh
Dung tham s6 AIC ii tim mo hinh thich hop nhdt tir cac mo hinh ton tai tren, ta c bang tong hgp nhu sau;
Bang 3: Gia tri .4/C ctia 10 mo hinh dybao
Mo hinh AIC
MAm ARm AR1UA(\.2.\) AR1MA(2.2.]-) ARIMA(\.2.2) ARJMA{1.2.3) ARJMA{2.2.2) ARI.IM(2.2.3) ARIMA(3.2.\) ARIMAQ.2.2)
372.8700 414.1900 320.7702 322.7702 321.9521 323.6193 323.7266 325.5603 324.1348 325.2461
So sanh AJC ciia cac mo hinh tren ta thay AIC cua mo hinh ARIAm\.2,l) nho nhat. Vay mo hinh chuoi thai gian thich hgp nhAt de du doan san lugng lua ca nam l a m 6 h i n h . 4 R « « ( 1 . 2 . 1 ) .
3.3 Du- b^o san lirffng lua giai doan 2011 - 2015
Tu cac phan tich tren, ta thSy Ichi sti dung mo hinh hoi quy thi mo hinh h6i quy tuy^n tinh la phCi hgp nhat. Neu sur dung mo hinh chuoi thai gian thi mo hinh phu hgp nhSt la md hinh ARIMA(] ,2-^)- KSt qua dir bao bang hai mo hinh nay cho giai doan 2011 - 2 0 1 5 cu the trong bang sau:
Bang 4: Dir biio san Iir^g liia ca nuvc giai doan 2021-2015 bing hoi quy tuyen tinh va ARlMA(ia,l)
Nita
Tuyeo tinh
San lirong (nghin tan) ARIMAliq,!) 2011
2012 2013 2014 2015
42112.09 43164.28 44216.47 45268.66 46320.85
40893.40 41838.30 42771.04 43707.45 44642.75 Trong 2 mo hinh tren. yl/C ctia hoi quy tuyan tinh (371.9016) cao ban y4/C ctia mo hinh ARIMA( 1.2.1) (320.7702). Nhu vay sil dung ARIMA( 1.2.1) de dtr bao cho san iugng Ilia ca nuac se cho ket qua phii hgp hon.
Hinh 6: Do thi du bao san luBug lua ca nuffc biing ino hinb ARIMA{\,2,i)
Tap chi Kboa hgc 2012-23b 125-134 Tru&ng Dgi hgc Cdn Tha
4 KIET QUA DlT BAO CHO TlTNGVU LUA TRONG NAM
Thyc hien viec dy bao sin Iugng Iiia vy ddng xuin. he thu va liia miia theo hai md hinh hdi quy va chudi thdi gian theo each Iim tucmg ty nhu dy bio san lugng lua ca nam di frinh bay d fren, ta cd ket qua dugc cho bdi bing tdng hgp sau:
B a n g S: C a c m o hinh hoi q a y va chnoi thoi gian d v bao cung cac gia tri AIC cho 3 vu Ilia trong nam
Vu Ilia D6ng xuSn
He thu Lua miia
Hoi Mo hinfa Tuyen tinh Tuyen tinh Tuyen tinh
M3 hinh dir bao qny
AIC 348.410 328.190 263.201
pfaii h9P nfaat Cfaudi thcri M6 fainh AR1MA(1,2,\) AIUMA{1.1,3) ARIMAO.i,^)
aian AIC 307.398 314.150 295.719
20100.73 11862.65 9167.61
20509.52 12076.37 9099.67
20987.66 12285.50 9161.41
21410.27 12490,14 9105.29 Sir dung mo hinh phii hgp nhat tir bang 5 (m6 hinh ARIMA(\,2,^) cho vu dong xiian, mo hmh ARIMA(.\,1,3) cho vu he thu, mo hmh/1/UAM(I,1,1) cho vu miia) de dtr bao san iugng lua giai doan 2011 — 2015 cho timg vu ta co ket qua cu the dugc tong hgp nhu sau:
Bang 5: Ket q u a d u biio san luong lua giai doan 2011-2015 cho 3 vu lua
V u l l i a 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 D o n g x u a n 19605.34
H e thu 11806.08 L u a miia 9 0 9 2 . 8 6
5 MOT S 6 NH4.N XET
Trong hai phuong phap du bao cho san lugng lua cua vu dong xuan. he thu. Iua mtia va ca n3m. phugng phap chuoi thai gian luon co ket qua du bao phu hgp han.
Trong cac mfi hinh chu6i thai gian thi mo hinh ARIMA lufin la su Iua chgn tot nhat.
Trong cac du bao san lugng lua ciia cac vu miia va ca nam, vu dfing xuan dugc danh gia sg cho co kk qua phii hgp nhk, vu he thu se cho ket qua thieu chac chan nhdt. Difiu nay co th^ dugc giai thich boi vu dong xuan it chiu anh huong cua thai tidt, sau hai, dien tich gieo xa lufin a mirc fin dinh- trong khi vu he thu thi nhimg ySu tfi nay thi ngugc lai. Hien tai tren trang web cua Bg Nfing nghiep va Phat tridn Nong thfin chua co sfi lieu chinh thirc vd san lugng Iiia nam 2011. nhimg theo danh gia so bg tai cugc hgp thang 2/2012 san Iugng nay uoc khoang 41 nghin tin. trong do vu dfing xuan khoang 19.6 trieu tin, he thu khoang 12.3 trieu tin va vu miia khoang 9.1 trieu tin. Cac ket qua du bao nam 2011 tir bang 4 va 5 chung minh nhiing nhan xet tren va cung cho thiy kdt qua du bao ngjn ban 6 trdn co thd chip nhan dugc.
Du bao san lugng lua that rit kho dd co dugc kit qua chinh xac cao bai vi nfi khong nhimg phu thugc vao thai tidt, thiiy van. djch hai ma con phu thugc vao cac chfnh sach vd cay Ilia, tfic do cong nghiep, do thi hoa cua dia phugng va chinh phu.
phu thufic vac ky thuat canh tac, su phat trien cua cac tidn bg ciia khoa hoc ky thuat phuc vu nfing nghiep trong tucmg lai. Tuy nhien. sit dung mfi hinh hfii quy, chuoi thai gian trong du bao san lugng Iua la mgt kdnh du bao quan trong dd tham
Tgp chi Khoa hgc 2012 23b 125.-134 Truang Dai hgc Cdn Tha
khao frong cic quy hoach phat tri^n. Ddi vdi phuang p h i p hdi q u \ . neu cd them dugc dir lieu cho cac bidn khac anh hudng den s i n lugng Ilia thi viec d y b i o se cho k^t q u i chinh xic hem. Hien tai, hai phuong p h i p nay ciing dugc sir dyng phd bien de dy b i o n g i n han cho nhieu linh vyc k h i c .
TAJ L I E U T H A M K H A O Dang Hiing Thing (1999). Thdng kevd ung dung.'Hyb Giaa Auc.
Hamparsum Bozdogan, 2000. Akaike's Infomiation Criterion and Recent Developments in Hoang Trong, Chu Nguyin Mong Himg, 2008. Thong ke irng dung Irong kinh te xd hoi. Nxb
Infomiation Complexitj', Journal of malheniaiical psychology, 44. pp. 62-91.
Ngujen Quang Dong. Nguyin Khac Minh, 1998. Kmh Iilugng. Nxb Khoa hpc Ky thuat.
Nguyen V5n Tuin. 2002. Phdn mim R, Nxb Klioa hpc Ky thuat.
Thong ke.
To Van Ban, 2010. Xdc sudi ihong ke, Nxb Giao due
