Bai Giang Phan Tich DL Va Du Bao KT.

KHOA CNG NGH THNG TINB MN HTTT KINH T=========== NGUYN TH THANH HUYNTh.s NGUYN VN HUNV XUN NAMPHN TCH V D BO KINH TThi Nguyn, 20092Mc lcChng 1: TNG QUAN V PHN TCH V D BO KINH T .......................... 5 1.1. Khi nim............................................................................................................. 5 1.2. ngha v vai tr ca phn tch v d bo trong qu trnh ra quyt nh kinh doanh........................................................................................................................... 5 1.2.1. ngha......................................................................................................... 5 1.2.2. Vai tr ............................................................................................................ 6 1.3. Cc loi d bo .................................................................................................... 6 1.3.1. Cn c vo di thi gian d bo:.............................................................. 6 1.3.2. Da vo cc phng php d bo: ............................................................... 7 1.3.3. Cn c vo ni dung (i tng d bo)....................................................... 7 1.4. Cc phng php d bo..................................................................................... 9 1.4.1. Phng php d bo nh tnh ...................................................................... 9 1.4.1.1. Ly kin ca ban iu hnh................................................................91.4.1.2. Ly kin ca ngi bn hng.............................................................91.4.1.3. Phng php chuyn gia (Delphi).........................................................91.4.1.4. Phng php iu tra ngi tiu dng................................................101.4.2. Phng php d bo nh lng ................................................................. 10 1.4.2.1. D bo ngn hn..................................................................................111.4.2.2. D bo di hn....................................................................................161.5. Quy trnh d bo ................................................................................................ 24 Chng 2: CC PHNG PHP PHN TCH V D BO................................. 28 2.1. D bo t cc mc bnh qun ....................................................................... 28 2.1.1. D bo t s bnh qun trt (di ng) ....................................................... 28 2.1.2. M hnh d bo da vo lng tng (gim) tuyt i bnh qun ................ 29 2.1.3. M hnh d bo da vo tc pht trin bnh qun .................................. 30 2.2. M hnh d bo theo phng trnh hi quy (d bo da vo xu th) ................ 32 2.2.1. M hnh hi quy theo thi gian.................................................................. 33 2.2.2. M hnh hi quy gia cc tiu thc ............................................................. 36 2.3. D bo da vo hm xu th v bin ng thi v............................................. 36 2.3.1. D bo vo m hnh cng........................................................................... 37 2.3.2. D bo da vo m hnh nhn .................................................................... 38 2.4. D bo theo phng php san bng m............................................................ 42 2.4.1. M hnh n gin ( phng php san bng m n gin).......................... 42 2.4.2. M hnh xu th tuyn tnh v khng c bin ng thi v ( M hnh san m Holt Winters) ...................................................................................................... 46 2.4.3. M hnh xu th tuyn tnh v bin ng thi v ......................................... 48 2.5. S dng chng trnh SPSS d bo theo cc m hnh ................................. 51 2.5.1. D on bng hm xu th............................................................................ 51 32.5.2. D on bng san bng m ......................................................................... 52 Chng 3: PHNG PHP HI QUY N V HI QUY BI V THNG K HI QUY ..................................................................................................................... 53 3.1. Phng php hi quy n ................................................................................. 53 3.2. Phng php hi quy bi: ................................................................................. 61 3.3. Phng php thng k hi quy.......................................................................... 62 Chng 4: PHNG PHP BOX - JENKINS (ARIMA) .......................................... 68 4.1. Tnh n nh ca mt chui.............................................................................. 68 4.2. Hm s t tng quan n v t tng quan ring phn................................. 68 4.3. Kim nh nhiu trng....................................................................................... 70 4.3.1. Phn tch hm t tng quan...................................................................... 70 4.3.2. Tham s thng k ca Box-Pierce v Ljung-box....................................... 70 4.4. M hnh AR(P) (Auto Regression)................................................................... 72 4.5. M hnh MA(q) (Moving Average).................................................................. 75 4.6. M hnh ARMA(p,q)........................................................................................ 77 4.7. M hnh ARMA m rng: ARIMA, SARIMA................................................ 79 4.8. Phng php Box - Jenkins .............................................................................. 80 Chng 5: DY S THI GIAN................................................................................ 91 5.1.Khi nim......................................................................................................... 91 5.2. Cc ch tiu phn tch........................................................................................ 92 5.2.1. Mc trung bnh theo thi gian................................................................ 92 5.2.2. Lng tng hoc gim tuyt i.................................................................. 93 5.2.3. Tc pht trin.......................................................................................... 94 5.2.3.2. Tc pht trin trung bnh................................................................955.2.4. Tc tng hoc gim ................................................................................ 95 5.2.4.1. Tc tng (gim) lin hon (tng k)..............................................955.2.4.2.Tc tng gim nh gc.................................................................965.2.4.3. Tc tng (gim) trung bnh.............................................................965.2.5.Tr tuyt i ca 1% tng (hoc gim) ....................................................... 96 5.3.Cc phng php biu hin xu hng pht trin ca hin tng....................... 96 5.3.1. Phng php m rng khong cch thi gian............................................. 96 5.3.2. Phng php s trung bnh trt................................................................ 97 5.3.3. Phng php hi quy ................................................................................... 98 5.3.4. Phng php biu hin bin ng thi v................................................. 101 4Chng 1: TNG QUAN V PHN TCH V D BO KINH T1.1. Khi nimD bo hnh thnh t u nhng nm 60 ca th k 20. Khoa hc d bo vi t cch mt ngnh khoa hc c lp c h thng l lun, phng php lun v phng php h ring nhm nng cao tnh hiu qu ca d bo. Ngi ta thng nhn mnh rng mt phng php tip cn hiu qu i vi d bo l phn quan trng trong hoch nh. Khi cc nh qun tr ln k hoch, trong hin ti h xc nh hng tng lai cho cc hot ng m h s thc hin. Bc u tin trong hoch nh l d bo hay l c lng nhu cu tng lai cho sn phm hoc dch v v cc ngun lc cn thit sn xut sn phm hoc dch v . Nh vy, d bo l mt khoa hc v ngh thut tin on nhng s vic s xy ra trong tng lai, trn c s phn tch khoa hc v cc d liu thu thp c. Khi tin hnh d bo ta cn c vo vic thu thp x l s liu trong qu kh v hin ti xc nh xu hng vn ng ca cc hin tng trong tng lai nh vo mt s m hnh ton hc. D bo c th l mt d on ch quan hoc trc gic v tng lai. Nhng cho d bo c chnh xc hn, ngi ta c loi tr nhng tnh ch quan ca ngi d bo. Ngy nay, d bo l mt nhu cu khng th thiu c ca mi hot ng kinh t - xc hi, khoa hc - k thut, c tt c cc ngnh khoa hc quan tm nghin cu. 1.2. ngha v vai tr ca phn tch v d bo trong qu trnh ra quyt nh kinh doanh1.2.1. ngha- Dng d bo cc mc tng lai ca hin tng, qua gip cc nh qun tr doanh nghip ch ng trong vic ra cc k hoch v cc quyt nh cn thit phc v cho qu trnh sn xut kinh doanh, u t, qung b, quy m sn xut, knh phn phi sn phm, ngun cung cp ti chnh v chun b y iu kin c s vt cht, k thut cho s pht trin trong thi gian ti (k hoch cung cp cc yu t u vo nh: lao ng, nguyn vt liu, t liu lao ng cng nh cc yu t u ra di dng sn phm vt cht v dch v).- Trong cc doanh nghip nu cng tc d bo c thc hin mt cch nghim tc cn to iu kin nng cao kh nng cnh tranh trn th trng.- D bo chnh xc s gim bt mc ri ro cho doanh nghip ni ring v ton b nn kinh t ni chung.5- D bo chnh xc l cn c cc nh hoch nh cc chnh sch pht trin kinh t vn ho x hi trong ton b nn kinh t quc dn- Nh c d bo cc chnh sch kinh t, cc k hoch v chng trnh pht trin kinh t c xy dng c c s khoa hc v mang li hiu qu kinh t cao.- Nh c d bo thng xuyn v kp thi, cc nh qun tr doanh nghip c kh nng kp thi a ra nhng bin php iu chnh cc hot ng kinh t ca n v mnh nhm thu c hiu qu sn xut kinh doanh cao nht.1.2.2. Vai tr-D bo to ra li th cnh tranh - Cng tc d bo l mt b phn khng th thiu trong hot ng ca cc doanh nghip, trong tng phng ban nh: phng Kinh doanh hoc Marketing, phng Sn xut hoc phng Nhn s, phng K ton ti chnh.1.3. Cc loi d bo1.3.1. Cn c vo di thi gian d bo: D bo c th phn thnh ba loi- D bo di hn: L nhng d bo c thi gian d bo t 5 nm tr ln. Thng dng d bo nhng mc tiu, chin lc v kinh t chnh tr, khoa hc k thut trong thi gian di tm v m.- D bo trung hn: L nhng d bo c thi gian d bo t 3 n 5 nm. Thng phc v cho vic xy dng nhng k hoch trung hn v kinh t vn ho x hi tm vi m v v m.- D bo ngn hn: L nhng d bo c thi gian d bo di 3 nm, loi d bo ny thng dng d bo hoc lp cc k hoch kinh t, vn ho, x hi ch yu tm vi m v v m trong khong thi gian ngn nhm phc v cho cng tc ch o kp thi.Cch phn loi ny ch mang tnh tng i tu thuc vo tng loi hin tng quy nh khong cch thi gian cho ph hp vi loi hin tng : v d trong d bo kinh t, d bo di hn l nhng d bo c tm d bo trn 5 nm, nhng trong d bo thi tit, kh tng hc ch l mt tun. Thang thi gian i vi d bo kinh t di hn nhiu so vi thang thi gian d bo thi tit. V vy, thang thi gian c th o bng nhng n v thch hp ( v d: qu, nm i vi d bo kinh t v ngy i vi d bo d bo thi tit).61.3.2. Da vo cc phng php d bo: D bo c th chia thnh 3 nhm- D bo bng phng php chuyn gia: Loi d bo ny c tin hnh trn c s tng hp, x l kin ca cc chuyn gia thng tho vi hin tng c nghin cu, t c phng php x l thch hp ra cc d on, cc d on ny c cn nhc v nh gi ch quan t cc chuyn gia. Phng php ny c u th trong trng hp d on nhng hin tng hay qu trnh bao qut rng, phc tp, chu s chi phi ca khoa hc - k thut, s thay i ca mi trng, thi tit, chin tranh trong khong thi gian di. Mt ci tin ca phng php Delphi l phng php d bo da trn c s s dng mt tp hp nhng nh gi ca mt nhm chuyn gia. Mi chuyn gia c hi kin v ri d bo ca h c trnh by di dng thng k tm tt. Vic trnh by nhng kin ny c thc hin mt cch gin tip ( khng c s tip xc trc tip) trnh nhng s tng tc trong nhm nh qua to nn nhng sai lch nht nh trong kt qu d bo. Sau ngi ta yu cu cc chuyn gia duyt xt li nhng d bo ca h trn x s tm tt tt c cc d bo c th c nhng b sung thm. - D bo theo phng trnh hi quy: Theo phng php ny, mc cn d bo phi c xy dng trn c s xy dng m hnh hi quy, m hnh ny c xy dng ph hp vi c im v xu th pht trin ca hin tng nghin cu. xy dng m hnh hi quy, i hi phi c ti liu v hin tng cn d bo v cc hin tng c lin quan. Loi d bo ny thng c s dng d bo trung hn v di hn tm v m.- D bo da vo dy s thi gian: L da trn c s dy s thi gian phn nh s bin ng ca hin tng nhng thi gian qua xc nh mc ca hin tng trong tng lai.1.3.3. Cn c vo ni dung (i tng d bo)C th chia d bo thnh: D bo khoa hc, d bo kinh t, d bo x hi, d bo t nhin, thin vn hc- D bo khoa hc: L d kin, tin on v nhng s kin, hin tng, trng thi no c th hay nht nh s xy ra trong tng lai. Theo ngha hp hn, l s nghin cu khoa hc v nhng trin vng ca mt hin tng no , ch yu l nhng nh gi s lng v ch ra khong thi gian m trong hin tng c th din ra nhng bin i.- D bo kinh t: L khoa hc d bo cc hin tng kinh t trong tng lai. D bo kinh t c coi l giai on trc ca cng tc xy dng chin lc pht trin kinh t - x hi v 7d n k hoch di hn; khng t ra nhng nhim v c th, nhng cha ng nhng ni dung cn thit lm cn c xy dng nhng nhim v . D bo kinh t bao trm s pht trin kinh t v x hi ca t nc c tnh n s pht trin ca tnh hnh th gii v cc quan h quc t. Thng c thc hin ch yu theo nhng hng sau: dn s, ngun lao ng, vic s dng v ti sn xut chng, nng sut lao ng; ti sn xut x hi trc ht l vn sn xut c nh: s pht trin ca cch mng khoa hc k thut v cng ngh v kh nng ng dng vo kinh t; mc sng ca nhn dn, s hnh thnh cc nhu cu phi sn xut, ng thi v c cu tiu dung, thu nhp ca nhn dn; ng thi kinh t quc dn v s chuyn dch c cu (nhp , t l, hiu qu); s pht trin cc khu vc v ngnh kinh t(khi lng ng thi, c cu, trnh k thut , b my, cc mi lin h lin ngnh); phn vng sn xut, khai thc ti nguyn thin nhin v pht trin cc vng kinh t trong nc, cc mi lin h lin vng; d bo s pht trin kinh t ca th gii kinh t. Cc kt qu d bo kinh t cho php hiu r c im ca cc iu kin kinh t - x hi t chin lc pht trin kinh t ng n, xy dng cc chng trnh, k hoch pht trin mt cch ch ng, t hiu qu cao v vng chc.- D bo x hi: D bo x hi l khoa hc nghin cu nhng trin vng c th ca mt hin tng, mt s bin i, mt qa trnh x hi, a ra d bo hay d on v tnh hnh din bin, pht trin ca mt x hi.- D bo t nhin, thin vn hc, loi d bo ny thng bao gm: + D bo thi tit: Thng bo thi tit d kin trong mt thi gian nht nh trn mt vng nht nh. Trong d bo thi tit c d bo chung, d bo khu vc, d bo a phng, v.v. V thi gian, c d bo thi tit ngn (1-3 ngy) v d bo thi tit di (ti mt nm).+ D bo thu vn: L loi d bo nhm tnh xc nh trc s pht trin cc qa trnh, hin tng thu vn xy ra cc sng h, da trn cc ti liu lin quan ti kh tng thu vn. D bo thu vn da trn s hiu bit nhng quy lut pht trin ca cc qu trnh, kh tng thu vn, d bo s xut hin ca hin tng hay yu t cn quan tm. Cn c thi gian d kin, d bo thu vn c chia thnh d bo thu vn hn ngn (thi gian khng qu 2 ngy), hn va (t 2 n 10 ngy); d bo thu vn ma (thi gian d bo vi thng); cp bo thu vn: thng tin khn cp v hin tng thu vn gy nguy him. Theo mc ch d bo, c cc loi: d bo thu vn phc v thi cng, phc v vn ti, phc v pht in,v.v. Theo yu t d bo, c: d bo lu lng ln nht, nh nht, d bo l, v.v.+ D bo a l: L vic nghin cu v hng pht trin ca mi trng a l trong tng lai, nhm ra trn c s khoa hc nhng gii php s dng hp l v bo v mi trng.8+ D bo ng t: L loi d bo trc a im v thi gian c kh nng xy ra ng t. ng t khng t nhin xy ra m l mt qu trnh tch lu lu di, c th hin ra trc bng nhng bin i a cht, nhng hin tng vt l, nhng trng thi sinh hc bt thng ng vt,v.v. Vic d bo thc hin trn c s nghin cu bn phn vng ng t v nhng du hiu bo trc. Cho n nay, cha th d bo chnh xc v thi gian ng t s xy ra.1.4. Cc phng php d bo1.4.1. Phng php d bo nh tnhCc phng php ny da trn c s nhn xt ca nhng nhn t nhn qu, da theo doanh s catng sn phm hay dch v ring bit v da trn nhng kin v cc kh nng c lin h ca nhng nhn t nhn qu ny trong tng lai. Nhng phng php ny c lin quan n mc phc tp khc nhau, t nhng kho st kin c tin hnh mt cch khoa hc nhn bit v cc s kin tng lai. Di y l cc d bo nh tnh thng dng: 1.4.1.1. Ly kin ca ban iu hnhPhng php ny c s dng rng ri cc doanh nghip. Khi tin hnh d bo, h ly kin ca cc nh qun tr cp cao, nhng ngi ph trch cc cng vic, cc b phn quan trng ca doanh nghip, v s dng cc s liu thng k v nhng ch tiu tng hp: doanh s, chi ph, li nhun...Ngoi ra cn ly thm kin ca cc chuyn gia v marketing, ti chnh, sn xut, k thut. Nhc im ln nht ca phng php ny l c tnh ch quan ca cc thnh vin v kin ca ngi c chc v cao nht thng chi phi kin ca nhng ngi khc. 1.4.1.2. Ly kin ca ngi bn hngNhng ngi bn hng tip xc thng xuyn vi khch hng, do h hiu r nhu cu, th hiu ca ngi tiu dng. H c th d on c lng hng tiu th ti khu vc mnh ph trch. Tp hp kin ca nhiu ngi bn hng ti nhiu khu vc khc nhau, ta c c lng d bo tng hp v nhu cu i vi loi sn phm ang xt. Nhc im ca phng php ny l ph thuc vo nh gi ch quan ca ngi bn hng. Mt s c khuynh hng lc quan nh gi cao lng hng bn ra ca mnh. Ngc li, mt s khc li mun gim xung d t nh mc.1.4.1.3. Phng php chuyn gia (Delphi).9Phng php ny thu thp kin ca cc chuyn gia trong hoc ngoi doanh nghip theo nhng mu cu hi c insn v c thc hin nh sau: - Mi chuyn gia c pht mt th yu cu tr li mt s cu hi phc v cho vic d bo. - Nhn vin d bo tp hp cc cu tr li, sp xp chn lc v tm tt li cc kin ca cc chuyn gia. - Da vo bng tm tt ny nhn vin d bo li tip tc nu ra cc cu hi cc chuyn gia tr li tip. - Tp hp cc kin mi ca cc chuyn gia. Nu cha tha mn th tip tc qu trnh nu trn cho n khi t yu cu d bo. u im ca phng php ny l trnh c cc lin h c nhn vi nhau, khng xy ra va chm gia cc chuyn gia v h khng b nh hng bi kin ca mt ngi no c u th trong s ngi c hi kin. 1.4.1.4. Phng php iu tra ngi tiu dngPhng php ny s thu thp ngun thng tin t i tng ngi tiu dng v nhu cu hin ti cng nh tng lai. Cuc iu tra nhu cu c thc hin bi nhng nhn vin bn hng hoc nhn vin nghin cu th trng. H thu thp kin khch hng thng qua phiu iu tra, phng vn trc tip hay in thoi... Cch tip cn ny khng nhng gip cho doanh nghip v d bo nhu cu m c trong vic ci tin thit k sn phm. Phng php ny mt nhiu thi gian, vic chun b phc tp, kh khn v tn km, c th khng chnh xc trong cc cutr li ca ngi tiu dng. 1.4.2. Phng php d bo nh lngM hnh d bo nh lng da trn s liu qu kh, nhng s liu ny gi s c lin quan n tng lai v c th tm thy c. Tt c cc m hnh d bo theo nh lng c th s dng thng qua chui thi gian v cc gi tr ny c quan st o lng cc giai on theo tng chui . - Tnh chnh xc ca d bo: Tnh chnh xc ca d bo cp n chnh lch ca d bo vi s liu thc t. Bi v d bo c hnh thnh trc khi s liu thc t xy ra, v vy tnh chnh xc ca d bo ch c th nh gi sau khi thi gian qua i. Nu d bo cng gn vi s liu thc t, ta ni d bo c chnh xc cao v li trong d bo cng thp. 10Ngi ta thng dng sai lch tuyt i bnh qun (MAD) tnh ton:MAD =Tng cc sai s tuyt i ca n giai onn giai onMAD=1niNhu cu thc t- nhu cu d bon1.4.2.1. D bo ngn hnD bo ngn hn c lng tng lai trong thi gian ngn, c th t vi ngy n vi thng. D bo ngn hn cung cp cho cc nh qun l tc nghip nhng thng tin a ra quyt nh v cc vn nh: - Cn d tr bao nhiu i vi mt loi sn phm c th no cho thng ti ? - Ln lch sn xut tng loi sn phm cho thngti nh th no ? - S lng nguyn vt liu cn t hng nhn vo tun ti l bao nhiu ?* D bo s b:M hnh d bo s b l loi d bo nhanh, khng cn chi ph v d s dng. V d nh:-S dng s liu hng bn ngy hm nay lm d bo cho lng hng bn ngy mai.- S dng s liu ngy ny nm ri nh l d bo lng hng bn cho ngy y nm nay.M hnh d bo s b qu n gin cho nn thng hay gp nhng sai st trong d bo.*Phng php bnh qun di ng: * Phng php bnh qun di ng c quyn s.Trong phng php bnh qun di ng c cp phn trn, chng ta xem vai tr ca cc s liu trong qu khl nh nhau. Trong mt vi trng hp, cc s liu ny c nh 11hng khc nhau trn kt qu d bo, v th, ngi ta thch s dng quyn s khng ng u cho cc s liu qu kh. Quyn s hay trng s l cc con s c gn cho cc s liu qu kh ch mc quan trng ca chng nh hng n kt qu d bo. Quyn s ln c gn cho s liu gn vi k d bo nht m ch nh hng ca n l ln nht.Vic chn cc quyn s ph thuc vo kinh nghim v s nhy cm ca ngi d bo.Cng thc tnh ton:11nA kt i iiFntkiiVi:Ft - D bo thi k th tAt-i - S liu thc t thi k trc (i=1,2,...,n)ki - Quyn s tng ng thi k iV d: Gi s rng ta c quyn s ca tun gn nht l 3, cch 2 tun trc l 2,5; cch 3 tun trc l 2 ; 4 tun trc l 1,5 ; 5 tun trc l 1. Theo v d 2.1, ta tnh d bo nhu cu d tr cho tun l th 18 cho thi k 5 tun nh sau:F18=(115x1)+(120x1,5)+(80x2)+(95x2,5)+(100x3)= 99,25 hay 993 triu ng 10C 2 phng php bnh qun di ng v bnh qun di ng c quyn s u c u im l san bng c cc bin ng ngu nhin trong dy s . Tuy vy, chng u c nhc im sau:- Do vic san bng cc bin ng ngu nhin nn lm gim nhy cm i vi nhng thay i thc c phn nh trong dy s. - S bnh qun di ng cha cho chng ta xu hng pht trin ca dy s mt cch tt nht. N ch th hin s vn ng trong qu kh ch cha th ko di s vn ng trong tng lai.* Phng php iu ha m.iu ha m a ra cc d bo cho giai on trc v thm vo mt lng iu chnh c c lng d bo cho giai on k tip. S iu chnh ny l mt t l no 12ca sai s d bo giai on trc v c tnh bng cch nhn s d bo ca giai on trc vi h s nm gia 0 v 1. H s ny gi l h s iu ha.Cng thc tnh nh sau: Ft = Ft1+ (At1Ft1) Trong : F t - D bo cho giai on th t, giai on k tip. F t -1 - D bo cho giai on th t-1, giai on trc. A t -1 - S liu thc t ca giai on th t-1V d: ng B trong v d 2.1, ni vi nh phn tch cng ty m rng, phi d bo nhu cu hng tun cho d tr trong nh kho ca ng. Nh phn tch ngh ng B xem xt vic s dng phng php iu ha m vi cc h s iu ha 0,1 ; 0,2 ; 0,3 . ng B quyt nh so snh mc chnh xc ca d bo ng vi tng h s cho giai on 10 tun l gn y nht.Kt qu bi ton:Chng ta tnh ton d bo hng tun cho tun lth 8 n tun l th 17. Tt c d bo ca tun l th 7 c chn mt cch ngu nhin, d bo khi u th rt cn thit trong phng php iu ha m. Thng thng ngi ta cho cc d bo ny bng vi gi tr thc ca giai on.Tnh ton mu - d bo cho tun l th 8:F8 = 85 + 0,1(85-85) =0,1 = 85F9 = 85 + 0,1(102 - 85) = 86,7F9 = 85 + 0,2(102 - 85) = 88,4 =0,2 Sau ta tnh lch tuyt i bnh qun MAD cho 3 d bo ni trn:13Tun lNhu cu d tr thc t = 0,1 = 0,2 = 0,3D bo AD D bo AD D bo AD 8 102 85,0 17,0 85,0 17,0 85,0 17,09 110 86,7 23,3 88,4 21,6 90,1 19,910 90 89,0 1,0 92,7 2,7 96,1 6,111 105 89,1 15,9 92,2 12,8 94,3 10,712 95 90,7 4,3 94,8 0,2 97,5 2,513 115 91,1 23,9 94,8 20,2 96,8 18,214 120 93,5 26,5 98,8 21,2 102,3 17,715 80 96,2 16,2 103,0 23,0 107,6 27,816 95 94,6 0,4 98,4 3,4 99,3 4,317 100 94,6 5,4 97,7 2,3 98,0 2,0Tng lch tuyt i 133,9 124,4 126,0MAD 13,39 12,44 12,6 H s iu ha = 0,2cho chng ta chnh xc cao hn = 0,1 v = 0,3.S dng = 0,2 tnh d bo cho tun th 18 :F18= F17 + ( A17 - F17)= 97,7 + 0,2(100 - 97,7)= 98,2 hay 982 triu ng.* Phng php iu ha m theo xu hngChng ta thng xem xt k hoch ngn hn, th ma v v xu hng l nhn t khng quan trng. Khi chng ta chuyn t d bo ngn hn sang d bo trung hn th ma v v xu hng tr nn quan trng hn. Kt hp nhn t xu hng vo d bo iu ha m c gi l iu ha m theo xu hng hay iu ha i.V c lng cho s trung bnh v c lng cho xu hng cho s trung bnh v h s iu ha c iu ha c hai. H s iu ha cho xu hng, c s dng trong m hnh ny Cng thc tnh ton nh sau: FTt = St - 1 + T t - 1(At -FTt )14Vi: St = FTt + (FTt - FTt - 1 - Tt - 1 )Tt = Tt - 1 Trong FTt - D bo theo xu hng trong giai on tSt - D bo c iu ha trong giai on tTt - c lng xu hng trong giai on tAt - S liu thc t trong giai on tt - Thi on k tip.t-1 - Thi on trc.- H s iu ha trung bnh c gi tr t 0 1- H s iu ha theo xu hng c gi tr t 0 1V d:ng A mun d bo s lng hng bn ra ca cng ty nhm ln k hoch tin mt, nhn s v nhu cu nng lc cho tng lai. ng tin rng trong sut giai on 6 thng qua, s liu lng hng bn ra c th i din cho tng lai. ng xy d bo iu ha m theo xu hng nu cho s =0,3 v s liu bn ra trong qu kh = 0,2 ;lng hng bn ra thng th 7nh sau (n v: 10 Triu ng).Thng (t) 1 2 3 4 5 6Doanh s bn (At) 130 136 134 140 146 150Kt qu bi ton:Chng ta c lng d bo bt u vo thng 1bng d bo s b, tc l bng s liu thc t. Ta c: FT1 = A1 = 130Chng ta c lng phn t xu hng bt u.Phng php c lng phn t xu hng l ly s liu thc t ca thng cui cng tr s liu thc t thng u tin, sau chia cho s giai on trong k ang xt. 6 1 150 1301 45 5A AT S dng d bo s b v phn t xu hng bt u tnh d bo doanh s bn ra trong tng thng cho n thng th 7.D bo theo xu hng cho thng th 2: FT2 = S1 + T115(A1 - FT1 ) = 130 + 0,2( 130 - 130 ) =S1 = FT1 +130T1 = 4 FT2 = 130 + 4 = 134D bo theo xu hng cho thng th 3: FT3 = S2 + T2 (A2 - FT2 ) = 134 + 0,2( 136 - 134 ) =S2 = FT2 +134,4(FT2 - FT1 - T1 ) = 4 + 0,3 (134 - 130 -T2 = T1 +4) = 4 FT3 = S2 + T2 = 134,4 + 4 = 138,4D bo tng t cho cc thng 4, 5, 6, 7 ta c bng sau:Thng (t) Doanh s bn (At) St - 1 Tt - 1 FTt1 130 - - 130,002 136 130,00 4,00 134,003 134 134,40 4,00 138,404 140 137,52 4,12 141,645 146 141,31 3,86 145,176 150 145,34 3,76 149,107 - 149,28 3,81 153,091.4.2.2. D bo di hnD bo di hn l c lng tng lai trong thi gian di, thng hn mt nm. D bo di hn rt cn thit trong qun tr sn xut tr gip cc quyt nh chin lc v hoch nh sn phm, quy trnh cng ngh v cc phng tin sn xut. V d nh:- Thit k sn phm mi.- Xc nh nng lc sn xut cn thit l bao nhiu? My mc, thit b no cn s dng v chng c t u ?- Ln lch trnh cho nhng nh cung ng theo cchp ng cung cp nguyn vt liu di hnD bo di hn c th c xy dng bng cch v mt ng thng i xuyn qua cc s liu qu kh v ko di n n tng lai. D bo trong giai on k tip c th c v vt ra khi th thng thng. Phng php tip cn theo kiu th i vi d bo di 16hn c th dng trong thc t, nhng im khng thun li ca n l vn v mt ng tng ng hp l nht i qua cc s liu qu kh ny.Phn tch hi qui s cung cp cho chng ta mt phng php lm vic chnh xc xy dng ng d bo theo xu hng.* Phng php hi qui tuyn tnh.Phn tch hi qui tuyn tnh l mt m hnh d bo thit lp mi quan h gia bin ph thuc vi hai hay nhiu bin c lp. Trong phn ny, chng ta ch xt n mt bin c lp duy nht. Nu s liu l mt chui theo thi gian th bin c lp l giai on thi gian v bin ph thuc thng thng l doanh s bn ra hay bt k ch tiu no khc m ta mun d bo.M hnh ny c cng thc:Y = ax + ba = 2 2( )n xy x yn x x b = 222( )x y x xyn x x Trong :y - Bin ph thuc cn d bo.x - Bin c lpa - dc ca ng xu hngb - Tung gcn - S lng quan st17Thi gianng xu hngDoanh sTrong trng hp bin c lp x c trnh by thng qua tng giai on theo thi gian v chng phi cch u nhau ( nh : x = 0 . V vy 2002, 2003, 2004...) th ta c th iu chnh li sao chovic tnh ton s tr nn n gin v d dng hn nhiu. Nu c mt s l lng mc thi gian: chng hn x = 0 l 5, th gi tr ca x c n nh nh sau : -2, -1, 0, 1, 2 v nh th gi tr ca x c s dng cho d bo trong nm ti l +3. Nu c mt s chn lng mc thi gian: chng hn x = 0 v l 6 th gi tr ca x c n nh l : -5, -3, -1, 1, 3, 5. Nh thgi tr ca x c dng cho d bo trong nm ti l +7.V d: Mt hng sn xut loi ng c in t cho cc van khi ng trong ngnh cng nghip, nh my hot ng gn ht cng sut sut mt nm nay. ng J, ngi qun l nh my ngh rng s tng trng trong doanh s bn ra vn cn tip tc v ng ta mun xy dng mt d bo di hn hoch nh nhu cu v my mc thit b trong 3 nm ti. S lng bn ra trong 10 nm qua c ghi li nh sau:Nm S lng bn Nm S lng bn1 1.000 6 2.0002 1.300 7 2.2003 1.800 8 2.6004 2.000 9 2.9005 2.000 10 3.200Kt qu bi ton:Ta xy dng bng tnh thit lp cc gi tr:18Nm Lng bn (y) Thi gian (x) x2 xy1 1.000 -9 81 -9.0002 1.300 -7 49 -9.1003 1.800 -5 25 -9.0004 2.000 -3 9 -6.0005 2.000 -1 1 -2.0006 2.000 1 1 2.0007 2.200 3 9 6.6008 2.600 5 25 13.0009 2.900 7 49 20.30010 3.200 9 81 28.800Tng 21.000 0 330 35.600a=nxyxy==xy-=3.5600= 107,8nx2( x)2x2330b=x2yxxy=y=21.000= 2.100nx2( x)2 n 10-Dng phng trnh hi qui tuyn tnh d bo hng bn ra trong tng lai:Y = ax + b = 107,8x + 2.100 d bo cho hng bn ra trong 3 nm ti ta thay gi tr ca x ln lt l 11, 13, 15 vo phng trnh.Y11 = 107,8 . 11 + 2.100 = 3.285 3.290 n v19Y12 = 107,8 . 13 + 2.100 = 3.5013.500 n v Y13 = 107,8 . 15 + 2.100 = 3.717 3.720 n vTrng hp bin c lp khng phi l bin thi gian, hi qui tuyn tnh l mt nhm cc m hnh d bo c gi l m hnh nhn qu. M hnh ny a ra cc d bo sau khi thit lp v o lng cc bin ph thuc vi mt hay nhiu bin c lp.V d: ng B, nh tng qun l ca cng ty k ngh chnh xc ngh rng cc dch v k ngh ca cng ty ng ta c cung ng cho cc cng ty xy dng th c quan h trc tip n s hp ng xy dng trong vng ca ng ta. ng B yu cu k s di quyn, tin hnh phn tch hi qui tuyn tnh da trn cc s liu qu kh v vch ra k hoch nh sau : - Xy dng mt phng trnh hi qui cho d bo mc nhu cu v dch v ca cng ty ng. - S dng phng trnh hi qui d bo mc nhu cu trong 4 qu ti. c lng tr gi hp ng 4 qu ti l 260, 290, 300 v 270 (VT:10 Triu ng). - Xc nh mc cht ch, cc mi lin h gia nhu cu v hp ng xy dng c a ra.Bit s liu tng qu trong 2 nm qua cho trong bng:(n v: 10 Triu ng). NmQiNhu cu ca cng tyTr gi hp ng thc hin11 8 1502 10 1703 15 1904 9 17021 12 1802 13 1903 12 2004 16 220 Kt qu bi ton: Xy dng phng trnh hi qui. ng A xy dng bng tnh nh sau:20Thi gian Nhu cu (y) Tr gi hp ng (x) x2xy y21 8 150 22.500 1.200 642 10 170 28.900 1.700 1003 15 190 36.100 2.850 2254 9 170 28.900 1.530 815 12 180 32.400 2.160 1446 13 190 36.100 2.470 1697 12 200 40.000 2.400 1448 16 220 48.400 3.520 256Tng 95 1.470 273.300 17.830 1.183S dng cng thc ta tnh ton c h s a =0,1173 ; b = -9,671 Phng trnh hi qui tm c l:Y = 0,1173x 9,671D bo nhu cu cho 4 qu ti: ng A d bo nhu cu ca cng ty bng cch s dng phng trnh trn cho 4 qu ti nh sau:Y1 = (0,1173 x 260) - 9,671 = 20,827;Y2 = (0,1173 x 290) - 9,671 = 24,346Y3 = (0,1173 x 300 )- 9,671 = 25,519;Y4 = (0,1173 x 270) - 9,671 = 22,000D bo tng cng cho nm ti l:Y = Y1+ Y2 +Y3 +Y4 = 20,827+ 24,346+25,519+22,000=930triu ng.92,7 nh gi mc cht ch mi lin h ca nhu cu vi s lng hp ng xy dngr =nxyxy n[nx2( x)2][ny2( y)2]=8x17.8301.470x95=2.990 0.894(8x273.30014702)(8x1.183952) 3.345,8r2 = 0,799;trong r l h s tng quan v r2 l h s xc nhR rng l s lng hp ng xy dng c nh hng khong 80% ( r2 = 0,799 ) ca bin s c quan st v nhu cu hng qu ca cng ty.H s tng quan r gii thch tm quan trng tng i ca mi quan h gia y v x; du ca r cho bit hng ca mi quan h v gi+1. Dutr tuyt i ca r ch cng 21ca mi quan h, r c gi tr t -1 ca r lun lun cng vi du ca h s a. Nu r m ch ra rng gi tr ca y v x c khuynh hng i ngc chiu nhau, nu r dng cho thy gi tr ca y v x i cng chiu nhau.Di y l vi gi tr ca r:r = -1. Quan h ngc chiu hon ton, khi y tng ln th x gim xung v ngc li.r = +1. Quan h cng chiu hon ton, khi y tng ln th x cng tng v ngc li.r = 0. Khng c mi quan h gia x v y.* Tnh cht ma v trong d bo chui thi gian.Loi ma v thng thng l s ln xung xy ra trong vng mt nm v c xu hng lp li hng nm. Nhng v ma ny xy ra c th do iu kin thi tit, a l hoc do tp qun ca ngi tiu dng khc nhau...Cch thc xy dng d bo vi phn tch hi qui tuyn tnh khi v ma hin din trong chui s theo thi gian. Ta thc hin cc bc:-Chn la chui s liu qu kh i din.-Xy dng ch s ma v cho tng giai on thi gian.0iYIi YVi iY - S bnh qun ca cc thi k cng tn

0Y- S bnh qun chung ca tt c cc thi k trong dy s. Ii - Ch s ma v k th i.- S dng cc ch s ma v ha gii tnh cht ma v ca s liu.-Phn tch hi qui tuyn tnh da trn s liu phi ma v.- S dng phng trnh hi qui d bo cho tng lai.- S dng ch s ma v ti ng dng tnh cht ma v cho d bo.V d: ng J nh qun l nh my ng c c bit ang c gng lp k hoch tin mt v nhu cu nguyn vt liu cho tng qu ca nm ti. S liu v lng hng bn ra trong vng 223 nm qua phn nh kh tt kiu sn lng ma v v c th ging nh trong tng lai. S liu c th nh sau: NmS lng bn hng qu (1.000 n v)Q1 Q2 Q3 Q41 520 730 820 5302 590 810 900 6003 650 900 1 650Kt qu bi ton:u tin ta tnh ton cc ch s ma v.Nm Qu 1 Qu 2 Qu 3 Qu 4 C nm1 520 730 820 530 2.6002 590 810 900 600 2.9003 650 900 1.000 650 3.200Tng 1.760 2.440 2.720 1.780 8.700Trung bnh qu 586,67 813,33 906,67 593,33 725Ch s ma v 0,809 1,122 1,251 0,818 - K tip, ha gii tnh cht ma v ca s liu bng cch chia gi tr ca tng qu cho ch s ma v tng ng. Chng hn : 520/0,809 = 642,8 ; 730/1,122 = 605,6 ... Ta c bng s liu nh sau: NmS liu hng qu phi ma v.Qu 1 Qu 2 Qu 3 Qu 41 642,8 650,6 655,5 647,92 729,2 721,9 719,4 733,53 803,5 802,1 799,4 794,6Chng ta phn tch hi qui trn c s s liu phi ma v (12 qu) v xc nh phng trnh hi qui.Qi X y x2xyQ11 1 642,8 1 642,8Q12 2 650,6 4 1.301,223Q13 3 655,5 9 1.966,5Q14 4 647,9 16 2.591,6Q21 5 729,3 25 3.646,5Q22 6 721,9 36 4.331,4Q23 7 719,4 49 5.035,8Q24 8 733,5 64 5.868,0Q31 9 803,5 81 7.231,5Q32 10 802,1 100 8.021,0Q33 11 799,4 121 8.793,4Q34 12 794,6 144 8.535,2Tng 78 8.700,5 650 58.964,9Xc nh c h s a = 16,865 v b = 615,421 .Phng trnh c dng: Y = 16,865x + 615,421By gi chng ta thay th gi tr ca x cho 4 qu ti bng 13, 14, 15, 16 vo phng trnh. y l d bo phi ma v trong 4 qu ti.Y41 = (16,865 x 13) + 615,421 = 834,666Y42 = (16,865 x 14) + 615,421 = 851,531Y43 = (16,865 x 15) + 615,421 = 868,396Y44 = (16,865 x 16) + 615,421 = 885,261 Tip theo, ta s dng ch s ma v ma v ha cc s liu.Qu Ch s ma v (I) D bo phi ma v (Yi) D bo ma v ha (Ymv)1 0,809 834,666 6752 1,122 851,531 9553 1,251 868,396 1.0864 0,818 885,261 7241.5. Quy trnh d boQuy trnh d bo c chia thnh 9 bc. Cc bc ny bt u v kt thc vi s trao i (communication), hp tc (cooperation) v cng tc (collaboration) gia nhng ngi s dng v nhng ngi lm d boBc 1: Xc nh mc tiu24- Cc mc tiu lin quan n cc quyt nh cn n d bo phi c ni r. Nu quyt nh vn khng thay i bt k c d bo hay khng th mi n lc thc hin d bo cng v ch.- Nu ngi s dng v ngi lm d bo c c hi tho lun cc mc tiu v kt qu d bo s c s dng nh th no, th kt qu d bo s c ngha quan trng.Bc 2: Xc nh d bo ci g- Khi cc mc tiu tng qut r ta phi xc nh chnh xc l d bo ci g (cn c s trao i)+ V d: Ch ni d bo doanh s khng th cha , m cn phi hi r hn l: Dbodoanhthubnhng(salesrevenue)haysnv doanhs(unit sales). D bo theo nm, qu, thng hay tun.+ Nn d bo theo n v trnh nhng thay i ca gi c.Bc 3: Xc nh kha cnh thi gianC 2 loi kha cnh thi gian cn xem xt:- Th nht: di d bo, cn lu : + i vi d bo theo nm: t 1 n 5 nm+ i vi d bo qu: t 1 hoc 2 nm+ i vi d bo thng: t 12 n 18 thng- Th hai: Ngi s dng v ngi lm d bo phi thng nht tnh cp thit ca d boBc 4: Xem xt d liu- D liu cn d bo c th t 2 ngun: bn trong v bn ngoi- Cn phi lu dng d liu sn c ( thi gian, n v tnh,)- D liu thng c tng hp theo c bin v thi gian, nhng tt nht l thu thp d liu cha c tng hp- Cn trao i gia ngi s dng v ngi lm d boBc 5: La chn m hnh-Lmsaoquyt nhcphngphpthchhpnht chomt tnhhungnht nh?25+ Loi v lng d liu sn c+ M hnh (bn cht) d liu qu kh+ Tnh cp thit ca d bo+ di d bo+ Kin thc chuyn mn ca ngi lm d boBc 6: nh gi m hnh- i vi cc phng php nh tnh th bc ny t ph hp hn so vi phng php nh lng - i vi cc phng php nh lng, cn phi nh gi mc ph hp ca m hnh (trong phm vi mu d liu)- nh gi mc chnh xc ca d bo (ngoi phm vi mu d liu)- Nu m hnh khng ph hp, quay li bc 5Bc 7: Chun b d bo- Nu c th nn s dng hn mt phng php d bo, v nn l nhng loi phng php khc nhau (v d m hnh hi quy v san m Holt, thay v c 2 m hnh hi quy khc nhau)- Cc phng php c chn nn c s dng chun b cho mt s cc d bo (v v trng hp xu nht, tt nht v c th nht)Bc 8: Trnh by kt qu d bo- Kt qu d bo phi c trnh by r rng cho ban qun l sao cho h hiu cc con s c tnh ton nh th no v ch ra s tin cy trong kt qu d bo- Ngi d bo phi c kh nng trao i cc kt qu d bo theo ngn ng m cc nh qun l hiu c- Trnh by c dng vit v dng ni- Bng biu phi ngn gn, r rng- Ch cn trnh by cc quan st v d bo gn y thi- Chui d liu di c th c trnh by di dng th (c gi tr thc v d bo)- Trnh by thuyt trnh nn theo cng hnh thc v cng mc vi phn trnh by vitBc 9: Theo di kt qu d bo26- Lch gia gi tr d bo v gi tr thc phi c tho lun mt cch tch cc, khch quan v ci m- Mc tiu ca vic tho lun l hiu ti sao c cc sai s, xc nh ln ca sai s- Trao i v hp tc gia ngi s dng v ngi lm d bo c vai tr rt quan trng trong vic xy dng v duy tr quy trnh d bo thnh cng.27Chng 2: CC PHNG PHP PHN TCH V D BOC nhiu phng php d bo thng k khc nhau ( phng php ly kin chuyn gia, d bo tng mc bnh qun, ngoi suy hm xu th, nhng khng phi phng php no cng c sdng ph binnhnhau.V vy, trongphnny chtrnh bymt s phng php thng dng nht v gii thiu mt s phng php ang c xu hng s dng nhiu trong thc t hin nay.2.1. D bo t cc mc bnh qun2.1.1. D bo t s bnh qun trt (di ng)Phng php sbnh qun di ng l mt trong nhng phng phpbiu hin xu hng pht trin c bn ca hin tng nghin cu, hay ni cch khc, m hnh ho s pht trin thc t ca hin tng nghin cu di dng dy cc s bnh qun di ng. Phng php bnh qun di ng cn c s dng trong d bo thng k. Trn c s xy dng mt dy s bnh qun di ng, ngi ta xy dng m hnh d bo.V d, c dy s thi gian v sn lng thp ca doanh nghip A trong 12 thng theo bng sau:Thi gian Sn lng(triu tn) (yi)Doanh s trung bnh di ng(triu tn) (Mi)1 79 -2 82 -3 85 824 82 835 88 856 86 85,37 98 90,68 105 96,39 110 104,310 115 11011 120 11512 118 117,6Nh vy, ng vi thng 3 ta c s bnh qun di ng l 82 triu tn, thng 4 l 83 triu tn, v.v v cui cng thng 12 l 117,6 triu tn. Ta gi cc s bnh qun di ng mi ny l 28Mi (i = k, k + 1, k + 2,n), trong k l khong cch thi gian san bng ( y k = 3, bnh qun t 3 mc thc t).M hnh d bo l: n+1 = MnKhong d bo s c xc nh theo cng thc sau:n+L11 t Sk+ (2.1)Trong tl gi tr tra trong bng tiu chun t- Student vi (k-1) bc t do v xc sut tin cy (1-). lch tiu chun mu iu chnh c tnh theo cng thc sau:S = 2( )1i iy Mk (2.2)Theo v d trn ta tnh c:S = 2 2 2 2 2 22 2 2 2(85 82) (82 83) (88 85) (86 85, 3) (98 90, 6) (105 96, 3)(110 104, 3) (115 110) (120 115) (118 117, 6)3 1 + + + + + + + + + = 10,78Trong v d trn, d on sn lng thp cho thng 1 nm sau l:Y13 = 117,6 triu tnTheo cng thc trn ta tnh c S = 10,78 nghn tn v t= 2,92 vi xc sut tin cy (1-) = 0,95 ( xc sut t 95%) v s bc t do bng 2. Do khong d on v sn lng thp thng 1 nm sau s nm trong khong:117,6 (2,92 x 10,78) 113+= 117,6 36,352.1.2. M hnh d bo da vo lng tng (gim) tuyt i bnh qun- Phng php ny c s dng trong trng hp lng tng ( gim) tuyt i lin hon xp x nhau qua cc nm (dy s thi gian c dng gn ging nh cp s cng):1yi iy y xp x nhau (i= z n).M hnh d bo theo phng trnh:n L Y+=ny+ . y L (2.3) Trong :n L Y+: Mc d on thi gian (n+L)ny: Mc cui cng ca dy s thi gian29y : Lng tng, gim tuyt i bnh qun L: Tm xa ca d on ( L=1,2,3,nm)Trong :11( )i iyy yn ( 2, ) i n = 11ny ynV d: Gi tr sn xut (GO)ca mt doanh nghip A qua cc nm nh sau:Thi gian Ch tiu2001 2002 2003 2004 2005 2006Gi tr sn xut (GO) (t ng 32 36 39 41 43 45Ta c:y = 45 326 1= 2,6 tD bo GO ca doanh nghip cho nm 2007 L=1. Ta c phng trnh:

2006 120062, 6*1 Y Y+ +2007 Y= 45+ 2,6= 47,6 (t)D bo GO ca doanh nghip nm 2008

2008 Y= 45+ 2,6x2= 50,2(t)Tng t, d bo cho GO nm 2011 ( tm xa xa d bo l 5) 2011 Y= 45+ 2,6x5= 58 (t)2.1.3. M hnh d bo da vo tc pht trin bnh qunThng p dng trong trng hp cc mc ca dy s bin ng theo thi gian c tc pht trin ( hoc tc tng, gim) tng k gn nhau (dy s thi gian c dng gn nh cp s nhn).C hai m hnh d on:* D don mc hng nm: (c th dng d bo trong di hn).- Phng php ny c p dng khi tc pht trin hon ton xp x nhau.- M hnh d on:30n L Y+= ny.( ) Lt(2.4)n L Y+: Mc d on thi gian (n+L)ny: Mc c dng lm k gc ngoi suyL: Tm xa ca d on ( L=1,2,3,nm)t: Tc pht trin bnh qun hng nm11nnyty Vi v d trn ta c: 6 1451, 07132t D on cho nm 2007 ( Ta chn nm gc l nm cui cng trong dy s -2006)Theo cng thc trn, GO ca doanh nghip l:Nm 2007: 2007 Y= 45x (1,071)1= 48,18 (t)Nm 2008: 2008 Y= 45x (1,071)2=51,5 (t)Tng t GO ca nm 2011 l: 2011 Y= 45x (1,071)5=63,4 (t)* D on mc ca khong thi gian di 1 nm (qu, thng- d bo ngn hn)ijjY y( )1 irtS(2.5)Trong :ij Y: L mc ca hin tng thi gian j (j=1,m) ca nm i1nj ijiy Y - Tng cc mc ca thi gian j ca nm i (i=1n)11nnyty : Tc pht trin bnh qun hngSr= 1 + (t) +(t)2 + (t)3 ++ (t)n-1n: c th l s nm hoc s lng mc ca tng nm.V d: C ti liu v tnh hnh sn xut mt loi sn phm ca x nghip A nh sau:31Qu jNm jI II III IV1nj ijiy Y 2004 20 21,5 22 23,5 86,552005 20,04 20,63 21,7 24,28 86,652006 21,04 22,83 23,5 25,63 93,03yj61,11 64,96 667,2 72,46 266,23T bng s liu trn ta c: 3 193, 031, 07586, 55t Sr= 1 + (t) +(t)2 = 1+ 1,075 +(1,075)2 = 3,231- D on sn lng cho cc qu ca nm 2007 ( i=4) ( )4 1rtS= ( )31, 0753, 231= 0,384T l ny dng iu tit cc khong thi gian ca nm.4.I Y=yI. ( )3rtS= 61,11. 0,384= 23,466 ( nghn tn)4.II Y=yII. ( )3rtS= 64,98. 0,384= 24,952 ( nghn tn)4.III Y=yIII. ( )3rtS= 67,2. 0,384= 25,805 ( nghn tn)4.IV Y=yIV. ( )3rtS= 72,46. 0,384= 27,825 ( nghn tn)2.2. M hnh d bo theo phng trnh hi quy (d bo da vo xu th)T xu hng pht trin ca hin tng nghin cu ta xc nh c phng trnh hi quy l thuyt, l phng trnh ph hp vi xu hng v c im bin ng ca hin tng nghin cu, t c th ngoi suy hm xu th xc nh mc pht trin trong tng lai.322.2.1. M hnh hi quy theo thi gian* V d: M hnh d bo theo phng trnh hi quy ng thng:Y= a+ bt (2.6)Trong : a,b l nhng tham s quy nh v tr ca ng hi quyT phng trnh ny, bng phng php bnh phng nh nht hoc thng qua vic t th t thi gian (t) trong dy s tnh cc tham s a,b.Nu t th t thi gian t sao chot khc 0 ( t 0), ta c cc cng thc tnh tham s sau:2 2. yt y tat tb=. y a t Nu t th t thi gian t sao chot khc 0 ( t =0), ta c cc cng thc tnh tham s sau:ya yn 2. y tbtV d: Hy d bo v doanh thu tiu th ca ca hng thng mi B trong nhng nm tip theo trn c s bng s liu sau:Thi gianCh tiu2001 2002 2003 2004 2005 2006Doanh thu tiu th(t ng) 70 98 115 120 136 180T ngun ti liu, ta c bng s liu sau (t th t thi gian cho ( t =0)Nm (n)Doanh thu (t ng) yiiu kintt =0T t2y.tY2001 70 -5 25 -350 72,0452002 98 -3 9 -294 91,1592003 115 -1 1 -115 120,27332003 120 1 1 120 129,3872005 136 3 9 408 148,582006 180 5 25 900 167,61N= 6 719 t =02t = 70 yt = 669Tnh cc tham s a v b theo iu kin tt =0:719119,836ya yn 2. 6699, 55770y tbt Hm xu th c dng: Y= 119,83 +9,55tT hm xu th ny ta c th d bo doanh thu ca ca hng B trong nhng nm tip theo nh sau:Doanh thu ca nm 2007 (t=7): 2007 119,83 9,557 7 186, 729 Y x + Doanh thu ca nm 2008 (t=9): 2008 119,83 9, 557 9 205,843 Y x + Doanh thu ca nm 2009 (t=11): 2009 119,83 9, 557 11 224, 957 Y x + Doanh thu ca nm 2010 (t=13): 2010 119,83 9, 557 13 244, 071 Y x + S liu d bo (Y) v s liu thc t yi c s chnh lch l do c sai s trong d on.+ Sai s d bo l s chnh lch gia mc thc t v mc tnh ton theo m hnh d bo.+ Sai s d bo ph thuc vo 03 yu t: bin thin ca tiu thc trong thi k trc, di ca thi gian ca thi k trc v di ca thi k d on.+ Vn quan trng nht trong d bo bng ngoi suy hm xu th l la chn hm xu th, xc nh sai s d on v khong d on:- Cng thc tnh sai s chun ( y)2iyy yn p _ ,Trong : 34Y- Gi tr tnh ton theo hm xu th n- S cc mc trong dy sp- S cc tham s cn tm trong m hnh xu thn-p- S bc t doCng thc ny c dng la chn dng hm xu th (so snh cc sai s chun tnh c) sai s no nh nht chng t rng hm tng ng vi sai s s xp x tt nht v c la chn lm hm xu th d on.Thng thng vic d on c tin hnh n gin ta vn chn hm xu th lm hm tuyn tnh.- Cng thc tnh sai s d bo:221 3( 2 1)1( 1)Lp ynSn n n+ + +Trong :N: S lng cc mc L: Tm xa ca d boSau xc nh khong d on theo cng thc sau;$pn Ly t S +tt- l gi tr theo bng ca tiu chun t- Student vi (n-2) bc t do v xc sut tin cy (t-).Tr li v d trn ta i tnhy( )22 22 2 270 72, 045 (98 91,159) (115 110, 27)(120 129, 387) (136 148) (180 167, 61)10,8766 2y + + + + + Sai s d bo:+ i vi nm 2007 (L=1): 1 22007 21 3(6 2 1)10,876 1 14,8566 6(6 1)pS+ + + + i vi nm 2008 (L=2): 2 22008 21 3(6 2 1)10,876 1 16, 936 6(6 1)pS+ + + Vi xc sut tin cy l 0,95 v s bc t do (n)= 4 khi t=2,132Ta c d bo ca nm 2007 l:186,729t 2,132 x14,856= 186,729t 31,6735Ta c d bo ca nm 2007 l:205,843t 2,132 x16,93= 205,843t 36...Nh vy ta chuyn t d bo im sang d bo khong.2.2.2. M hnh hi quy gia cc tiu thc* M hnh hi quy tuyn tnh gia hai tiu thcT vic xy dng phng trnh hi quy tuyn tnh gia cc tiu thc nu phn trn, ta c th d on cc gi tr ca Y trong tng lai khi cc bin trong hm hi quy thay i, c th:i vi phng trnh tuyn tnh gin n: Yx= a+ bxTrong : a, b l nhng tham s quy nh v tr ca ng hi quy. Hng s a l im ct trc tung (biu hin ca tiu thc kt qu ) khi tiu thc nguyn nhn x bng 0. dc b chnh l lng tng gim ca tiu thc kt qu khi tiu thc nguyn nhn thay i.T phng trnh ny, ta s d on c gi tr ca tiu thc kt qu trong tng lai khi c s thay i ca tiu thc nguyn nhn.Tng t nh trong hi quy gin n, trong hi quy bi, gi tr d on ca Y c c tng ng vi cc gi tr cho trc ca k bin X bng cc thay cc gi tr ca k bin X vo phng trnh hi quy bi.Cc gitr cho trc ca bin X ln lt l x1,n+1,x2,n+1,,xk,n+1 th gi tr d on Yn+1 s l:Yn+1= a+ b1. x1,n+1 + b2 x2,n+1++ bkxk,n+12.3. D bo da vo hm xu th v bin ng thi vPhng php d bo ny p dng i vi hin tng nghin cu chu tc ng ca nhiu nhn t bin ng. Nh bin ng thi v, bin ng xu hng v bin ng bt thng.- M hnh d bo s c th da vo hm xu th kt hp vi bin ng thi v:Yt= Y+tv+bt (2.7)- Hoc d bo da vo hm xu th kt hp nhn t vi bin ng thi v:Yt= Yx tv xbt (2.8)Trong :Y: Mc l thuyt xc nh t hm xu th ( hoc cc phng php nu trn)tv: nh hng ca nhn t thi vbt: nh hng ca nhn t bt thng36Nhn chung, hm xu th, ch s thi v c xc nh tng m hnh cn nhng nhn t bin ng bt thng thng khng d bo c, do vy m hnh ch cn li hai nhn t: bin ng xu hng v bin ng thi v.2.3.1. D bo vo m hnh cngV d: C ti liu v sn lng ca doanh nghip A nh sau:Nm (t)QuSn lng ( nghn tn)Cng theo cng qu jy Mc bnh qun tng qu iyCh s thi vitvyIy2002 2003 2004 2005 2006I 20 25 27 31 29 132 26,4 0,678II 25 32 30 37 36 160 32 0,82II 38 38 45 44 47 212 42,4 1,14IV 40 60 55 62 58 275 55 1,41Cng theo cng nm jy 123 155 157 174 170 779 38,95. t y 123 310 471 696 850* Trc tin xc nh hm xu th tuyn tnh sn lng doanh nghip c dng l:Y= a+ btTrong : a, b l cc tham s quy nh v tr ca hm xu th tuyn tnh, c tnh theo cng thc sau:212 . 12 . ( 1)jt y nb ym m mn n + _ ,=12m+212 2450 5 1.779 0, 7064 2.4 4.5(5 1)+ _ ,. 1. 2jymna bmn+ = 779 4.5 10, 706 31, 5374.5 2+ Trong :n: S nm37m: Khong cch thi gian trong mt nm ( m= 4 i vi qu, m=12 i vi nm)t: Th t thi gian trong dy s (nm)Do vy, hm xu th c dng: Y= 31,537 + 0,706tMc bnh qun mt qu tnh chung chi 5 nm: iy = 38,95* Tnh cc mc mang tnh thi v theo cng thc sau:tv= iy - jy- b(i- 12m+) vi i= 1,2,3,4Do vy, mc d bo v thi v cho cc qu ca nm 2007 nh sau:- Qu I: (26,4- 38,95) 0,706.(1-4 12+)= - 11,49- Qu II: (32- 38,95) 0,706.(2-4 12+)= - 6,597- Qu III: (42,4- 38,95) 0,706.(3- 4 12+)= 3,097- Qu IV: (55- 38,95) 0,706.(4- 4 12+)= 14,99Sau khi xc nh xong hm xu th v bin ng thi v th m hnh d bo kt hp cng gia xu th bin ng v tnh thi v c dng: tY Y tv +D bo sn lng qu I nm 2007 ( t= 21) 1Y = 31,537 + 0,706 x 21 11,49= 34,837Qu II ( t=22): 2Y = 31,537 + 0,706 x 22 6,597= 40,472C tip tc nh vy cho n cc qu tip theo2.3.2. D bo da vo m hnh nhnM hnh d bo theo kt hp nhn c dng:Yt= Yx tv (2.9)38 d bo theo m hnh ny, trc ht phi tnh c hm xu th, hm xu th trong trng hp ny phi c loi tr bin ng thi v bng cch xy dng dy s bnh qun trt (ty ) vi s lng mc bng 4 vi ti liu qu v 12 vi ti liu thng.T ta tnh c ttyy, t xc nh thnh phn thi v (tvt) bng cch tnh cc s bnh qun ttvsau tnh h s iu chnh H:H= tmtv ( vi m= 4) i vi ti liu qu, 12 i vi ti liu thng )T tnh ch s thi v Itv= ttvx HSau khi xc nh c tvt th xc nh dy s ft l dy s loi b thnh phn thi v nh sau: tttyftvTheo v d trn ta c th lp bng tnh ton sau y:39STT Yttyttyytvttttyftv1 20 - - 0,7 28,572 25 - - 0,838 29,833 38 30,75 1,236 1,08 35,194 40 32 1,25 1,376 29,075 25 33,75 0,74 0,7 35,716 32 33,75 0,948 0,838 38,197 38 38,75 0,98 1,08 35,198 60 39,25 1,529 1,376 43,69 27 38,75 0,697 0,7 38,5710 30 40,5 0,74 0,838 35,811 45 39,25 1,146 1,08 41,6712 55 40,25 1,366 1,376 39,9713 31 42 0,738 0,7 44,2814 37 41,75 0,866 0,838 44,1515 44 43,5 1,011 1,08 40,7416 62 43 1,441 1,376 45,0617 29 42,75 678 0,7 41,1318 36 43,5 827 0,838 42,9619 47 42,5 1,105 1,08 43,520 58 - - 1,376 42,15T ft ta lp bng sau:QuNmI II III IV2002 - - 1,236 1,252003 0,74 0,948 0,98 1,5292004 0,697 0,74 1,146 1,3662005 0,738 0,886 1,011 1,4412006 0,678 0,827 1,105 -Bnh qun qu (ttv ) 0,713 0,85 1,096 1,396Vi ti liu trong bng tnh ta tnh c cc i lng trn nh sau: 40H= tmtv = 40, 9860, 713 0,85 1, 096 1, 036 + + +* Trc tin, tnh cc ch s thi v: Itv=ttv .HQu I= 0,713 x0,986 = 0,7Qu II= 0,85 x0,986 = 0,838Qu I= 1,906 x0,986 = 1,08Qu I= 1,396 x0,986 = 1,376* Xy dng hm xu th: Y= a+ bt tin theo di, t (ft) talp bng sau: Qu NmI II III IVTng nm (N)t.y2002 28,57 29,83 35,19 29,07 122,66 122,66200335,7138,19 35,19 43,6 152,69 305,38200438,5735,8 41,67 39,97 156,01 468,03200544,2844,15 40,74 45,06 174,23 696,92200641,4342,96 43,5 42,15 170,04 850,2Tng qu (Q)188,56190,93 196,29 199,85 755,66. t y =2443,19Bnh qun qu37,7138,186 39,26 39,97Cc tham s ca hm xu th c tnh nh sau:212 . 12 . ( 1)t y nb Nm m mn n + _ ,=212 2443,19 5 1.775, 63 0, 7274 2.4 4.5(5 1)+ _ ,. 1. 2N mna bmn+ = 775, 63 4.5 10, 727 29, 74.5 2+ Hm xu th c dng: Y= 29,7+ 0,727t41Do m hnh nhn c dng: yt= (29,7+0,727t).ItvD bo sn lng ca doanh nghip nm 2007 theo cc qu l:- Qu I (t=21): Yt1= (29,7+ 0,727 x 21)x 0.7= 31,476- Qu I (t=22): Yt2= (29,7+ 0,727 x 22)x 0.838= 38,29- Qu I (t=23): Yt3= (29,7+ 0,727 x 23)x 1,08= 50,13- Qu I (t=24): Yt4= (29,7+ 0,727 x 24)x 1,376= 64,875Vi hm kt hp nhn ta c th d bo cho nhng nm tip theo2.4. D bo theo phng php san bng mPhng php san bng m ( hay cn gi l phng php d on bnh qun m) l mt phng php d on thng k ngn hn hin c s dng nhiu trong cng tc d on thc t trn th gii.Nu nh mt s phng php d on thng k cp trn coi gi tr thng tin ca cc mc trong dy s thi gian l nh nhau, phng php san bng m li coi gi tr thng tin ca mi mc l tng dn k t u dy s cho n cui dy s. V trn thc t nhng thi gian khc nhau th hin tng nghin cu chu s tc ng ca nhng nhn t khc nhau v cng khng ging nhau. Cc mc ngy cng mi ( cui dy s thi gian) cng cn phi c ch n nhiu hn so vi cc mc c ( u dy s). Hay ni cch khc, mc cng xa so vi thi im hin ti th cng t gi tr thng tin, do cng t nh hng n mc d on.Tu thuc vo c im dy s thi gian ( chui thi gian) c bin ng xu th, bin ng thi v hay khng m phng php san bng m c th s dng mt trong cc phng php c bn sau:2.4.1. M hnh n gin ( phng php san bng m n gin)iu kin p dng: i vi dy s thi gian khng c xu th v khng c bin ng thi v r rt.Trc ht, dy s thi gian c san bng nh c s tham gia ca cc s bnh qun m, tc l cc s bnh qun di ng gia quyn theo quy lut hm s m. Theo phng php ny, thi gian t no da vo cc gi tr thc t bit c lng gi tr hin ti ( thi gian t) ca hin tng v gi tr hin ti ny d ton gi tr tng lai (thi gian t+1). M hnh san bng m gin n c Brown xy dng nm 1954 da trn 2 nguyn tc:42- Trng s ca cc quan st trong dy s thi gian cng gim i khi n cng cch xa hin ti.- Sai s d bo hin tai ( k hiu et = yt- ty ) Phi c tnh n trong nhng d bo k tipGi s thi gian t, c mc thc t l yt, mc d on l tY .Mc d on ca hin tng thi gian (t+1) c th vit:)1(1 )t t tY y Y + + ( 2.10)t 1 , ta c: )1 t t tY y Y + +(2.11) vc gi l cc tham s san bng vi + =1 v , [ ] 0;1 .Nh vy mc d on 1 t Y+ l trung bnh cng gia quyn ca yt v tYvi quyn s tng ng l v- Mc d on ca hin tng thi gian t l: 11tt tY Y Y +thay vo (2.12) ta c: 21 11t tt tY y Y Y + + + (2.11)- Mc d on ca hin tng thi gian (t-1) l: 1 22t ttY Y Y +thay vo ( 2.12)Ta c: 2 31 21 2t tt t tY y Y Y Y + + + + (2.13)- Mcdoncahintngthi gian(t-2)l: 2 33t ttY Y Y + thay vo (2.13) Ta c: 2 3 41 41 2 3t tt t t tY y Y Y Y Y + + + + + ( 2.14)Bng cch tip tc tng t thay vo cc mc d on 3 4.... , t t Y Y ta s c cng thc tng qut. 111ni it t it iiY y Y ++ +(*)Trong :1 t Y+: S bnh qun m ti thi im t+143yt-i: Cc mc thc t ca ca hin tng ti thi im (t-i) (i=0 n)1 t Y: S bnh qun m ti thi im (t-i) ( i=0n) vc gi l cc tham s san bng( vl hng s vi + =1 v , [ ] 0;1 .)n: S lng cc mc ca dy s thi gianV [ ] 0;1 nn khi iTh 1 110 01i it iiiY + + 'Khi cng thc (*) tr thnh:11nitt iiY y + Nh vy: mc d on 1 t Y+ l trung bnh cng gia quyn cu cc mc ca dy s thi gian m trong quyn s gim dn theo dng m ( khi i=0 n) tu thuc vo mc c ca dy s. V th, phng php ny c gi l phng php san bng m. C 2 vn quan trng nht trong phng php san bng m.- Thnht: h s san bng m l h s san iu chnh trong s ca cc quan st ring bit ca dy s thi gian. V vy, khi la chn phi va m bo kt qu d bo s gn vi quan st thc t, va phi m bo tnh linh hot ( nhanh nhy vi cc thay i gn hin ti).Vi =1 th theo phng trnh d bo (1). Gi tr d bo 1 t Y+ bng gi tr thc t thi k ngay lin trc (Yt+1) v cc mc trc khng c tnh n.Vi =0 theo phng trnh d bo (1). Gi tr d bo 1 t Y+ bng gi tr d bo thi k trc (tY ) v gi tr thc t thi k ngay lin trc khng c tnh n.Nu c chn cng ln th cc mc cng mi s cng c ch , thch hp vi chui thi gian khng c tnh n nh cao.Ngc li, nu c chn cng nh th cc mc cng c s cng c ch , thch hp vi chui thi gian c tnh n nh cao.44Do , phi da vo c im bin ng ca hin tng qua thi gian v kinh nghim nghin cu la chon cho ph hp. Ni chung, gi tr tt nht l gi tr lm cho tng bnh phng sai s d on nh nht.SSE= $( ) mint ty y t et = yt- tyl cc sai s d on thi gian t hay cn gi l phn d thi gian t.Theo kinh nghim ca cc nh d bo th thch hp cho vn phng php san m c th c chn bng.21nn +: di chui thi gian- Th hai: Xc nh gi tr ban u ( iu kin ban u ) k hiu y0Phng php san bng m c thc hin theo php quy, tnh 1 t Y+ th phi c t Y, c t Yth phi c 1 t Y. Do tnh ton cn phi phi xc nh gi tr ban u (y0) da vo mt s phng php.+ C th ly mc u tin ca dy s.+ Trung bnh ca mt s cc mc ca dy sV d: C hai ti liu v doanh thu mt ca hng thng mi X qua mt s nm nh sau:NmCh tiu2002 2003 2004 2005 2006Doanh thu ( t ng)15y115,3y214,8y315,5y415,2y5Yu cu: D on doanh thu cho nm 2007 ca ca hng.Vi n= 5 =2 20, 31 5 1 n + +y0= 511 15 15, 3 15,8 15, 5 15, 25 5iiy+ + + + = 15,16 ( t ng)Cng thc tng qut vi n= 545i=05 $ $5111(1 ) (1 )i it i t t iiy y y + + + =1- $ $2 3 4 5 61 2 3 4 5 1 5( )t t t t t t t ty y y y y y y y + + + + + + +Vi t=5 dbo doanh thu 2007 l:$ $2 3 4 5 65 4 3 2 1 0 6 0( ) y y y y y y y y + + + + + +$2 364 5 62007 0, 3(15, 2 0, 7.15, 5 0, 7 .14,8 0, 7 .15, 30, 7 .15 0, 7 .15,16) 0, 7 .15,16 15,19y DT + + ++ + + * Hoc thay vo cng thc (1) ta c th s bo doanh thu hng nm ( t ng) nh sau:Vi t=0, ta c:$0 10(1 ) y y y + = 0,3 x 15,16+(1-0,3).15,16= 15,16Vi t=1, ta c: $ $1 2 1(1 ) y y y + = 0,3 x15 +(1-0,3).15,16= 15,112Vi t=2, ta c: $ $2 3 2(1 ) y y y + = 0,3 x 15,3 +(1-0,3).15,112= 15,1684Vi t=3 ta c: $ $3 4 3(1 ) y y y + = 0,3 x 14,8 + (1-0,3).15.1684= 15,05788Vi t=4 ta c: $ $4 5 4(1 ) y y y + = 0,3 x 15,5 + (1-0,3).15,05788= 15,19Vi t=5, ta c: $ $5 6 5(1 ) y y y + = 0,3 x 15,2 + (1-0,3). 15,19=15,193y l gi tr d on cho doanh thu ca Cng ty nm 20072.4.2. Mhnhxuthtuyntnhvkhngcbinngthi v(MhnhsanmHolt Winters)M hnh ny thng p dng i vi s bin ng ca hin tng qua thi gian c xu th l tuyn tnh v khng c bin ng thi v.- Gi s chng ta c dy s thi gian y1, y2, y3,, yn vi bin ng c tnh xu th.Bc 1: Chn cc h s , ( 0 < , < 1)Nu chn hng s san nh tc l chng ta coi cc mc hin thi ca dy s t nh hng n mc d bo. Ngc li nu chn hng s san ln tc l chng ta mun dy s san s m phn ng mnh vi nhng thay i hin ti.Bc 2: Tin hnh san m cho gi tr c lng v xu th ca dy s:46Coi gi tr ca dy s thi gian l tng ca 2 thnh phn: Thnh phn trung bnh c trng s ca cc gi tr thc t (k hiu l St gi tr c lng ca hin tng thi im t) v thnh phn xu th (k hiu l Tt). Ta c m hnh san s m: $1 t t ty S T+ +(2.15)Trong : 1 ( 1)(1 ) (1 )t t t t t tS y S T y S 1 + + + ](2.16)1 ( 1)( ) (1 ).t t t tT S S T + (2.17)t S2 = Y2T2 = Y2 Y1Tin hnh san s m t thi im th 3 tr i, ta c: 3 3 2 23 3 2 24 4 3 34 4 3 3(1 )( )( ) (1 )(1 )( )( ) (1 )...S Y S TT S S TS Y S TT S S T + + + + + + Bc 3: S dng mc v xu th c san s m ti thi im d on cho cc thi im trong tng lai d on gi tr ca hin tng thi im tng lai t + 1:$1 t t ty S T+ + (2.18) thi im tng lai (t + h) (h=2, 3 )$t t t hy S hT+ +(2.19)V d: Theo s liu ca tng cc thng k v GDP theo gi thc t ca Vit Nam qua thi gian nh sau:Nm Ch tiu2002 2003 2004 2005 2006GDP(t ng)421295 535762 613443 715307 839211p dng san m Holt Winters d on cho 5 nm tiBc 1: Chn h s san: = 0,7; = 0,6Bc 2: Tin hnh san s m cho mc v cho xu th ca dy s thi gian47S2= y2 = 535762T2= Y2 Y1 = 535762 421295 = 114467S3= Y3 + (1 - )(S2 + T2)= 0,7.613443 + (1-0,7)(535.762 + 114467)= 624478,8T3= (S3 S2) + (1- )T2= 0,6(624478,8 535762) + (1-0,6).114467 = 99016,88S4= Y4 + (1-)(S3 + T3)= 0,7.715307 + (1-0,7)(624478,8 + 99016,88)= 717763,6T4= (S4 S3) + (1- )T3= 0,6(717763,6 24478,8) + 0,4.99016,88 = 95577,63S5= Y5 + (1 - )(S4 + T4)= 0,7.839211 + 0,3(717763,6 + 95577,63) = 831450,07T5 = (S5 S4) + (1 - )T4 = 0,6(831450,07 717763,6) + 0,4.95577,63 = 106442,93Nh vy, mc d bo GDP ca nhng nm tip theo s l:$6y= S5 + T5 = 831450,07 + 106442,93 = 937893$7y= S5 + 2T5 = 831450,07 + 2.106442,93 = 1044335,93 (t ng)$8y= S5 + 3T5 = 831450,07 + 3.106442,93 = 1150778,86 (t ng)$9y= S5 + 4T5 = 831450,07 + 4.106442,93 = 1257221,7 (t ng)$10y = S5 + 5T5 = 831450,07 + 5.106442,93 = 1363664,63 (t ng)2.4.3. M hnh xu th tuyn tnh v bin ng thi vM hnh ny thng p dng i vi d bo thi gian m cc mc ca n l ti liu thng hoc qu ca mt s nm m cc mc trong dy s c lp li sau 1 khong thi gian h (h = 4 i vi qu, h = 12 i vi nm). Vic d on c th c thc hin theo mt trong hai m hnh sau: + M hnh cng $1 1 t t t ty S T V+ + + + (2.19)48Trong :[ ]1 ( 1)( ) (1 )t t t tS y V t h S T 1 + + ](2.20)1 ( 1)( ) (1 )t t t tT S S T + (2.21)( )( ) (1 )t t t t hV y S V + (2.22)+ M hnh nhn:$1 1( ).t t t ty S T V+ + + (2.23)Trong 1 ( 1)(1 )( )( )tt t tyS S TV t h + +1 1 1( )( ) (1 )(1 ).tt t ttt htT S S TyV VS + + Vi , , l cc tham s san bng nhn gi tr trong on [0;1]., , nhn gi tr tt nht khi tng bnh phng sai s l nh nht.$2( ) mint tSSE y y - Tham s , , khng c xt mt cch khch quan m t nhiu thng qua trc gic ch quan, kt qu d bo s ph thuc vo s la chn cc tham s ny.- Vi0a(0) c th l mc u tin trong dy s.- a1(0) c th l lng tng (gim) tuyt i trung bnh.Sj(0): L cc ch s thi v ban u (j=1,2,3,k); k = 4 i vi qu; k = 12 i vi thng.Nu t = 1, 2, 3, 4, 5,, n.L th t thi gian hay tng ng vi th t cc mc theo thi k trong chui thi gian th yu t thi v Vj(0) ca cc mc trong chui thi gian c tnh s tng ng vi cc gi tr t k.(0) ;j jV V xH

1kjjjVVkjV ch s bnh qun thi v cho mt qu hay mt thng ca mi nm trong chui thi gian.tjtyVyYt mc trong chui thi gian thi gian t.49Vj ch s thi v ca tng qu hoc thng trong tng nm nay thi gian t:tyS bnh qun trt loi tr thnh phn thi v v thnh phn ngu nhin vi s lng mc bng 4 i vi ti liu qu v bng 12 i vi ti liu thng.jkHVV d: Tr li v d mc (3.3.1), d on doanh thu ca cc qu theo m hnh nhn nh sau:V d: C ti liu v sn lng ca Doanh nghip (A) nh sau:Nm (t)QuSn lng (nghn tn) Cngtheo cng qu ( )jy 2002 2003 2004 2005 2006I 20 25 27 31 29 132II 25 32 30 37 36 160III 38 38 45 44 47 212IV 40 60 55 62 58 275Cngtheocng nm ( )jy123 155 157 174 170 779Mc bnh qun nm30,75 38,75 39,25 43,5 42,5S(0): Bnh qun ca 4 mc u tin (bnh qun nm)(0)20 25 38 4030, 754S+ + + T0: Lng tng tuyt i bnh qun ca qu058 20220 1T Cc ch s thi v Itv: ( tnh trong phn 3.2.2.)Qu I = 0,713 x 0,986 = 0,7Qu II = 0,85 x 0,986 = 0,838Qu III = 1,096 x 0,986 = 1,08Qu IV = 1,396 x 0,986 = 1,37650Vi cc tham s cho , , ln lt l: 0,4; 0,4; 0,8Nu phi la chn mt trong hai m hnh d on th tu thuc vo c im bin ng ca hin tng.i vi hin tng t bin i qua thi gian th dng m hnh cng.i vi hin tng bin i nhiu qua thi gian th dng m hnh nhn.* u, nhc im ca phng php san bng m:u im:n gin v c kt qu tng i chnh xc ph hp vi d on ngn hn cho cc nh kinh doanh cng nh lp k hoch ngn hn cp v m.- H thng d bo c th c iu chnh thng qua 1 tham s duy nht (tham s san bng m)- D dng chng trnh ho v ch phi thc hin mt s php ton s cp xc nh gi tr d bo.Hn ch:- Phng php san m ch b hp trong phm vi d bo ngn hn v khng tnh n s thay i cu trc ca chui thi gian m phi tun th tnh n nh theo thi gian ca cc qu trnh kinh t - xc hi.2.5. S dng chng trnh SPSS d bo theo cc m hnh2.5.1. D on bng hm xu th* Nhp ti liu+Mt ctl bintheoth t cc nm, mtctl thi gian (Years nm; Years, quarters nm, qu; Years, months (nm, thng) (nu l nm ta nhp chut vo years, nh s hin s 1900, ta xo i v nh s nm u tin trong dy s). * Thm d bng th * Analyze/ Regression/ curve Estimation- a y vo (Dependent) v Years vo Variable- Time/ Linear/ Display ANOVA table/ Save/ Predicted values/ Predict throug/ nh s nm cn d bo vo hnh ch nht ng sau year/ continue/ OK* Mt s kt quConstant tham s aTime tham s b512.5.2. D on bng san bng m* M hnh n gin- Nhp ti liu- Analyze/ Time Serier/ Exponential Smoothing- Save/ Do not create/ Continue/ OK- a Y vo hnh vung bn phi- Simple/ Parameters/ Grid search (nm trong hnh vung th nht General)/ Continue/ OK* M hnh xu th tuyn tnh khng bin ng thi v-ChnHolt/ Parameters/ GridSearch(cchGeneral hnhvungbntri)/ Grid Search (hnh vung bn phi c ch Trend)- Continue/ OK- Parameters- Nhp chut vo Value (tri) nh s 0.9- Nhp chut vo Value (phi) nh s 0.0- Continue/ Save/ Predict through/ nh s nm cn d bo vo Year/ Continue/ OK/ ng ca mn hnh Output s c kt qu d bo* M hnh xu th tuyn tnh c bin ng thi v- Nhp ti liu- Define Dates/ Year Quarters/ nh s nm u tin trong dy s vo hnh ch nht th nht.- Analyze/ Time Serier/ Exponental Smoothing/ Winters- a Y vo hnh vung di ch Variables- a Quarters vo hnh ch nht di ch Seasonal - Parameters/ GridSearch trongcc hnhvungca General (Alpha), Trend (Gramma), Seasonal (Delta)/ Continue/ OK./.52Chng 3: PHNG PHP HI QUY N V HI QUY BI V THNG K HI QUY* Phng php hi quyHi quy - ni theo cch n gin, l i ngc li v qu kh (regression) nghin cu nhng d liu (data) din ra theo thi gian (d liu chui thi gian - time series) hocdin ra ti cng mt thi im (d liu thi im hoc d liu cho - cross section) nhmtm n mt quy lut v mi quan h giachng. Mi quan h c biu din thnh mt phng trnh (hay m hnh) gi l: phng trnh hi quy m da vo , c th gii thch bng cc kt qu lng ho v bn cht, h tr cng c cc l thuyt v d bo tng lai. Theothut ngton, phntchhi quylsnghincumcnhhngcamt haynhiubins(bingii thchhaybinclp- independentvariable), n mt bin s (bin kt qu hay bin ph thuc - dependentvariable), nhm d bo bin kt qu da vo cc gi tr c bit trc ca cc bin gii thch. Trong phn tch hot ng kinh doanh cng nh trong nhiu lnh vc khc, hi quy l cng c phn tch y sc mnh khng th thay th, l phng php thng k ton dng c lng, d bo nhng s kin xy ra trong tng lai da vo quy lut qu kh. 3.1. Phng php hi quy n Cngi lhi quynbin, dngxt mi quanhtuyntnhgia1binkt quv1bingii thchhaylbinnguynnhn(nugiachngcmiquan h nhnqu). Trongphngtrnh hi quy tuyn tnh, mt bin gi l: binph thuc; mt bin kia l tc nhn gy ra s bin i, gi l bin c lp. Phng trnh hi quy n bin (ng thng) c dng tng qut: Y = a + bX (3.1)Trong : Y: bin s ph thuc (dependent variable); X: bin s c lp (independent variable); a: tung gc hay nt chn (intercept);b: dc hay h s gc (slope). Y trong phng trnh trn c hiu l Y c lng, ngi ta thng vit di hnhthc c nn ^Y53V d: Phng trnh tng chi ph ca doanh nghip c dng: Y = a + bX Trong : Y: Tng chi ph pht sinh trong k; X: Khi lng sn phm tiu th; a: Tng chi ph bt bin; b: chi ph kh bin n v sn phm; bX: Tng chi ph kh bin. th 3.1. ng x ca cc loi chi phNhn xtVi phng trnh trn, tng chi ph Y chu nh hng trc tip ca khilng hot ng X theo quan h t l thun. Khi X tng dn n Y tng; khi Xgim dn n Y gimKhi X = 0 th Y = a: Cc chi ph nh tin thu nh, chi ph khu hao, tinlng thi gian v cc khon chi ph hnh chnh khc l nhng chi ph bt bin, khng chu nh hng t thay i ca khi lng hot ng. ngbiudinasongsongvi trchonh. Tr salhscnh, thhin chi ph ti thiu trong k ca doanh nghip (nt chn trn th).Tr sbquyt nhdc(tcnghingcangbiudinchi ph trn th)ngtngchi ph Y=a+bXvngchi ph khbinbXsongsongvinhauv giachngccngchungmt dcb(slope). Xut pht imcangtngchi ph bt utnt chna (intercept =a) trntrc tung; trongkhi54XYHnh 4.9Y= a+ bXbX0a, ngchi ph khbinli bt utgctrctov cnt chnbng0(intercept =0). Hayni mt cchkhc, theoni dungkinht, khi khi lnghot ng bng 0 (X=0) th chi ph kh bin cng s bng 0 (bX=0). V d chi tit: C tnh hnh v chi ph hot ng (ti khon 641 v ti khon 642: chi phbn hng v chi ph qun l doanh nghip) v doanh thu (ti khon 511) ti mtdoanh nghip c quan st qua cc d liu ca 6 k kinh doanh nh sau: (n v tnh: triu ng). K kinh doanh Doanh thu bn hng Chi ph hot ng1 1.510 3232 1.820 3653 2.104 4124 2.087 4105 1.750 3546 2.021 403Bng 3.1. Tnh hnh thc hin chi ph ca 6 k kinh doanhYu cu:Phn tch c cu chi ph hot ng (bt bin, kh bin) cadoanhnghip. Hng dn: Yucucavnlthit lpphngtrnhchi ph hot ngcadoanhnghip, tci tmgitr ccthngsa, bvi mcchpht hinquylut bini cachi ph nytrcsthayi cadoanhthu, nhmnvicdbochiph cho cc quy m hot ng khc nhau hoc cho cc k kinh doanh tip theo. Phng trnh chi ph hot ng c dng: Y = a + bX Trong : a: Tng chi ph bt bin b: chi ph kh bin 1 n v doanh thu X: Doanh thu bn hng Y: Tng chi ph hot ng 55C nhiu phng php thng k tnh a, b nh: Phng php cc tr: Cn gi l phng php cn trn - cn di (High - low method). C th tm tr s a,b ca phng trnh theo v d trn bng cch s dng cng thcv cch tnh ton nh sau:b=Hiu s ca chi ph cao nht v thp nhtHiu s ca doanh thu cao nht v thp nhtTrong : Chi ph cc i: 412 Chi ph cc tiu: 323 Doanh thu cc i: 2.104Doanh thu cc tiu: 1.510 T phng trnh: Y = a +bX, suy ra: a = Y - bX; Ti im t doanh thu cao nht (high), ta c: a = 412 - 0,15 x 2.104 = 96,4 Ti im t doanh thu thp nht (low), ta c: a = 323 - 0,15 x 1.510 = 96,4 Phng trnh chi ph kinh doanh c thit lp: Y = 96,4 + 0,15X Lu : - Phng php cc tr rt n gin, d tnh ton nhng thiu chnh xc trong nhngtrng hp d liu bin ng bt thng. - Trng hp tp d liu c s quan st ln, vic tm thy nhng gi tr cc tr gpkh khn v d nhm ln, Microsoft Excel s cung cp mt cch nhanh chng v chnh xccc gi tr thng k: Max, min, range (=Max-Min) nh sau: Lnh s dng trong Microsoft Excel: Tools / Data Analysis/ Descriptive Statistics/OK / Summary Statistics / OK. b =412 - 323= 0,152.104 - 1.51056Column1 (doanh thu) Column2 (chi ph) Gii thchMean 1.882,00 Mean 377,83 Gi tr trung bnhStandard Error 94,92 Standard Error 14,80 Sai s chunMedian 1.920,50 Median 384,00 Trung vMode #N/A Mode #N/A Yu vStandard Deviation 232,50 Standard Deviation 36,26 lch chunSample Variance 54.056,40 Sample Variance 1.314,97 Phng sai (mu)Kurtosis -0,49 Kurtosis -1,30 chpSkewness -0,76 Skewness -0,58 nghingRange 594,00 Range 89,00 Khong (min)Minimum 1.510,00 Minimum 323,00 Gi tr ti thiuMaximum 2.104,00 Maximum 412,00 Gi tr ti aSum 11.292,00 Sum 2.267,00 Tng cng gi trCount 6,00 Count 6,00 S ln quan stBng 3.2. Kt qu cc i lng c trng thng k trong Microsoft ExcelNu trong Tools khng hin hnh sn Data Analysis, ta dng lnh:Tools / Add -Ins / Analysis ToolPak / OK. Gii thch cc thng s tnh c c th ti ct chi ph: Mean (gi tr trung bnh): l bnh qun s hc (Average) ca tt c cc gi tr quanst. c tnh bng cch ly tng gi tr cc quan st (Sum) chia cho s quan st (Count). 572, 2671377.836nXiiXn Standard Error(sai s chun): dng o tin cy ca gi tr trung bnh mu.c tnh bng cch ly lch chun (Standard Deviation) chia cho cn bc 2 ca s quanst.Ta c th ni: c kh nng 95% l gi tr trung bnh nm trong khong cng tr (+/-)2 ln sai s chun so vi gi tr trung bnh. Theo v d trn, l khong:[377,83- (2 x 14,8);377,83 + (2x14,8) tc l khong: [348,23 ; 407,43]Da vo cng thc trn ta cng thy rng: vi lch chun s khng i, n cng lnth S cng nh. Tc khong dao ng s hp hn v chnh xc s cao hn. Ngi ta cngda vo cng thc ny tnh s quan st cn thit n.Median(trung v): l gi tr nm v tr trung tm (khc vi gi tr trung bnhMean). c tnh bng cch:- Nu s quan st n l s l: sp xp cc gi tr quan st t nh n ln, gi tr ngv tr chnh gia l s trung v.- Nu s quan st n l s chn: sp xp cc gi tr quan st t nh n ln, trung bnhcng ca 2 gi tr ng v tr chnh gia l s trung v. Theo v d trn, ta sp xp cc quan st c gi tr t nh n ln: 323, 354, 365, 403,410, 412.Median =365 + 403= 3842Mode (yu v): l gi tr xut hin nhiu ln nht. Theo v d trn, ta khng c yu vno c (#N/A) Standard Deviation( lch chun): c xem nh l lch trung bnh, i dincho cc lch (hiu s) gia cc gi tr quan st thc v gi tr trung bnh (Mean). lchchun l i lng dng o mc phn tn (xa hay gn) ca cc gi tr quan st xungquanh gi tr trung bnh. c tnh bng cch ly cn bc hai ca phng sai 2 ( trung bnh ca phng cc lch: lch m- negative deviation v lch dng positive deviation)2 == 36,26( c l sagma )Sample Variance (phng sai mu): L trung bnh ca bnh phng cc lch.Ging nh lch chun, n cng dng xem mc phn tn cc gi tr quan st thc5836, 2614, 806SXn xung quanh gi tr trung bnh. c tnh bng cch ly tng cc bnh phng cc lch(tng cc hiu s gia gi tr quan st thc v gi tr trung bnh) chia cho s quan st tr 1(n - 1). Theo v d trn ta c:

2( )2 11.314,971nX Xiin (2c l sigma bnh phng )Kurtosis ( chp): l h s c trng thng k dng o mc ng nht cacc gi tr quan st. - ng cong rt chp (very peaked): nhn ng, kurtosis > 3. Nu ng biu dindi y m t phn phi cc gi tr doanh thu, ta c th ni rng a s cc gi tr doanh thurt gn vi nhau (the same revenue) d c mt s t mang gi tr rt nh hoc rt ln. -ng cong rt bt (very flat): phng nm, kurtosis < 3. Nu ng biu din diy m t phn phi cc gi tr doanh thu, ta c th ni rng a s cc gi tr doanh thuc tri u t nh n ln trong mt khong rng hn. Theo v d trn, chp bng: - 1,30Skewness ( nghing): l h s dng o nghing khi phn phi xc sutkhng cn xng theo hnh chung u. -Nghing v tri ta cn gi l nghing m (Skewned to the left), skewness < -1:nghing nhiu, > 0,5: nghing t. Nu ng biu din di y m t phn phi cc gi trdoanh thu, ta c th ni rng a s cc gi tr doanh thu gn vi doanh thu ln nht d c59mt s t mang gi tr nh hn hoc rt nh ( bn tri). -Nghing v phi ta cn gi l nghing dng (Skewned to the right), skewness >1: nghing nhiu, < 0,5: nghing t. Nu ng biu din di y m t phn phi cc gitr doanh thu, ta c th ni rng a s cc gi tr doanh thu gn vi doanh thu nh nht d cmt s t mang gi tr ln hn hoc rt ln ( bn phi). Theo v d trn, nghing bng: -0,58. Range (khong) also range width (hay b rng ca khong): l di ca khongquan st (khong bin thin), c tnh bng ly gi tr quan st cc i Max tr i gi trquan st cc tiu Min. Range = Max - Min = 412 - 323 = 89 Minimum (gi tr quan st cc tiu): gi tr nh nht trong cc quan st. Min = 323 Maximum(gi tr quan st cc i): gi tr ln nht trongcc quan st.Max = 412 Sum (tng cng gi tr ca cc quan st): l tng cng tt c cc gi tr ca tt c ccquan st trong tp d liu. Theo v d trn, ta c: 602.2671nSum Xii Count (s quan st): l s m ca s ln quan st (n). Theo tp d liu v d trn,ta c: n = 6 3.2. Phng php hi quy bi: Cn gi l phng php hi quy a bin, dng phn tch mi quan h gia nhiubin s c lp (tc bin gii thch hay bin nguyn nhn) nh hng n 1 bin phthuc (tc bin phn tch hay bin kt qu). Trong thc t, c rt nhiu bi ton kinh t - c lnh vc kinh doanh v kinh t hc,phi cn n phng php hi quy a bin. Chng hn nh phn tch nhng nhn t nhhng n thu nhp quc dn, s bin ng ca t gi ngoi hi; xt doanh thu trongtrng hp c nhiu mt hng; phn tch tng chi ph vi nhiu nhn t tc ng; phntch gi thnh chi tit; nhng nguyn nhn nh hng n khi lng tiu th Mt ch tiu kinh t chu s tc ng cng lc ca rt nhiu nhn t thun chiuhoc tri chiu nhau. Chng hn nh doanh thu l thuc v gi c, thu nhp bnh qun xhi, li sut tin gi, ma v, thi tit, qung co tip th Mt khc, gia nhng nhn tli cng c s tng quan tuyn tnh ni ti vi nhau. Phn tch hi quy gip ta va kimnh li gi thit v nhng nhn t tc ng v mc nh hng, va nh lng ccc quan h kinh t gia chng. T , lm nn tng cho phn tch d bo v c nhngquyt sch ph hp, hiu qu, thc y tng trng. Phng trnh hi quy a bin di dng tuyn tnh: Y = b0 + b1X1 + b2X2 + + biXi + bnXn + e (3.2)Trong :Y: bin s ph thuc (kt qu phn tch); b0: tung gc; b1: cc dc ca phng trnh theo cc bin Xi; Xi: cc bin s (cc nhn t nh hng); e: cc sai s Lu : Y trong phng trnh trn c biu hin l Y c lng, ngi ta thngvit di hnh thc c nn (Y)Mc tiu ca phng php hi quy a bin l da vo d liu lch s cc bin sYi, Xi, dng thut ton i tm cc thng s b0 v bi xy dng phng trnh hi quy d bo cho c lng trung bnh ca bin Yi. 61 lch (deviation): Yi--ng hi quy bnh qun ti thiu. t3.3. Phng php thng k hi quyCn gi l thng k hi quy n gin (simple regression statistical) dng phngphp thng k ton tnh cc h s a, b ca phng trnh hi quy da trn ton b quanst ca tp d liu. y l phng php ng tin cy nht v v vy i hi cng phu hn. Vn dng s liu v d trn, lp bng tnh cc tr s c s ri cn c vo cng thc tnh cc thng s ca phng trnh. Ta c cng thc trong thng k ton a = - b Chng minh cng thcCng thc trn c chng minh t phng php hi quy cc bnh phng ti thiuca cc hiu s ( lch : Deviation) gia cc gi tr quan st v gi tr c lng ca bins ph thuc( Y= a +bXi)Vi phng php tng cc bnh phng ti thiu, gi 2i e$ l bnh phng cc lch,ta c:== (3.3)Min(3.4)Gii h phng trnh vi phn tm gi tr cc thng s.Ly o hm ring phn theo a v cho bng 0:( )210ni iiY a bXa (3.5)Ly o hm ring phn theo a v cho bng 0:( )210ni iiY a bXb (3.6)Ly o hm ri cng chia cho -2 ( hay nhn vi ) ta c h phng trnh chun vi62 lch (deviation): Yi--ng hi quy bnh qun ti thiu. t( )( )12( )1nX X Y Yii ibnX Xii n quan st:2XY a X b X + (3.7)Y na b X + (3.8)Dng phng php kh, gii h phng trnh c 2 n s, ta ln lc c c gi trcc thng s a, b nh cc cng thc (1.3) v (1.4) nn trn. D dng thy c ngha cc lch ti thiu qua th sau: th3.2. lch ca cc tr quan st so vi gi tr c lngGii thch th: ng hi quy Y =a+ bX l ng c lng tt nht, cha cc gi tr c lngca Y m lch trung bnh gia chng v gi tr quan st thc l nh nht (ti thiu). Cc lch nm pha trn ng c lng nhn t gc ca trc to , gi l lch dng (Positive deviation); cc lch nm pha di ng c lng nhn tgc ca trc to , gi l lch m (Negative deviation). Ti sao l bnh phng ti thiu? Mc ch cui cng ca phng php hi quy l dng gii thch hoc d bo mti tng cn nghin cu. C th l i tm gi tr cc thng s a, b xy dng phngtrnh hi quy tuyn tnh (ng thng) c dng tng qut: Y=a+ bX.Migitr clng(clngim)lgitr clngtrungbnhim cabinkt quYi. Khnngch cthxyraccgitr trongmt khongc lng vi mt tin cy nht nh m thi. V xc sut gi tr thc Yi bng vi63 lch (deviation): Yi--ng hi quy bnh qun ti thiu. t0Yi^YXYXigi tr c lng imi Y l bng 0, hay ni cch khc l rt kh c kh nng xy ra. ngha ca phng php bnh phng ti thiu l lm sao cho lch trung bnhgia Yv Yi nh nht ( Yi- ^Y)0Trong , Yi l cc gi tr quan st thc v Y=a+ bX l cc gi tr c lng (gi trtrung bnh) ca Yi. Khi y, gi tr c lng gn vi gi tr quan st thc v phng trnh hi quydng d bo s tr nn kh thi, thch hp nht v chnh xc nht trong iu kin c th. Bng 3.3. Cc tr s c s thng kTrc ht, xt mc tng quan (correlation) gia bin s ph thuc v bin sc lp bng cng thc: N Xi Yi Xi2Yi2Xi YiiX X iY Y iX X iY Y ( )2iX X ( )2iY Y 1 1.510 323 2.280.100 104.329 487.730 -372 -55 20.398 138.384 3.0072 1.820 365 3.312.400 133.225 664.300 -62 -13 796 3.844 1653 2.104 412 4.426.816 169.744 866.848 222 34 7.585 49.284 1.1674 2.087 410 4.355.569 168.100 855.670 205 32 6.594 42.025 1.0355 1.750 354 3.062.500 125.316 619.500 -132 -24 3.146 17.424 5686 2.021 403 4.084.441 162.409 814.463 139 25 3.498 19.321 63311.292 2.267 21.521.826 863.123 4.308.511 0 0 42.017 270.282 6.57564( )2( )12 2( ) ( )1 1nX X Y Yii iRn nX X Y Yi ii i 2.267377,83 3786Y R = +1: tng quan hon ton v ng bin;R = -1: tng quan hon ton v nghch bin;R=cng gn 1:tng quan cng mnh (0,8< R 1,96, th hin s c ngha v mtthng k mc ngha 5% trong khong: cn trn -Upper, cn di - Lower. Cn trnv cn di ca Intercept l (118,44 ; 52,09) v ca Slope l (0,17 ; 0,14). Mt s ch tiu dng kim nh, nh ANOVA trong bng kt qu hi quykhng cp ht trong phm vi mn hc ny. 67Chng 4: PHNG PHP BOX - JENKINS (ARIMA)4.1. Tnh n nh ca mt chui Trc khi x l mt chui thi gian nghin cu cc tnh ngu nhin ca n l bc cn thit cho php ta nh gi mt cch tng qut v s liu nghin cu. Nu k vng ton v phng sai ca n thay i theo thi gian, chui c xem nh l khng n nh. Trong trng hp ngc li ta ni chui n nh. Xt chui yt, v mt ton hc mt chui n nh phi tha cc iu kin sau: E(yt) = E(yt+m) = cteky v m Var(yt) < kr

Cov(yt ;yt+k) = E ((yt - )( yt+k- ) = =hng s Vi tnh cht nh vy ta c th thy mt nhiu trng (gii thiu sau) l mt chui n nh v n tha mn tnh cht nu trn. Mt chui thi gian l n nh khi n l i din ca mt qu trnh nghin cu n nh. Ni mt cch c th hn l chui khng c tnh xu th, khng c tnh chu k 4.2. Hm s t tng quan n v t tng quan ring phn H s tng quan ring phn lh s dng nh gi quan h gia hai bin khinh hng ca bin th ba c loi tr Hm s t tng quan pk nhm xc nh s tng quan ca chui v chnh n nhng lch i mt chu k k bt k (xem bng sau). Cng thc xc nh hm s tng quan pk nh sau: Tnh cht: p 0 =1v p k = p -k Bng sau y gii thiu cch tnh hm t tng quan Kho st chui quan trc yt. Cc chui lch yt-k tng ng cng c gii thiu: 68k 0 1 2 3 4t ytyt-1ytytyt-21 1232 130 1233 125 130 1234 138 125 130 1235 145 138 125 130 1236 142 145 138 125 1307 141 142 145 138 1258 146 141 142 145 1389 147 146 141 142 14510 157 147 146 141 14211 150 157 147 146 14112 145 150 157 147 146Bng 4.1. Xc nh cc chui lch yt-kKt qu tnh gi tr trung bnh v phng sai ca cc chui v hm s t tng quan k c trnh by trong bng sau: Trung bnh yt 140.7 142.3 143.6 145.6 146.6Trung bnh yt-k140.7 140.3 139.4 137.4 136.2Phng sai yt95 72.4 62.8 27.1 22.2Phng sai yt-k95 101.8 101.8 74.9 71.4p k1 0.77 0.62 0.59 0.55Bng 4.2Vi nh ngha ca hm s t tng quan trn ta thy khng tin li trong vic tnh ton v n i hi phi li li khi tnh mi s hng rk Do trong thc t p dng ta thng tnh hm t tng quan cho mu bng mt cng thc n gin hn nh sau: vigi tr trung bnh ca chui tnh trn n chu k. Khi s lng quan trc ln, hai cch tnh gi tr hm t tng quan trn cho kt qu rt gn nhau (p k~ p -k) Hm s t tng quan ring phn bt ngun t khi nim tng quan ring phn. Vi khi nim ny cho php ta nh gi, v d, nh hng ca x1 ln x2 trong bi cnh loi ht cc nh hng ca cc bin khc x3 x4xk 69Tng t nh vy ta nh ngha hm t tng quan ring phn c mc tr k nh l h s tng quan ring phn gia yt v yt-k; c ngha l trong cc nh hng ca cc bin yt-l, yt-2 yk+l c loi b .4.3. Kim nh nhiu trng4.3.1. Phn tch hm t tng quan Mc ch ca phn tch hm t tng quan nhm xc nh kh nng c tnh t tng quan trong chui kho st (thng l chui sai s) hay khng. Khi chng ta phn tch hm t tng quan ca mt chui thi gian, mt cu hi lun lun t ra l cc h s p k no khc 0. Tht vy, nu ta hon ton khng c gi tr no ca p k khc 0 ta ni qu trnh nghin cu khng c >. N hon ton khng c tnh xu th cng nh khng c tnh chu k. V d trong trng hp nu chui c tnh chu k theo thng ta s thy gi tr ca p12 s ln (tng quan gia yt v yt-12) Chui chc chnc tnh chu k. Kim nh cho p k c gi tr khc 0 c thc hin da vo nguyn tc kim nh gi thit nh sau: H0: p k = 0 H1: p k0 Trong thc hnh, tc gi Quenouille chng minh c rng vi mt mu c kch thc tng i ln, h s p k tin mt cch tim cn v mt phn phi chun c gi tr trung bnh bng 0 v lch chun l Khong tin cyca h s pknh sau: vi n l s lng quan trc.Nu h s p k tnh c nm ngoi khong trn ta kt lun p k khc 0 vi ri ro% (thng ta ly=5%). 4.3.2. Tham s thng k ca Box-Pierce v Ljung-box Kim nh ca Box-pierce cho php nhn bit l nhiu trng hay khng. Chng ta phi kim nh Cov(yt,yt-k)=o V p k=0 vi. Mt qu trnh nhiu trng bt buc phi c: p 1=p 2=p 3==h chng ta c th kim nh ring l cc gi tr ca p, tuy nhin thng ta hay s dng gi tr thng k Q nh ngha bi Box-Pierce nh sau: Q=n vi h s lng ca s tr, p k gi tri t tng quan kinh nghim bc k v n ch s quan trc.Gi tr thng k Q tun theo gn nh mt phn phi c2 c bc t do h. Vi mc ri ro a% v bc t do h ta c gi tr co 70cho t bng tra. Nu c2 >c2a s .chp nhn gi thit H1: khng phi l mt nhiu trng. V ngc li ta s kt lun l mt nhiu trng. th sau y cho ta thy bin i ca mt nhiu trng. H.4.1

Biu tng quan n v biu tng quan ring phn tng ng ca chui ny nh sau: 71Hnh 4.2Trong thc hnh kho st l mt nhiu trng hay khng ta s s dng cc kim nh Bartleu v Quenouille. Kim nh lin quan n ln ca cc gi tr h s tng quan v tng quan ring phn.Khi ta thy cng ca nhiu ton b nm trong gii hn cho php, ta kt lun l mt nhiu trng. i vi trng hp hnh trn, ta nhn thy kim nh Quenoulle cn c gi tr vt qu gii hn, y cha phi l mt nhiu trng hon ton.4.4. M hnh AR(P) (Auto Regression) Trong mt qu trnh t hi quy bc p, s liu quan trc ti thi im hin ti yt c to ra bi mt tng trung bnh c trng s ca cc gi tr quan trc trong qu kh tnh cho n gi tr quan trc qu kh th p Cng thc nh ngha nh sau: AR(1): yt = q1*yt-l + et AR(2): yt = q1*yt-l +q2*yt-2 + et -------------------------------------------------------- AR(P): yt = q1*yt-l +q2*yt-2 + +qp*yt-p +et

Trong q1; q2; ; qpl cc thng s cn phi xc nh. etl mt nhiu trng ngu nhin c dng Gaussien. Chng ta cng c th thm vo qu trnh ny mt hng s m n vn 72khng nh hng n nh cht ngu nhin ca chui. Phng trnh trn c th vit di dng n gin hn nh vo nh ngha ton t lch pha D nh sau: ( 1- q1*D - q2D2 - . . .- qpDp)*yt = et Tnh cht: - Ngi ta chng minh biu tng quan n ca mt qu trnh AR(P) c m t bi mt cp s nhn c cng bi nh hn 1 (chui gim) c dng: p k = p -k - Biu tng quan ring phn chi c p s hng u tin l khc 0. Cc v d sau y cho php chng ta nhn bit m hnh dng AR da trn phn tch biu tng quan n v tng quan ring phn. Xt mt m hnh AR(L) c dng: yt = 1 + 0 9*yt-l+ et vi et l gi tr thng d. 73Cc biu tng quan ca m hnh trn c dng sau: Hnh 4.3Ta thy gi tr u tin ca biu tng quan ring phn rt ln so vi cc gi tr cn li v biu tng quan n c gi tr gim n. l biu th c th cho php chng ta nhn dng l mt m hnh AR(L). Xt mt m hnh AR(2) c dng: yt = 0 9*yt-2+1+ et Cc biu tng quan ca m hnh trn c dng sau: 74Hnh 4.4So vi trng hp trc ta thy c s khc nhau. Thay v gi tr th 1 nh v d trc, trng hp ny ta thy gi tr th 2 trong biu tng quan ring phn ln tri hn hn so vi cc gi tr cn li. Trong khi tnh cht ca biu tng quan n cng ging nh trc. iu ny cho php ta bit y l mt m hnh AR(2). Ta cng lu thm vi s hng AR(1) l khng ng k. 4.5. M hnh MA(q) (Moving Average) Trong mt qu trnh trung bnh ng bc q, s liu quan trc ti thi im hin ti yt c tnh bi tng trung bnh c trng s gi tr ca cc nhiu ngu nhin cho n nhiu th q. Cng thc nh ngha nh sau: . MA(1):yt = et - a1*et-1 MA(2):yt =et - a1*et-1- a2*et-2 -------------------------------------------------------------------- MA(q):yt = et - a1*et-1- a2*et-2-- aq*et-q 75Trong a1, a3, , ap l cc thng s cn phi xc nh et l mt nhiu trng ngu nhin c dng Gaussien. Phng trnh trn c th vit di dng n gin hn nh vo nh ngha mt ton t lch pha D nh sau: (l -a1D- a2D2 -...- apDp) et = yt

Trong qu trnh dng ny cng nh tt c cc m hnh t hi quy cc nhiu ngu nhin c gi thit l c to ra bi mt Chng ta c th hiu qu trnh trung bnh ng l mt chui thi gian dao ng ngu nhin chung quanh gi tr trung bnh ca chng. Tnh cht: - Chui trung bnh ng bc 1 chnh l mt qu trnh t hi quy bc p v hn. - Biu tng quan n ca mt qu trnh trung bnh ng bc q, MA(q), c xc nh bi: p k = khi p k = 0khik>q iu ny c ngha l ch c q s hng u tin ca biu tng quan l khc 0. i vi biu tng quan ring phn s c m t bi mt chui cp s gim theo hng cc chm pha trong qu kh. Cc v d sau y cho php chng ta nhn bit theo kinh nghim, hnh dng MA da trn c s phn tch biu tng quan n v tng quan ring phn. Xt mt m hnh MA(L) c dng: yt = 5 + et + 0.9*et-1 vi et l gi tr thng d thi im t 76Hnh 4.5Cc biu tng quan ca m hnh trn c dng sau: Ta thy gi tr u tin ca biu tng quan n vt tri so vi cc gi tr cn li v biu tng quan ring phn gim dn dn. l dng c th ca mt m hnh MA c bc l 1. Xt trng hp cho mt m hnh MA(2) c dng: yl = 5 +et + 1 . 1 et-2Cc biu tng quan ca m hnh trn c dng sau: Trong trng hp ny, thay v gi tr u tin trn biu tng quan c gi tr ln tri nh trc, ta thy gi tr th 2 trn biu ny ln tri hn so vi cc gi tr cn li v gi tr ca biu tng quan ring phn gim dn dn; l biu th c th ca mt m hnh MA(2). 4.6. M hnh ARMA(p,q) M hnh ARMA(p,q) l mt qu trnh c to ra bi t t hp gia cc gi tr ca chui trong qu kh v cc gi tr ca nhiu trong qu kh. N c xc nh bi phng trnh sau y: 77Ta c th ni y l mt m hnh c c t s tng hp ca 2 loi m hnh AR v MA. Tnh cht: ARMA( 1 ,0)=AR( 1 ); ARMA(0, 1 )=MA( 1 )Ta ch trong trng hp ny, biu tng quan n v biu tng quan ring phn s phc tp hn so vi 2 trng hp trn. Do vy chng ta phi lu khi xc nh cc thng s p,q ca m hnh ARMA t cc biu ny. V d 5Xt m hnh ARMA(L,l) sau y: y = 5 + 0.8yt-l + 1 . l Cc biu tng quan ca m hnh trn c dng sau: Hnh 4.6 Vi biu trn ta thy y l mt s pha ln gia hai loi m hnh AR v MA. Ta thy u c gi tr u tin vt tri trong cc biu tng quan. Cng trong cc biu cng tt dn. D on bc ca m hnh i hi phi c mt kinh nghim nht nh. 784.7. M hnh ARMA m rng: ARIMA, SARIMA Trong trng hp chui quan trc c xu th khng n nh (c xu th tng hoc gim theo thi gian), ta nh ngha mt m hnh c dng ARMA(p,d,q) vi d l bc ca ng xu th. Ni mt cch khc i, d biu th cho s ln ly cn thit ln chui quan trc ta c th nhn c mt chui nghin cu c tnh n nh theo xu th. V d trong trng hp chui c xu th tuyn tnh ta c d=l; trong trng hp ng xu th l mt hm bc 2 ta c d=2. Tht vy gi s chui c mt xu th tuyn tnh biu th bi phng trnh sau y: y =a+btnh ngha sai bit bc 1 Dyt ta c: Dyt =yt-yt-1 =(a+bt)-(a+b[t1])=b=cte Ta thy chui sai bit bc 1 c xu th n nh. Trong trng hp c xu th bc 2 phng trnh c dng: yt =a+bt+ct2 Tnh sai bit bc 1 ta c: Dyt =yt-yt-1 = (a+bt+ct2)-(a+b[t-l]+c*[t-1]2)=b-c+2tc Ta thy chui Dyt c xu th bc 1 . c xu th n nh ta ch cn tnh thm mt ln na cho s khc bit nh trng hp ta c trong trng hp xu th l tuyn tnh trn. Nh vy ta c hai ln ly sai bit cho trng hp bc 2 ny chui quan trc tr nn n nh v xu th. Tm li ta c th vit chui (l-D)d*ytl mt ARMA(p,q) khi ytl mt ARIMA(p,d,q); vi D c nh ngha l ton t sai bit: D(yt)=yt- yt-l M hnh SARIMA cho php gii quyt vn sai bit lin quan n bin i ma. S bin i c nh ngha nh sau: (1 - Ds)*yt = yt - yt-s vi s biu th tnh chu k ca s liu (s=4 cho mt chui bin i theo qu, s=12 cho chui bin i theo thng). Ch : Chng ta chi p dng m hnh ARMA nghin cu cho cc chui khng c xu th. 794.8. Phng php Box - Jenkins Di y nghin cu mt cch c h thng cc dng khc nhau ca chui thi gian da vo cc tnh cht ca n. Mc tiu l tm trong s tt c cc m hnh ARIMA (AR: t hi quy, MA: trung bnh ng, I: thng s cho bit bc cn thit c th to mt chui n nh) 1 m hnh thch hp nht vi s liu ca hin tng nghin cu. Phng php bao gm 3 bc chnh sau y: Bc 1: Tm cc m hnh thch hp nht y l bc quan trng v kh nht. N cho php nhn bit c trong h tt c cc m hnh ARLMA m hnh no l c kh nng thch hp nht. Phng php da vo nghin cu cc biu tng quan n v cc biu tng quan ring phn. Mt vi nguyn tc sau y cho php tm cc thng s p,d,q ca m hnh ARIMA. * Kh tnh chu k n gin trong trng hp chui nghin cu c cha yu t bin i c tnh chu k ta nn > yu t ny trc khi i vo cc x l thng k nhm n gin ha cho cc bc tnh sau. * Kho st v xc nh bc ca xu th nu c Trong trng hp biu tng quan n gim chm hoc hon ton khng gim, chui c cha mt xu th. Trong trng hp ny ta s loi tnh xu th n nh vo p dng ca ton t sai bit ln chui. Trong thc t ta c th gp trng hp d=l hoc 2. Gi tr thch hp ca d s cho ta mt biu tng quan n c xu th gim nhanh. * Xc nh p,q ca m hnh ARMA nh vo biu tng quan - Nu biu tng quan n ch c q gi tr u tin l khc 0 (q=3 l ln nht) v cc gi tr ca biu tng quan ring phn gim t t ta c th tin on c mt MA(q). - Nu biu tng quan ring phn ch c p gi tr u tin l khc 0 (p=3 l ln nht) v cc gi tr ca biu tng quan n gim t t ta c th tin on c mt AR(P). - Nu biu tng quan n v biu tng quan ring phn khng c s ct ngn nh hai trng hp trn, ta s c mt qu trnh ARMA v cc thng s ca n ty thuc vo dng c th ca cc biu tng quan. Trong thc hnh,phng php phn tch th ch cho ta tmcpqtrong cc trng hp n gin m thi. Trong trng hp tng qut, ta c th p dng cc tiu chun sau y xc nh cc thng s p, q trong mt m hnh ARMA. Thc cht chung ca cc tiu chun ny l da vo s kho st cc gi tr lin quan n phng sai ca chui sai s cho bi m hnh vi thng s ngh. 80C 3 tiu chun thng dng c s dng nh sau: Tiu chun Akaike: Akaike = Log(%rss) + 2Tiu chun BIC: BIC = Log(%rss) + (p + q) * Tiu chun HQ: HQ = Log(%rss) + 2(p + q) * 270 vi: %rss : tng cc thng d bnh phng ca m hnh ngh %nobs : s lng quan trc. Trong trng hp l tng, gi tr chn ca p,q tng ng vi trng hp cho ta cc gi tr Akaike, BIC, HQ cc tiu. Trong p dng ta c th c trng hp gi tr p,q ngh khng lm cho 3 tiu chun ny ng thi cc tiu. Tuy vy thng cc tiu chun ny cho gi tr p,q ti u khng khc nhau ln. Trong trng hp ny ta s kho st tng t hp (p,q) c th quyt nh chn m hnh hp l nht. Bc 2: c lng cc h s ca m hnh Trong trng hp m hnh AR(P), tc gi p dng phng php bnh phng ti thiu hay s dng quan h gia tnh t tng quan v cc h s ca m hnh (phng trnh Yule Walker). c lng cc h s cho m hnh MA(Q) tng i phc tp hn. Cc tc gi ngh s dng mt phng php lp di dng qut m chng ta c th hiu mt cch n gin nh sau. Gi s ta c 1 m hnh ARMA(2,2) xc nh bi: (l-q1D-q2D2)yt = (l-aD1-a2D2)*et v Chng ta c th vit di dng: yt = Ta t: 81Do : T chng ta c th khi u bng cch tnh qut vi 2 khong gi tr chp nhn c cho a1 v a2 v vi mt gia s cho trc. Tip theo, cho mi cp gi tr ca a1 v a2 ta t no = o V n1 =o v Chng ta s c lng gi tr ca vl theo cc bc sau: n2 = y2 n3= y3 + a2 n2 n4= y4 + a1 n1+a2 n2 etc.... sau khi tnh tt c cc gi tr ca nt ta s c lng cc thng s q1 V q2 bi phng php bnh phng ti thiu p dng vo phng trnh sau: nt= q1nt-1 + q2nt-2 +

et

v chng ta s ly gi tr al, a2 sao cho cc tng bnh phng ca cc thng d t phng trnh hi quy trn ti thiu. Ch phng php ny ch c gi tr trong trng hp s lng cc thng s cn xc nh khng nhiu lm. Ngoi phng php bnh phng ti thiu ta cn c th p dng phng php cc i ha cc hm tng thch. Bc 3: Kim tra gi tr ca m hnh v d bo Sau khi cc thng s ca m hnh c xc nh, chng ta s kim nh cc kt qu ca c lng ny. Cc h s ca m hnh phi khc 0 (kim nh Student c in). Nu c mt hay nhiu h s khng tha mn, ta s loi b n ra khi m hnh AR hoc MA ang xt. Phn tch cc gi tr thng d c thc hin t 2 tiu chun sau: - Gi tr trung bnh s hc trit tiu, trong trng hp ngc li ta nn thm mt hng s vo m hnh. - Chui gi tr thng d l mt nhiu trng. Cc gi tr th.ng k ca Box-pierce v ca Ljung-box cho php kim nh tnh cht ny. Nu n khng phi l mt nhiu trng ta kt lun m hnh l khng hon chnh v ta phi thm vo m hnh cc bc b sung cn thit. - Bc kim nh m hnh rt quan trng? v c th ta phi tr li bc th 1 nu m hnh ngh khng thch hp. Mt khi m hnh c kim nh, ta c th tin hnh d bo gii hn trong mt vi chu k. Phn tch chui thi gian vi m hnh SARLMA ch cho php 82tin hnh cc d bo ngn hn. N khng cho php mt d bo trung hn v di hn vi chnh xc cn c, v bin ca sai s gia tng rt nhanh trong trng hp ny. Chng ta co th tm tt cc bc c bn ca phng php Box-Jenkins nh sau:

Vi d:p dng phng php Boxjenkins Doanh thu ca mt cng ty trong chu k 01/82 n 09/90 c trnh by bi th sau y: 83Tm cc thng tin thch hp, kh tnh chu k, kho st v xc nh bc ca xu thPhn tch biu tng quan n v tng quan ring phn: xc nh bin p,q ca m hnh AR v MAD boY= a+ bXc lng cc h s ca m hnhKim tra m hnh: Phn tch cc h s v thng dD boY= a+ bXc lng cc h s ca m hnhHnh 4.7 Hy phn tch chui trn bng phng php Box-jenkins v d bo cho doanh s trong 6 thng tip theo (lo/90 - 3/91). Hng dn (Kt qu tnh ton c thc hin vi logiciel RATS) Biu tng quan n v biu tng quan ring phn ca chui trn nh sau:84Ta thy trn cc biu tng quan xut hin 1 > rt r khi k=12. Nhn xt ny cho ta kt lun s liu c tnh chu k (T=12 thng). kh tnh chu k trong chui, ta s nh ngha chui Yt nh vo mt bin i nh sau: Yt = yt - yt-12 ; t

Biu tng quan n v biu tng quan ring phn ca chui Yt trn nh sau: Ta thy biu tng quan c cng gim n rt chm, iu ny c ngha l ta c mt xu th trong s liu. kh xu th ta p dng bin i sau:(D)Yt = Yt - Yt-1 ;Biu tng quan ca D(YT) nh sau: 85Hnh 4.8Ta thy gi tr u tin ca biu tng quan n ln hn hn s vi cc gi tr tip theo, trong khi gi tr ca biu tng quan ring phn gim t t; ta c th d on y l mt m hnh c dng MA(1). Tm li m hnh ngh cho chui s liu trn nh sau SARIMA(0,1,1) vi s=12. Kt qu cho t logiciel RATS nh sau: Bin nghin cu VENTE -c lg bi Box-Jenkins S ln lp 21 Chui s liu 83:02 n 90:09 S quan trc hiu dng 92 Bc t do 90 H s xc nh R**20.921215H s xc nh hiu chnh 0.920340 Gi tr bin nghin cu 646. 71640217 lch chun ca/ bin nghin cu365.927404 Sai s chun ha ca c lng103.28000630 Tng c c thng d bnh phng 960008.37314 Gi tr thng k Durbin-watson1.751202 Gi tr thng k ca Ljung-box Q(23-2) 29.883511 a tng ng ca Q 0.09435394 86Hnh 4.9 BinH s lch chun T-student a ****** ****************************************************************** 1 AR(12) 1.0581690.03280332.258040.000 2. Ma(1) 0.8208170.060968 -13.463070.000

Biu tng quan n v biu tng quan ring phn ca thng d cho bi m hnh c chn t phng php Box Jenkins nh sau:87 nh gi cht lng ca m hnh ta phi kim tra xem gi tr thng d trn c phi l mt nhiu trng hay khng. Sau y l kt qu ca kim nh Bartlett v Quenouille: Ta thy cng ca h s tng quan n v tng quan ring phn hon ton nm trong gii hn cho php trong c 2 loi kim nh. Do chui gi tr thng d cho bi m hnh chn l mt nhiu trng nhmong i. 88D bo ngn hn: Tin hnh d bo ngn hn v doanh s ca cng ty cho bi m hnh Box-jenkins c trnh by trong bng sau: Thi gian 90:10 90:11 90:12 91:01 91:02 91:03 91:04D bo 1055.3 1480.7 1901.4 676.1 561.8 561.8 714.6 th sau biu din tng hp gia doanh thu trong qu kh v d bo ngn hn ca cng ty nh sau: 8990Chng 5: DY S THI GIAN5.1.Khi nim Mt lng ca hin tng thng xuyn bin ng qua thi gian. Trong thng k nghin cu s bin ng ny ta thng da vo dy s thi gian. Dy s thi gian l dy s cc tr s ca ch tiu thng k c sp xp theo th t thi gian. V d: c s liu v doanh thu ca Bu in X t nm 1999 -2003 nh sau: VT: t ng.Nm 1999 2000 2001 2002 2003Doanh thu 23,9 28,1 37,3 47,2 67,4.Bng 5.1V d trn y l mt dy s thi gian v ch