KHOA CNG NGH THNG TIN B MN HTTT KINH T ===========

NGUYN TH THANH HUYN Th.s NGUYN VN HUN V XUN NAM PHN TCH V D BO KINH T Thi Nguyn, 2009 Su tm bi: www.daihoc.com.vn 1Mc lc Chng 1: TNG QUAN V PHN TCH V D BO KINH T......................... 3 1.1. Khi nim............................................................................................................. 3 1.2. ngha v vai tr ca phn tch v d bo trong qu trnh ra quyt nh kinh doanh........................................................................................................................... 3 1.2.1. ngha.......................................................................................................... 3 1.2.2. Vai tr............................................................................................................ 4 1.3. Cc loi d bo .................................................................................................... 4 1.3.1. Cn c vo di thi gian d bo:............................................................. 4 1.3.2. Da vo cc phng php d bo:............................................................... 5 1.3.3. Cn c vo ni dung (i tng d bo)...................................................... 5 1.4. Cc phng php d bo..................................................................................... 7 1.4.1. Phng php d bo nh tnh...................................................................... 7 1.4.1.1. Ly kin ca ban iu hnh................................................................ 7 1.4.1.2. Ly kin ca ngi bn hng............................................................. 7 1.4.1.3. Phng php chuyn gia (Delphi). ....................................................... 8 1.4.1.4. Phng php iu tra ngi tiu dng.................................................. 8 1.4.2. Phng php d bo nh lng .................................................................. 8 1.4.2.1. D bo ngn hn ................................................................................... 9 1.4.2.2. D bo di hn .................................................................................... 14 1.5. Quy trnh d bo................................................................................................ 23 Chng 2: CC PHNG PHP PHN TCH V D BO................................. 26 2.1. D bo t cc mc bnh qun....................................................................... 26 2.1.1. D bo t s bnh qun trt (di ng)...................................................... 26 2.1.2. M hnh d bo da vo lng tng (gim) tuyt i bnh qun............... 27 2.1.3. M hnh d bo da vo tc pht trin bnh qun ................................ 28 2.2. M hnh d bo theo phng trnh hi quy (d bo da vo xu th) ............... 31 2.2.1. M hnh hi quy theo thi gian ................................................................... 31 2.2.2. M hnh hi quy gia cc tiu thc............................................................. 34 2.3. D bo da vo hm xu th v bin ng thi v............................................. 34 2.3.1. D bo vo m hnh cng ........................................................................... 35 2.3.2. D bo da vo m hnh nhn.................................................................... 37 2.4. D bo theo phng php san bng m ............................................................ 40 2.4.1. M hnh n gin ( phng php san bng m n gin) ......................... 40 2.4.2. M hnh xu th tuyn tnh v khng c bin ng thi v ( M hnh san mHolt Winters) ...................................................................................................... 44 2.4.3. M hnh xu th tuyn tnh v bin ng thi v.......................................... 46 2.5. S dng chng trnh SPSS d bo theo cc m hnh................................. 49 2.5.1. D on bng hm xu th ........................................................................... 49 2.5.2. D on bng san bng m ........................................................................ 50 Su tm bi: www.daihoc.com.vn 2Chng 3: PHNG PHP HI QUY N V HI QUY BI V THNG K HI QUY..................................................................................................................... 51 3.1. Phng php hi quy n.................................................................................. 51 3.2. Phng php hi quy bi:.................................................................................. 59 3.3. Phng php thng k hi quy.......................................................................... 60 Chng 4: PHNG PHP BOX - JENKINS (ARIMA) ......................................... 67 4.1. Tnh n nh ca mt chui ............................................................................... 67 4.2. Hm s t tng quan n v t tng quan ring phn.................................. 67 4.3. Kim nh nhiu trng ....................................................................................... 69 4.3.1. Phn tch hm t tng quan...................................................................... 69 4.3.2. Tham s thng k ca Box-Pierce v Ljung-box ........................................ 69 4.4. M hnh AR(P) (Auto Regression).................................................................... 71 4.5. M hnh MA(q) (Moving Average)................................................................... 73 4.6. M hnh ARMA(p,q) ......................................................................................... 75 4.7. M hnh ARMA m rng: ARIMA, SARIMA................................................. 77 4.8. Phng php Box - Jenkins ............................................................................... 78 Chng 5: DY S THI GIAN ............................................................................... 89 5.1.Khi nim.......................................................................................................... 89 5.2. Cc ch tiu phn tch......................................................................................... 90 5.2.1. Mc trung bnh theo thi gian ............................................................... 90 5.2.1.1 i vi dy s thi k.......................................................................... 90 5.2.1.2. i vi dy s thi im..................................................................... 91 5.2.2. Lng tng hoc gim tuyt i ................................................................. 92 5.2.2.1. Lng tng (gim) tuyt i tng k (lin hon) ............................... 92 5.2.2.2. Lng tng (hoc) gim tuyt i nh gc........................................ 92 5.2.2.3. Lng tng gim tuyt i trung bnh ................................................ 92 5.2.3. Tc pht trin ......................................................................................... 93 5.2.3.1. Tc pht trin tng k (lin hon................................................... 93 5.2.3.2. Tc pht trin nh gc .................................................................. 93 5.2.3.2. Tc pht trin trung bnh................................................................ 93 5.2.4. Tc tng hoc gim................................................................................ 93 5.2.4.1. Tc tng (gim) lin hon (tng k) .............................................. 93 5.2.4.2.Tc tng gim nh gc................................................................. 94 5.2.4.3. Tc tng (gim) trung bnh ............................................................ 94 5.2.5.Tr tuyt i ca 1% tng (hoc gim) ...................................................... 94 5.3.Cc phng php biu hin xu hng pht trin ca hin tng....................... 94 5.3.1. Phng php m rng khong cch thi gian............................................ 94 5.3.2. Phng php s trung bnh trt................................................................ 95 5.3.3. Phng php hi quy .................................................................................. 96 5.3.4. Phng php biu hin bin ng thi v .................................................. 99 Su tm bi: www.daihoc.com.vn 3Chng 1: TNG QUAN V PHN TCH V D BO KINH T 1.1. Khi nim Dbohnhthnhtunhngnm60cathk20.Khoahcdbovit cch mt ngnh khoa hc c lp c h thng l lun, phng php lun v phng php h ringnhmnngcaotnhhiuqucadbo.Ngitathngnhnmnhrngmt 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 .Nhvy,dbolmtkhoahcvnghthuttinonnhngsvicsxyra trongtnglai,trncsphntchkhoahcvccdliuthuthpc. Khi tin hnh d bo ta cn c vo vic thu thp x l s liu trong qu kh v hin ti xcnhxuhngvnngcacchintngtrongtnglainhvomtsmhnh 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 doanh 1.2.1. ngha - Dng d bo cc mc tng lai ca hin tng, qua gip cc nh qun tr doanhnghipchngtrongvicracckhochvccquytnhcnthitphcv 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 sphttrintrongthigianti(khochcungcpccyutuvonh:laong, 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. Su tm bi: www.daihoc.com.vn 4- D bo chnh xc s gim bt mc ri ro cho doanh nghip ni ring v ton b nn kinh t ni chung. - 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 -Cngtcdbolmtbphnkhngththiutronghotngcaccdoanh 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 bo 1.3.1. 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. -Dbongnhn:Lnhngdbocthigiandbodi3nm,loidbony 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 loiny chmang tnh tng ituthuc 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 Su tm bi: www.daihoc.com.vn 5thigiandbothitit.Vvy,thangthigiancthobngnhngnvthchhp( v d: qu, nm i vi d bo kinh t v ngy i vi d bo d bo thi tit). 1.3.2. 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 chquantccchuyngia.Phngphpnycuthtrongtrnghpdonnhng 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 phngphpDelphilphngphpdbodatrncssdngmttphpnhng nhgicamtnhmchuyngia.Michuyngiachikinvridbocah 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.-Dbotheophngtrnhhiquy:Theophngphpny,mccndbophi 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 ngcahintngnhngthigianquaxcnhmccahintngtrong 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. Su tm bi: www.daihoc.com.vn 6- 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 d 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 trinkinhtvxhicatncctnhnsphttrincatnhhnhthgiivcc 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, ngthivccutiudung,thunhpcanhndn;ngthikinhtqucdnvs chuyndchccu(nhp,tl,hiuqu);sphttrincckhuvcvngnhkinht(khi lng ng thi, c cu, trnh k thut , b my, cc mi lin h lin ngnh); phn vngsnxut,khaithctinguynthinnhinvphttrinccvngkinhttrongnc, 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 phttrinkinhtngn,xydngccchngtrnh,khochphttrinmtcchch 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:+Dbothitit:Thngbothititdkintrongmtthigiannhtnhtrnmt 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). +Dbothuvn:Lloidbonhmtnhxcnhtrcsphttrinccqa 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, khtngthuvn,dbosxuthincahintnghayyutcnquantm.Cnc thigiandkin,dbothuvncchiathnhdbothuvnhnngn(thigian 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 thuvn gy nguyhim. Theo mc ch dbo, c cc loi: d bo thuvn phc v thicng, 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. Su tm bi: www.daihoc.com.vn 7+Dboal:Lvicnghincuvhngphttrincamitrngaltrong tng lai, nhm ra trn c s khoa hc nhng gii php s dng hp l v bo v mi trng. + 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 bo 1.4.1. Phng php d bo nh tnh Cc phng php nyda 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 hnh Phng php ny c s dng rng ri cc doanh nghip.Khi tin hnh d bo, hlykincaccnhquntrcpcao,nhngngiphtrchcccngvic,ccb phn quan trng ca doanh nghip, v s dng cc s liu thng k v nhng ch tiu tng hp:doanhs,chiph,linhun...Ngoiracnlythmkincaccchuyngiav 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 hng Nhng 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.Tphpkincanhiungibnhngtinhiukhuvckhcnhau,tacc 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. Su tm bi: www.daihoc.com.vn 81.4.1.3. Phng php chuyn gia (Delphi). Phng 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.-Davobngtmttnynhnvindbolitiptcnuracccuhicc chuyn gia tr li tip.-Tphpcckinmicaccchuyngia.Nuchathamnthtiptcqu 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 dng Phngphpnysthuthpngunthngtintitngngitiudngvnhu cu hin ti cng nh tng lai. Cuc iu tra nhu cu c thc hin bi nhng nhn vin bnhnghocnhnvinnghincuthtrng.Hthuthpkinkhchhngthngqua 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 lng M 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 thsdngthngquachuithigianvccgitrnycquanstolngccgiai 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 Su tm bi: www.daihoc.com.vn 9bo 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.Ngi ta thng dng sai lch tuyt i bnh qun (MAD) tnh ton: Tng cc sai s tuyt i ca n giai on MAD = n giai on 1ni=Nhu cu thc t- nhu cu d bo MAD= n 1.4.2.1. D bo ngn hn D 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:Su tm bi: www.daihoc.com.vn 10* 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 hng khc nhau trnkt qu d bo, v th, ngi ta thchs dng quyn skhng 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 iiFntkii=== Vi:Ft - D bo thi k th t At-i - S liu thc t thi k trc (i=1,2,...,n) ki - Quyn s tng ng thi k i Vd:Gisrngtacquynscatungnnhtl3,cch2tuntrcl2,5; 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: (115x1)+(120x1,5)+(80x2)+(95x2,5)+(100x3) F18= 10 = 99,25 hay 993 triu ngC2phngphpbnhqundingvbnhqundingcquynsucu imlsanbngcccbinngngunhintrongdys.Tuyvy,chnguc nhc im sau: -Dovicsanbngccbinngngunhinnnlmgimnhycmivi 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 ttnht.Nchthhinsvnngtrongqukhchchathkodisvnng trong tng lai. Su tm bi: www.daihoc.com.vn 11* 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 casaisdbogiaiontrcvctnhbngcchnhnsdbocagiaion 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-1 V 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 l th 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 = 85 F9 = 85 + 0,1(102 - 85) = 86,7 F9 = 85 + 0,2(102 - 85) = 88,4 =0,2 Sau ta tnh lch tuyt i bnh qun MAD cho 3 d bo ni trn: Su tm bi: www.daihoc.com.vn 12 = 0,1= 0,2= 0,3D boADD boADD boAD Tun l Nhu cu d tr thc t 810285,017,085,017,085,017,0 911086,723,388,421,690,119,9 109089,01,092,72,796,16,1 1110589,115,992,212,894,310,7 129590,74,394,80,297,52,5 1311591,123,994,820,296,818,2 1412093,526,598,821,2102,317,7 158096,216,2103,023,0107,627,8 169594,60,498,43,499,34,3 1710094,65,497,72,398,02,0 Tng lch tuyt i133,9124,4126,0 MAD13,3912,4412,6 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 hng Chngtathngxemxtkhochngnhn,thmavvxuhnglnhnt 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 ) Vi: St = FTt + (FTt - FTt - 1 - Tt - 1 )Tt = Tt - 1Su tm bi: www.daihoc.com.vn 13Trong FTt - D bo theo xu hng trong giai on t St - D bo c iu ha trong giai on t Tt - c lng xu hng trong giai on t At - S liu thc t trong giai on t t - 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 1 V d: ng A mun d bo s lng hng bn ra ca cng ty nhm ln k hoch tinmt,nhnsvnhucunnglcchotnglai.ngtinrngtrongsutgiaion6 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)123456 Doanh s bn (At)130136134140146150 Kt qu bi ton: Chng ta c lng d bo bt u vo thng 1 bng d bo s b, tc l bng s liu thc t. Ta c: FT1 = A1 = 130 Chng 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 + T1 Su tm bi: www.daihoc.com.vn 14 (A1 - FT1 ) = 130 + 0,2( 130 - 130 ) =S1 = FT1 +130 T1 = 4 FT2 = 130 + 4 = 134 D 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 = 138,4 D bo tng t cho cc thng 4, 5, 6, 7 ta c bng sau: Thng (t)Doanh s bn (At)St - 1Tt - 1FTt 1130--130,00 2136130,004,00134,00 3134134,404,00138,40 4140137,524,12141,64 5146141,313,86145,17 6150145,343,76149,10 7-149,283,81153,09 1.4.2.2. D bo di hn D bo di hn l c lng tng lai trong thi gian di, thng hn mt nm. D bodihnrtcnthittrongquntrsnxuttrgipccquytnhchinlcv hoch nh sn phm, quy trnh cng ngh v cc phng tin sn xut. V d nh: - Thit k sn phm mi. -Xcnhnnglcsnxutcnthitlbaonhiu?Mymc,thitbnocns dng v chng c t u ? -Lnlchtrnhchonhngnhcungngtheocchpngcungcpnguynvt liu di hn Dbodihncthcxydngbngcchvmtngthngixuynqua 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 Su tm bi: www.daihoc.com.vn 15dihncthdngtrongthct,nhngimkhngthunlicanlvnvmt 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 + b a = 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 lp a - dc ca ng xu hng b - Tung gc n - S lng quan st Thi gian ng xu hngDoanh s Su tm bi: www.daihoc.com.vn 16Trongtrnghpbinclpxctrnhbythngquatnggiaiontheothi 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. Vd:Mthngsnxutloingcintchoccvankhingtrongngnh cng nghip, nh my hot ng gn ht cng sut sut mt nm nay. ng J, ngi qun l nhmy ngh rng s tng trng trongdoanh s bn ra vncn tip tc vng tamun 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: NmS lng bnNmS lng bn 11.00062.000 21.30072.200 31.80082.600 42.00092.900 52.000103.200 Kt qu bi ton: Ta xy dng bng tnh thit lp cc gi tr: Su tm bi: www.daihoc.com.vn 17 NmLng bn (y)Thi gian (x)x2xy 11.000-981-9.000 21.300-749-9.100 31.800-525-9.000 42.000-39-6.000 52.000-11-2.000 62.000112.000 72.200396.600 82.60052513.000 92.90074920.300 103.20098128.800 Tng21.000033035.600 nxyxyxy3.5600 a= nx2( x)2 == x2 -= 330 = 107,8 x2yxxyy21.000 b= nx2( x)2 = n = 10 = 2.100 -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 v Su tm bi: www.daihoc.com.vn 18 Y12 = 107,8 . 13 + 2.100 = 3.501 3.500 n v Y13 = 107,8 . 15 + 2.100 = 3.717 3.720 n v Trng 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 nshpngxydngtrongvngcangta.ngByucuksdiquyn,tin hnh phn tch hi qui tuyn tnh da trn cc s liu qu kh v vch ra k hoch nh sau : -Xydngmtphngtrnhhiquichodbomcnhucuvdchvca 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). -Xcnhmcchtch,ccmilinhgianhucuvhpngxydng c a ra. Bit s liu tng qu trong 2 nm qua cho trong bng:(n v: 10 Triu ng). Nm Qi Nhu cu ca cng ty Tr gi hp ngthc hin 18150 210170 315190 1 49170 112180 213190 312200 2 416220 Kt qu bi ton: Xy dng phng trnh hi qui. ng A xy dng bng tnh nh sau: Su tm bi: www.daihoc.com.vn 19 Thi gianNhu cu (y)Tr gi hp ng (x)x2xyy2 1815022.5001.20064 21017028.9001.700100 31519036.1002.850225 4917028.9001.53081 51218032.4002.160144 61319036.1002.470169 71220040.0002.400144 81622048.4003.520256 Tng951.470273.30017.8301.183 S dng cng thc ta tnh ton c h s a = 0,1173 ; b = -9,671Phng trnh hi qui tm c l:Y = 0,1173x 9,671 D 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 = 24,346 Y3 = (0,1173 x 300 )- 9,671 = 25,519;Y4 = (0,1173 x 270) - 9,671 = 22,000 D 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 dng nxyxy r = [nx2( x)2][ny2( y)2] 8x17.8301.470x952.990 = (8x273.30014702)(8x1.183952) = 3.345,8 0.894 r2 = 0,799;trong r l h s tng quan v r2 l h s xc nh R 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. Su tm bi: www.daihoc.com.vn 20H 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 ca 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 cay 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. Loimavthngthnglslnxungxyratrongvngmtnmvcxu 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... Cchthcxydngdboviphntchhiquituyntnhkhivmahindin 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 Y= ViiY - 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. Su tm bi: www.daihoc.com.vn 21V 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 3 nmqua phnnh kh tt kiu sn lngma v v c th ging nh trong tng lai. S liu c th nh sau: S lng bn hng qu (1.000 n v) Nm Q1Q2Q3Q4 1520730820530 2590810900600 36509001650 Kt qu bi ton: u tin ta tnh ton cc ch s ma v. NmQu 1Qu 2Qu 3Qu 4C nm 15207308205302.600 25908109006002.900 36509001.0006503.200 Tng1.7602.4402.7201.7808.700 Trung bnh qu586,67813,33906,67593,33725 Ch s ma v0,8091,1221,2510,818- 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: S liu hng qu phi ma v. Nm Qu 1Qu 2Qu 3Qu 4 1642,8650,6655,5647,9 2729,2721,9719,4733,5 3803,5802,1799,4794,6 Chng ta phn tch hi qui trn c s s liu phi ma v (12 qu) v xc nh phng trnh hi qui. Su tm bi: www.daihoc.com.vn 22QiXyx2 xy Q111642,81642,8 Q122650,641.301,2 Q133655,591.966,5 Q144647,9162.591,6 Q215729,3253.646,5 Q226721,9364.331,4 Q237719,4495.035,8 Q248733,5645.868,0 Q319803,5817.231,5 Q3210802,11008.021,0 Q3311799,41218.793,4 Q3412794,61448.535,2 Tng788.700,565058.964,9 Xc nh c h s a = 16,865 v b = 615,421 . Phng trnh c dng: Y = 16,865x + 615,421 By 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 = 834,666 Y42 = (16,865 x 14) + 615,421 = 851,531 Y43 = (16,865 x 15) + 615,421 = 868,396 Y44 = (16,865 x 16) + 615,421 = 885,261 Tip theo, ta s dng ch s ma v ma v ha cc s liu. QuCh s ma v (I)D bo phi ma v (Yi)D bo ma v ha (Ymv) 10,809834,666675 21,122851,531955 31,251868,3961.086 40,818885,261724 Su tm bi: www.daihoc.com.vn 23 1.5. Quy trnh d bo Quy 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 bo Bc 1: Xc nh mc tiu -Ccmctiulinquannccquytnhcnndbophicnir.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)haysnvdoanhs(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 gian C 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 bo Bc 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,) Su tm bi: www.daihoc.com.vn 24- 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 bo Bc 5: La chn m hnh -Lmsaoquytnhcphngphpthchhpnhtchomttnhhungnht nh? + 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 bo Bc 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-iviccphngphpnhlng,cnphinhgimcphhpcam 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 5 Bc 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 Su tm bi: www.daihoc.com.vn 25- 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 vit Bc 9: Theo di kt qu d bo - 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 -Traoivhptcgiangisdngvngilmdbocvaitrrtquan trng trong vic xy dng v duy tr quy trnh d bo thnh cng. Su tm bi: www.daihoc.com.vn 26Chng 2: CC PHNG PHP PHN TCH V D BO C nhiu phng php d bo thng k khc nhau ( phng php ly kin chuyn gia,dbotngmcbnhqun,ngoisuyhmxuth,nhngkhngphiphng php no cng c s dng ph bin nh nhau. V vy, trong phn ny ch trnh by mt 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 qun 2.1.1. D bo t s bnh qun trt (di ng) Phngphpsbnhqundinglmttrongnhngphngphpbiuhinxu 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 gianSn lng (triu tn) (yi) Doanh s trung bnh di ng (triu tn) (Mi) 179- 282- 38582 48283 58885 68685,3 79890,6 810596,3 9110104,3 10115110 11120115 12118117,6 Su tm bi: www.daihoc.com.vn 27Nhvy,ngvithng3tacsbnhqundingl82triutn,thng4l83 triutn,v.vvcuicngthng12l117,6triutn.Tagiccsbnhqunding mi ny l Mi (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 = Mn Khong 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 + + + + + + + + + = 10,78 Trong v d trn, d on sn lng thp cho thng 1 nm sau l: Y13 = 117,6 triu tn Theo cng thc trn ta tnh c S = 10,78 nghn tn vt= 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 36,35 2.1.2. 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= zn). M hnh d bo theo phng trnh: n L Y+ = ny + . y L (2.3) Trong : Su tm bi: www.daihoc.com.vn 28n L Y+ : Mc d on thi gian (n+L) ny : Mc cui cng ca dy s thi gian y : 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 yn V d: Gi tr sn xut (GO)ca mt doanh nghip A qua cc nm nh sau: Thi gian Ch tiu 200120022003200420052006 Gi tr sn xut (GO) (t ng323639414345 Ta c:y = 45 326 1= 2,6 t D 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 qun Thng 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: Su tm bi: www.daihoc.com.vn 29* 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: n L Y+ = ny .( ) Lt (2.4) n L Y+ : Mc d on thi gian (n+L) ny : Mc c dng lm k gc ngoi suy L: Tm xa ca d on ( L=1,2,3,nm) t : Tc pht trin bnh qun hng nm 11nnyty =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 i 1nj ijiy Y= = - Tng cc mc ca thi gian j ca nm i (i=1n) 11nnyty = : Tc pht trin bnh qun hng Sr= 1 + ( t ) +( t )2 + ( t )3 ++ ( t )n-1 Su tm bi: www.daihoc.com.vn 30n: 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: Qu j Nm j IIIIIIIV 1nj ijiy Y= =20042021,52223,586,55 200520,0420,6321,724,2886,65 200621,0422,8323,525,6393,03 yj 61,1164,96667,272,46266,23 T 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= 0,384 T 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) Su tm bi: www.daihoc.com.vn 312.2. 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 quylthuyt,lphngtrnhphhpvixuhngvcimbinngcahin tngnghincu,tcthngoisuyhmxuthxcnhmcphttrintrong tng lai. 2.2.1. 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 quy T 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 t=b=. 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 tbt=V 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 gian Ch tiu 200120022003200420052006 Doanh thu tiu th(t ng)7098115120136180 T ngun ti liu, ta c bng s liu sau (t th t thi gian cho ( t =0) Su tm bi: www.daihoc.com.vn 32iu kintt =0 Nm (n) Doanh thu(t ng) yi Tt2 y.t Y 200170-525-35072,045 200298-39-29491,159 2003115-11-115120,27 200312011120129,387 200513639408148,58 2006180525900167,61 N= 6719t =0 2t = 70 yt = 669 Tnh 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 +9,55t T 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. +Saisdbols chnhlchgiamcthctvmctnhtontheom hnh d bo. +Saisdbophthucvo03yut:binthincatiuthctrongthik trc, di ca thi gian ca thi k trc v di ca thi k d on. Su tm bi: www.daihoc.com.vn 33+ 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 :Y- Gi tr tnh ton theo hm xu th n- S cc mc trong dy s p- S cc tham s cn tm trong m hnh xu th n-p- S bc t do Cng 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 lachnlmhmxuthdon.Thngthngvicdonctinhnhn 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 bo Sau xc nh khong d on theo cng thc sau; $pn Ly t S +t- 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 tnh y( )22 22 2 270 72, 045 (98 91,159) (115 110, 27)(120 129, 387) (136 148) (180 167, 61)10,8766 2y + + + + + = = Su tm bi: www.daihoc.com.vn 34Sai s d bo: + i vi nm 2007 (L=1):

1 2200721 3(6 2 1)10,876 1 14,8566 6(6 1)pS+ = + + = + i vi nm 2008 (L=2):

2 2200821 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=2,132 Ta c d bo ca nm 2007 l:186,729 2,132 x14,856= 186,729 31,67 Ta c d bo ca nm 2007 l:205,843 2,132 x16,93= 205,843 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 thc T 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+ bx Trong : 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. Tngtnhtronghiquyginn,tronghiquybi,gitrdoncaYc 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+1 2.3. D bo da vo hm xu th v bin ng thi v Phng 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: Su tm bi: www.daihoc.com.vn 35Yt=

Y +tv+bt (2.7) - Hoc d bo da vo hm xu th kt hp nhn t vi bin ng thi v: Yt=

Y x 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 v bt: nh hng ca nhn t bt thng Nhn 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 cng V d: C ti liu v sn lng ca doanh nghip A nh sau: Sn lng ( nghn tn)Nm (t) Qu 20022003200420052006 Cng theo cng qu jy Mc bnh qun tng quiyCh s thi v itvyIy=I202527312913226,40,678 II2532303736160320,82 II383845444721242,41,14 IV4060556258275551,41 Cng theo cng nm jy 12315515717417077938,95 . t y 123310471696850 * Trc tin xc nh hm xu th tuyn tnh sn lng doanh nghip c dng l:

Y = a+ bt Su tm bi: www.daihoc.com.vn 36Trong : 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 nm m: Khong cch thi gian trong mt nm ( m= 4 i vi qu, m=12 ivi nm) t: Th t thi gian trong dy s (nm) Do vy, hm xu th c dng:

Y = 31,537 + 0,706t Mc 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= 1,2,3,4 Do 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+)= 14,99 Sau 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 = +Su tm bi: www.daihoc.com.vn 37D bo sn lng qu I nm 2007 ( t= 21)

1Y = 31,537 + 0,706 x 21 11,49= 34,837 Qu II ( t=22):

2Y = 31,537 + 0,706 x 22 6,597= 40,472 C tip tc nh vy cho n cc qu tip theo 2.3.2. D bo da vo m hnh nhn M hnh d bo theo kt hp nhn c dng: Yt=

Y x tv(2.9) 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 H Sau khi xc nh c tvt th xc nh dy s ft l dy s loi b thnh phn thi v nh sau: tttyftv=Theo v d trn ta c th lp bng tnh ton sau y: Su tm bi: www.daihoc.com.vn 38 STTYt tyttyy tvt tttyftv=120--0,728,57 225--0,83829,83 33830,751,2361,0835,19 440321,251,37629,07 52533,750,740,735,71 63233,750,9480,83838,19 73838,750,981,0835,19 86039,251,5291,37643,6 92738,750,6970,738,57 103040,50,740,83835,8 114539,251,1461,0841,67 125540,251,3661,37639,97 1331420,7380,744,28 143741,750,8660,83844,15 154443,51,0111,0840,74 1662431,4411,37645,06 172942,756780,741,13 183643,58270,83842,96 194742,51,1051,0843,5 2058--1,37642,15 T ft ta lp bng sau: Qu Nm IIIIIIIV 2002--1,2361,25 20030,740,9480,981,529 20040,6970,741,1461,366 20050,7380,8861,0111,441 20060,6780,8271,105- Bnh qun qu (ttv )0,7130,851,0961,396 Vi ti liu trong bng tnh ta tnh c cc i lng trn nh sau:Su tm bi: www.daihoc.com.vn 39H= tmtv = 40, 9860, 713 0,85 1, 096 1, 036 =+ + + * Trc tin, tnh cc ch s thi v: Itv=ttv .H Qu I= 0,713 x0,986 = 0,7 Qu II= 0,85 x0,986 = 0,838 Qu I= 1,906 x0,986 = 1,08 Qu I= 1,396 x0,986 = 1,376 * Xy dng hm xu th:

Y = a+ bt tin theo di, t (ft) talp bng sau: QuNm I IIIIIIV Tng nm (N) t.y 200228,5729,8335,1929,07122,66122,66 2003 35,71 38,1935,1943,6152,69305,38 2004 38,57 35,841,6739,97156,01468,03 2005 44,28 44,1540,7445,06174,23696,92 2006 41,43 42,9643,542,15170,04850,2 Tng qu (Q) 188,56 190,93196,29199,85755,66 . t y = 2443,19 Bnh qun qu 37,71 38,18639,2639,97 Cc 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+ =Su tm bi: www.daihoc.com.vn 40Hm xu th c dng:

Y = 29,7+ 0,727t Do m hnh nhn c dng: yt= (29,7+0,727t).Itv D 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= 64,875 Vi hm kt hp nhn ta c th d bo cho nhng nm tip theo 2.4. D bo theo phng php san bng m Phngphpsanbngm(haycngilphngphpdonbnhqunm)l mtphngphpdonthngkngnhnhincsdngnhiutrongcngtcd 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 nhngthigiankhcnhauthhintngnghincuchustcngcanhngnhnt khc nhau v cng khng ging nhau. Cc mc ngy cngmi ( 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 Su tm bi: www.daihoc.com.vn 41gian 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: - 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 tip Gi 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 lv- 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) -Mcdoncahintngthigian(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) Bngcchtiptctngtthayvoccmcdon 3 4.... , t t Y Y tasccng thc tng qut. 111ni it t it iiY y Y ++ = = + (*) Trong : Su tm bi: www.daihoc.com.vn 42

1 t Y+ : S bnh qun m ti thi im t+1 yt-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 gian V [ ] 0;1 nn khi i Th 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 ml h s san iu chnh trong s ca cc quan st ring bit ca dy s thi gian. Vvy,khilachn phivamboktqudbosgnviquanstthct,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. Nuc chn cng ln th ccmc cngmi scng cch , thchhp vi chui thi gian khng c tnh n nh cao. Ngcli,nucchncngnhthccmccngcscngcch, thch hp vi chui thi gian c tnh n nh cao. Su tm bi: www.daihoc.com.vn 43Do , phi da vo c im bin ng ca hin tng qua thi gian v kinh nghim nghin cu la choncho ph hp. Ni chung, gi trtt 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 ththch 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 y0 Phng php san bng m c thc hin theo php quy, tnh

1 t Y+ th phi c

t Y ,c

t Y thphic

1 t Y .Dotnhtoncnphiphixcnhgitrbanu(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 s V d: C hai ti liu v doanh thu mt ca hng thng mi X qua mt s nm nh sau: Nm Ch tiu 20022003200420052006 Doanh thu ( t ng) 15 y1 15,3 y2 14,8 y3 15,5 y4 15,2 y5 Yu 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= 5 Su tm bi: www.daihoc.com.vn 44i=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= 15,16 Vi t=1, ta c: $ $1 2 1(1 ) y y y = + = 0,3 x15 +(1-0,3).15,16= 15,112 Vi t=2, ta c: $ $2 3 2(1 ) y y y = + = 0,3 x 15,3 +(1-0,3).15,112= 15,1684 Vi t=3 ta c: $ $3 4 3(1 ) y y y = + = 0,3 x 14,8 + (1-0,3).15.1684= 15,05788 Vi t=4 ta c: $ $4 5 4(1 ) y y y = + = 0,3 x 15,5 + (1-0,3).15,05788= 15,19 Vi t=5, ta c: $ $5 6 5(1 ) y y y = + = 0,3 x 15,2 + (1-0,3). 15,19=15,193 y l gi tr d on cho doanh thu ca Cng ty nm 2007 2.4.2.Mhnhxuthtuyntnhvkhngcbinngthiv(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 3.Nungbiu dindiymtphnphiccgitrdoanhthu,tacthnirngasccgitr doanh thu rt gn vinhau (the same revenue)d cmtstmang gitr rt nh hoc rt ln. -ngcongrtbt(veryflat):phngnm,kurtosis 0,5: nghing t. Nu ng biu din di y m t phn phi cc gi tr doanh thu, ta c th ni rng a s cc gi tr doanh thu gn vi doanh thu ln nht d c mt 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 gi tr doanh thu, ta c th ni rng a s cc gi tr doanh thu gn vi doanh thu nh nht d c mt s t mang gi tr ln hn hoc rt ln ( bn phi). Theo v d trn, nghing bng: -0,58.Range(khong)alsorangewidth(haybrngcakhong):ldicakhong quan st (khong bin thin), c tnh bng ly gi tr quan st cc i Max tr i gi tr quan st cc tiu Min.Range = Max - Min = 412 - 323 = 89Minimum (gi tr quan st cc tiu): gi tr nh nht trong cc quan st.Min = 323Maximum(gitrquanstcci):gitrlnnhttrongccquanst.Max = 412Sum(tngcnggitrcaccquanst):ltngcngttcccgitrcattc cc quan st trong tp d liu.Theo v d trn, ta c: Su tm bi: www.daihoc.com.vn 59 Count(squanst):lsmcaslnquanst(n).Theotpdliuvd trn, ta c: n = 63.2. Phng php hi quy bi:Cn gi l phng php hi quy a bin, dng phn tch mi quan h gia nhiu binsclp(tcbingiithchhaybinnguynnhn)nhhngn1binph thuc (tc bin phn tch hay bin kt qu).Trongthct,crtnhiubitonkinht-clnhvckinhdoanhvkinht hc, phi cn nphng phphiquya bin. Chnghnnh phn tch nhng nhn tnhhngn thu nhp qucdn, sbinngca t gi ngoi hi;xtdoanh thu trong trng hp c nhiu mt hng; phn tch tng chi ph vi nhiu nhn t tc ng; phn tch gi thnh chi tit; nhng nguyn nhn nh hng n khi lng tiu thMt ch tiu kinh t chu s tc ng cng lc ca rt nhiu nhn t thun chiu hoc tri chiunhau.Chnghn nhdoanh thu lthucvgic,thu nhpbnhqun xhi,lisuttingi,mav,thitit,qungcotipthMtkhc,gianhng nhn t li cng c s tng quan tuyn tnh ni ti vi nhau. Phn tch hi quy gip ta va kimnh li gi thit v nhngnhn ttc ng vmc nh hng, va nh lng c cc quan h kinh t gia chng. T , lm nn tng cho phn tch d bo v c nhng quyt 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 binXi; Xi: cc bin s (cc nhn t nh hng); e: cc sai sLu : Y trong phng trnh trn c biu hin l Y c lng, ngi ta thng vit di hnh thc c nn (

Y ) 2 . 2 6 71nS u m Xii= == Su tm bi: www.daihoc.com.vn 60Mc tiu ca phng php hi quy a bin l da vo d liu lch s cc bin s Yi, 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.3.3. Phng php thng k hi quy Cngilthngkhiquyngin(simpleregressionstatistical)dngphng php thng k ton tnh cc h s a, b ca phng trnh hi quy da trn ton b quan st ca tp d liu. y l phng php ng tin cy nht v v vy i hi cng phu hn.Vndngsliuvdtrn,lpbngtnhcctrscsricncvocng thc tnh cc thng s ca phng trnh. Ta c cng thc trong thng k tona = - b

Chng minh cng thc Cngthctrncchngminhtphngphphiquyccbnhphngti thiucacchius(lch:Deviation)giaccgitrquanstvgitrclng ca bin s ph thuc( Y = a +bXi) Viphngphptngccbnhphngtithiu,gi 2i e$lbnhphngcc 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: ( )( )12( )1nX X Y Yii ibnX Xii === Su tm bi: www.daihoc.com.vn 61( )210ni iiY a bXb= = (3.6) Lyohm ricng chia cho -2 (hay nhnvi)ta chphngtrnhchun vi 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 tr cc 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 lng Gii thch th:ng hi quy Y =a+ bX l ng c lng tt nht, cha cc gi tr c lng ca 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 , gil lch dng (Positive deviation); cc lch nm pha di ng c lng nhn t gc ca trc to , gi l lch m (Negative deviation).Ti sao l bnh phng ti thiu?Mcchcuicngcaphngphphiquyldnggiithchhocdbo mtitngcnnghincu.Cthlitmgitrccthngsa,bxydng phng trnh hi quy tuyn tnh (ng thng) c dng tng qut: lch (deviation): Yi- ^Yng hi quy bnh qun ti thiu. Y a bX = +0 Yi^Y X Y Xi Su tm bi: www.daihoc.com.vn 62

Y =a+ bX. Migitrclng(clngim)lgitrclngtrungbnhimcabinktquYi.Khnngchcthxyraccgitrtrongmtkhongc lng vi mt tin cy nht nh m thi. V xc sut gi tr thc Yi bng vi gi tr c lng imi

Yl 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 bnh gia

Y v Yi nh nht ( Yi- ^Y)0 Trong , Yi l cc gi tr quan st thc v

Y =a+ bX l cc gi tr c lng (gi tr trung bnh) ca Yi.Khiy,gitrclnggnvigitrquanstthcvphngtrnhhiquy dng 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 k NXi Yi Xi2 Yi2 Xi Yi iX X iY Y iX X iY Y ( )2iX X ( )2iY Y 11.5103232.280.100104.329487.730-372-5520.398138.3843.007 21.8203653.312.400133.225664.300-62-137963.844165 32.1044124.426.816169.744866.848222347.58549.2841.167 42.0874104.355.569168.100855.670205326.59442.0251.035 51.7503543.062.500125.316619.500-132-243.14617.424568 62.0214034.084.441162.409814.463139253.49819.321633 11.2922.26721.521.826863.1234.308.5110042.017270.2826.575 2.267377, 83 3786Y= = Su tm bi: www.daihoc.com.vn 63Trcht,xtmctngquan(correlation)giabinsphthucvbins c lp bng cng thc: 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,thhins c nghavmt thng k mc ngha 5% trong khong: cn trn -Upper, cn di - Lower. Cn trn v cn di ca Intercept l (118,44 ; 52,09) v ca Slope l (0,17 ; 0,14).Mtschtiudngkimnh,nhANOVAtrongbngktquhiquy khng cp ht trong phm vi mn hc ny. Su tm bi: www.daihoc.com.vn 67Chng 4: PHNG PHP BOX - JENKINS (ARIMA) 4.1. Tnh n nh ca mt chuiTrckhixlmtchuithigiannghincucctnhngunhincanlbc 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) = ctekyv m Var(yt) < krCov(yt ;yt+k) = E ((yt - )( yt+k- ) = =hng sVi 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 k4.2. Hm s t tng quan n v t tng quan ring phnH s tng quan ring phn l h s dng nh gi quan hgia hai binkhi nh hng ca bin th ba c loi trHm 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:

p0 =1v

pk =

p-k Bng sau y gii thiu cch tnh hm t tng quanKho st chui quan trc yt. Cc chui lch yt-k tng ng cng c gii thiu: Su tm bi: www.daihoc.com.vn 68k01234 tytyt-1ytytyt-2 1123 2130123 3125130123 4138125130123 5145138125130123 6142145138125130 7141142145138125 8146141142145138 9147146141142145 10157147146141142 11150157147146141 12145150157147146 Bng 4.1. Xc nh cc chui lch yt-k Kt 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 140.7142.3143.6145.6146.6 Trung bnh yt-k 140.7140.3139.4137.4136.2 Phng sai yt 9572.462.827.122.2 Phng sai yt-k 95101.8101.874.971.4

pk 10.770.620.590.55 Bng 4.2 Vinhnghacahmsttngquantrntathykhngtinlitrongvictnh 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.Khislngquantrcln,haicchtnhgitrhmttngquantrnchokt qurtgnnhau( pk~

p -k)Hmsttngquanringphnbtnguntkhinim Su tm bi: www.daihoc.com.vn 69tng 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 x4xkTng 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 trng 4.3.1. Phn tch hm t tng quanMc 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

pk no khc0. Tht vy, nu ta hon tonkhng c gitr no ca

pk khc 0 tani qutrnhnghincukhngc.Nhontonkhngctnhxuthcngnh 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

pk c gi tr khc 0 c thc hin da vo nguyn tc kim nh gi thit nh sau:H0:

pk = 0H1:

pk0 Trong thc hnh, tc gi Quenouille chngminh c rngvimtmuc kch thctngiln,hs

pktinmtcchtimcnvmtphnphichuncgitr trung bnh bng 0 v lch chun lKhong tin cyca h s

pknh sau: vi n l s lng quan trc. Nu h s

pk tnh c nm ngoi khong trn ta kt lun

pk khc 0 vi ri ro% (thng ta ly=5%).4.3.2. Tham s thng k ca Box-Pierce v Ljung-boxKim nh ca Box-pierce cho php nhn bit l nhiu trng hay khng. Chng ta phikimnhCov(yt,yt-k)=oV

pk=0vi .Mtqutrnhnhiutrngbtbucphic:

p1= p2=

p3==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 Su tm bi: www.daihoc.com.vn 70s tr,

pk 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 cho 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

Su tm bi: www.daihoc.com.vn 71Biu tng quan n v biu tng quan ring phn tng ng ca chui ny nh sau: Hnh 4.2 Trong 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 torabimttngtrungbnhctrngscaccgitrquantrctrongqukhtnhcho 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 Su tm bi: www.daihoc.com.vn 72Trong q1; q2; ; qp l cc thng s cn phi xc nh. et l mt nhiu trng ngu nhincdngGaussien.Chngtacngcththmvoqutrnhnymthngsmn vn khng 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:

pk =

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.Cc biu tng quan ca m hnh trn c dng sau: Hnh 4.3 Su tm bi: www.daihoc.com.vn 73Tathygitrutincabiutngquanringphnrtlnsoviccgitr 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: Hnh 4.4 Sovitrnghptrctathycskhcnhau.Thayvgitrth1nhvd 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: .Su tm bi: www.daihoc.com.vn 74MA(1):yt = et - a1*et-1MA(2):yt =et - a1*et-1- a2*et-2 --------------------------------------------------------------------

MA(q):yt = et - a1*et-1- a2*et-2-- aq*et-q

Trong 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 Trongqutrnhdngnycngnhttcccmhnhthiquyccnhiungu 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 trungbnh 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:

pk = khi

pk = 0khik>qiu 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 tSu tm bi: www.daihoc.com.vn 75 Hnh 4.5 Cc 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-2 Cc 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 biuth c th ca mtm 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:Su tm bi: www.daihoc.com.vn 76 Ta 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 5 Xt m hnh ARMA(L,l) sau y:y = 5 + 0.8yt-l + 1 . lCc biu tng quan ca m hnh trn c dng sau: Hnh 4.6Vi 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.Su tm bi: www.daihoc.com.vn 774.7. M hnh ARMA m rng: ARIMA, SARIMATrong 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+bt nh ngha sai bit bc 1 Dyt ta c:Dyt =yt-yt-1 =(a+bt)-(a+b[t1])=b=cteTa 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+2tcTa 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 nnhvxuth.Tmlitacthvitchui(l-D)d*ytlmtARMA(p,q)khiytlmt ARIMA(p,d,q); vi D c nh ngha l ton t sai bit:D(yt)=yt- yt-lM 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. Su tm bi: www.daihoc.com.vn 784.8. Phng php Box - JenkinsDiynghincumtcchchthngccdngkhcnhaucachuithigian da vo cctnh chtca n.Mc tiu l tm trongs tt c ccm 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 nhty 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 nghincu c chayu 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 cTrongtrnghpbiutngquanngimchmhochontonkhnggim, chui c chamt xuth. Trong trng hpnyta s loi tnh xu th n nh vo pdng catontsaibitlnchui.Trongthcttacthgptrnghpd=lhoc2.Gitr 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.Trongthchnh,phngphpphntchthchchotatmcpqtrongcc 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.Su tm bi: www.daihoc.com.vn 79C 3 tiu chun thng dng c s dng nh sau:Tiu chun Akaike:Akaike = Log(%rss) + 2 Tiu chun BIC:BIC = Log(%rss) + (p + q) * Tiu chun HQ:HQ = Log(%rss) + 2(p + q) * 270vi: %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 hnhTrongtrnghpmhnhAR(P),tcgipdngphngphpbnhphngti 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: Su tm bi: www.daihoc.com.vn 80Do : Tchngtacthkhiubngcchtnhqutvi2khonggitrchpnhn 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 vchngtaslygitral,a2 saochocctngbnhphngcaccthngdt phng trnh hi quy trn ti thiu. Ch phng php ny ch c gi tr trong trng hp slngccthngscnxcnhkhngnhiulm.Ngoiphngphpbnhphngti 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 boSau khi cc thng s ca m hnh c xcnh, 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).Nucmthaynhiuhskhngthamn,tasloibnrakhimhnhAR 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 hnhnghkhngthchhp.Mtkhimhnhckimnh,tacthtinhnhd bo gii hn trong mt vi chu k. Phn tch chui thi gian vi m hnh SARLMA ch cho Su tm bi: www.daihoc.com.vn 81phptinhnhccdbongnhn.Nkhngchophpmtdbotrunghnvdihn 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: pdngphngphpBoxjenkinsDoanhthucamtcngtytrongchuk01/82 n 09/90 c trnh by bi th sau y:Tm cc thng tin thch hp, kh tnh chu k, kho st v xc nh bc ca xu th Phn tch biu tng quan n v tng quan ring phn: xc nh bin p,q ca m hnh AR v MA Kim tra m hnh: Phn tch cc h s v thng d Su tm bi: www.daihoc.com.vn 82 Hnh 4.7 HyphntchchuitrnbngphngphpBox-jenkinsvdbochodoanhs 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: Su tm bi: www.daihoc.com.vn 83 Ta 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 ; tBiu 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:

Hnh 4.8 Su tm bi: www.daihoc.com.vn 84 Ta thy gi tr u tin ca biu tng quan n ln hn hn s vi cc gi tr tip theo,trongkhigitrcabiutngquanringphngimtt;tacthdon 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-JenkinsS ln lp 21Chui s liu 83:02 n 90:09S quan trc hiu dng 92 Bc t do 90H s xc nh R**20.921215H s xc nh hiu chnh 0.920340Gi tr bin nghin cu 646. 71640217 lch chun ca/ bin nghin cu365.927404Sai s chun ha ca c lng103.28000630Tng c c thng d bnh phng 960008.37314Gi tr thng k Durbin-watson1.751202Gi tr thng k ca Ljung-box Q(23-2) 29.883511a tng ng ca Q 0.09435394

Su tm bi: www.daihoc.com.vn 85

BinH s lch chun T-student a****** ******************************************************************1 AR(12) 1.0581690.03280332.258040.0002. 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 phpBox Jenkins nh sau: Su tm bi: www.daihoc.com.vn 86 nhgichtlngcamhnhtaphikimtraxemgitrthngdtrnc 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.Su tm bi: www.daihoc.com.vn 87 D bo ngn hn:TinhnhdbongnhnvdoanhscacngtychobimhnhBox-jenkins c trnh by trong bng sau:Thi gian90:1090:1190:1291:0191:0291:0391:04 D bo1055.31480.71901.4676.1561.8561.8714.6 th sau biu din tng hp gia doanh thu trong qu kh v d bo ngn hn ca cng ty nh sau:Su tm bi: www.daihoc.com.vn 88 Su tm bi: www.daihoc.com.vn 89Chng 5: DY S THI GIAN 5.1.Khi nimMt 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.Dysthigianldyscctrscachtiuthngkcspxptheotht thi gian.V d: c s liu v doanh thu ca Bu in X t nm 1999 -2003 nh sau:VT: t ng. Nm19992000200120022003 Doanh thu23,928,137,347,267,4. Bng 5.1 V d trn y l mt dy s thi gian v ch tiu doanh thu ca n v Bu in ny tnm1999-2003.Quadysthigiancthnghincucccimvsbinng cahintng,vchrxuhngvtnhquylutcasphttrin,ngthidon cc mc ca hin tng trong tng lai.Mi dy s thi gian c hai thnh phn:- Thi gian: c th l ngy, tun, thng, qu, nm, . . .. di gia hai thi gian lin nhau c gi l khong cch thi gian. - Ch tiu v hin tng nghin cu: ch tiu ny c th l s tuyt i, s tng i, s bnh qun. Tr s ca ch tiu cn gi l mc ca dy s.* Phn loi dy s thi gian:Cn c vo tnh cht thi gian ca dy s, c th phn bit thnh 2 loi:1.Dysthik:ldysbiuhinmtlngcahintngquatngthiknht nh2. Dy s thi im: l loi dy s biu hin mt lng ca hin tng qua cc thi im nht nh. Dy s ny cn c phn bit thnh 2 loi:- Dy s thi im c khong cch thi gian u nhau.V d: C gi tr v hng ha tn kho ca cng ty X vo cc ngy u thng 1, 2, 3, 4 nm 1995,nh sau: Su tm bi: www.daihoc.com.vn 90Ngy1-12-13-14-1 Gi tr hng tn kho (triu ng)356364370352 Bng 5.2 -Dy s thi im c khong cch thi gian khng u: C s liu v s d tin vay ngn hng ca cng ty Y, nh sau: Ngy (thi im)1-120-115-210-3 S d tin vay (triu ng)400600500700 Bng 5.3 * Cc yu t nh hng n bin ng thi gian:1. Bin ng c xu hng.2. Bin ng theo thi v.3. Bin ng theo chu k.4. Bin ng bt thng.5.2. Cc ch tiu phn tch phn nh c im bin ng qua thi gian ca hin tng nghin cu,ngi ta thng tnh cc ch tiu sau y:5.2.1. Mc trung bnh theo thi gian Chtiunyphnnhmcibiucaccmctuytitrongmtdys thi gian. Mc trung bnh theo thi gian c xc nh theo cc cng thc khc nhau, ty theo tnh cht thi gian ca dy s.5.2.1.1 i vi dy s thi k:Muntnhmcbnhqun:tacngccmctrongdysrichiachoscc mc , tc l:11 2 3 1...nn iyy y y yyn n=+ + + += = Trong : Yi (i = 1,, n): cc mc ca dy s thi k n: s mc ca dy s Su tm bi: www.daihoc.com.vn 91T v d trn ta doanh thu bnh qun mi nm ca n v Bu in X l: y= (23,9 + 28,1 + 37,3 + 47,2 + 67,4)/5 = 40,78 ( t ng) Kt qu c ni ln trong thi k t nm 1996 n 2000, doanh thu trung bnh hng nm ca Bu in X l40,78t ng.5.2.1.2. i vi dy s thi im:* Dy s c khong cch thi gian bng nhau: mc trung bnh c tnh theo cng thc sau:y= (y1 /2 + y2 + y3 + + yn-1 + yn / 2) / (n -1)Trong : yi (i=1,2, . . . ,n)l cc mc ca dy s thi im. n: s mc ca dy sT v d (2) ta tnhy :y= (256 / 2 + 364 + 370 + 352 /2) = 362,666C ngha l hng ha tn kho trung bnh ca qu I l 362,666 triu ng.*Dysthiimckhongcchthigiankhngbngnhau,mctrungbnh c tnh theo cng thc: 1 1 2 2 3 3 11 2 31......ni in n inniiy ty t y t y t y tyt t t tt==+ + + += =+ + + + Trong : yi (i=1,2,3, . . ., n): cc mc ca dy s thi im.ti (i=1,2, . . . , n): di ca cc khong cch thi gian.T v d (3), tnh y ta lp bng sau:yIti(s ngy)yitI 40019 (1.1 n 19.1)7.6 60026 (20.1 n 14.2)15.6 50023 (15.2 n 9.3)11.5 70022 (10.3 n 31.3)15.4 Cng90 ngy50100 Bng 5.4 Kt qu trn ni ln s dtin vay trung bnh ca qu Il 556,7 triu ng.Su tm bi: www.daihoc.com.vn 925.2.2. Lng tng hoc gim tuyt i Lchtiuphnnhsthayivtrstuyticachtiugia2thigian nghin cu. Ty theo mc ch nghin cu ta c:5.2.2.1. Lng tng (gim) tuyt i tng k (lin hon) Ch tiu ny cho thy lng tng (hoc gim) tuyt i ca hin tng qua 2 k lin nhau.Cng thc tnh: 1 i iy y = yi : mc ca k nghin cuyi-1 :mc ca k ng lin trc .* Nhn xt:mt dy s thi gian c n mc th ch c th tnh c nhiu nht l (n-1) lng tng (gim) tuyt i tng k.T v d (1) ta c:1 2 1y y = =3 3 2y y = = 3 4 3y y = = 5.2.2.2. Lng tng (hoc) gim tuyt i nh gcChtiunyphnnhlngtng(hocgim)cahintngnghincuquamt thi gian di.Cng thc tnh: 1 y iy y = yi : mc ca k nghin cu.y1 : mc k gc (thng l mc u tin ca dy s).+ Mi quan h gia y v yTng i s ca cc lng tng (gim) tuyt i tng k bng lng tng (gim) tuyt i nh gc:y yi = 5.2.2.3. Lng tng gim tuyt i trung bnhCh tiu ny phn nh lng tng (gim) tuyt i in hnh ca hin tng trong c thi k nghin cu:1/ ( 1) / ( 1) ( ) / ( 1) yyi y nn n y y n = = = Su tm bi: www.daihoc.com.vn 935.2.3. Tc pht trin L mt s tng i (thng c biu hin bng ln hoc %) phn nh tc v xu hng bin ng ca hin tng qua thi gian. (tu theomc chnghin cu ta c tc pht trin sau y:)5.2.3.1. Tc pht trin tng k (lin hon) Chtiunyphnnhhintngphttrinvitcphttrincthlbao nhiu qua 2 k lin nhau:ki= yi/ (yi -1) (VT: ln hoc %) * Nhn xt: dy s thi gian c n mc , ch c th tnh c nhiu nht l (n-1) tc pht trin tng k.5.2.3.2. Tc pht trin nh gc Ch tiu ny nh gi nhp pht trin ca hin tng nghin cu qua 1 thi gian di. K = yn / y1 (ln) hoc K= yn x100/ y1 (%) Trong : yi : mc tng k nghin cu (i=2,3, . . . .,n)yi : mc k gc (thng l mc u tin ca dy s).* Mi quan h gia K v k: tch s ca cc tc pht trin tng k bng tc pht trin nh gc.k1.k2.. .. . . kn-1. = K 5.2.3.2. Tc pht trin trung bnh Chtiunyphnnhtcphttrininhnhcahintngtrongcthik nghin cu: 1111 2 3 111. . ...nnnnnn iiyk k k k k ky== = = (ln hoc %) 5.2.4. Tc tng hoc gim L ch tiu cho thy nhp tng trng ca hin tng nghin cu qua thi gian. 5.2.4.1. Tc tng (gim) lin hon (tng k) Ch tiu ny phn nhhin tng tng (hoc gim)vi tc lbao nhiu qua 2 thi k nghin cu linnhau Su tm bi: www.daihoc.com.vn 9411 11yi ii iy ya ky y = = = hoc a =100 k (%) 5.2.4.2.Tc tng gim nh gc Ch tiu ny phn nhhin tng tng (hoc gim)vi tc lbao nhiu qua 1 thi gian di. 11 11yiy yb Ky y= = = (ln) hoc b = K 100 (%) 5.2.4.3. Tc tng (gim) trung bnh Ch tiu ny cho thynhp tng (gim) in hnh ca hin tng trong c thi k nghin cu.1 a k = (ln) hoc100 a k = (%) 5.2.5.Tr tuyt i ca 1% tng (hoc gim) Ch tiu ny dng nh gi tr s tuyt i tng ng vi 1% ca tc tng (hoc gim) tng k. 1 1100 100yi i iy y yca k = = = (VT trng vi VT ca lng bin) 5.3.Cc phng php biu hin xu hng pht trin ca hin tng 5.3.1. Phng php m rng khong cch thi gian Phng php ny c s dng khi 1 dy s thi k c khong cch thi gian tng i ngn v c nhiu mc m qua cha phn nh c xu hng bin ng ca hin tng.V d: C ti liu v sn lng hng thng ca nm 1999 1 x nghip nh sau: Su tm bi: www.daihoc.com.vn 95 ThngSn lngThngSn lng (1.000 tn)(1.000 tn) 140,4740,8 236,8844,8 340,6949,4 438,01048,9 542,21146,2 648,51242,2 Bng 5.5 Dy s trn cho thy sn lng cc thng th tng, khi th gim tht thng, khng ni r xu hng bin ng. Ngi ta c th m rng khong cch thi gian t thng sang qu:QuSn lng (1.000 tn) 1117,8 2128,7 3135,0 4137,3 Bng 5.6 Dokhongcchthigiancmrng(tthngsangqu),nntrongmimc ca dy s mi chu s tc ng ca cc nhn t ngu nhin (vi chiu hng khc nhau) phn no c b tr (trit tiu) v do cho ta thy r xu hng bin ng c bn l: tnh hnh sn xut ca x nghip tng dn t qu 1 n qu 4 ca nm 1999.5.3.2. Phng php s trung bnh trtStrungbnhtrt(cngilstrungbnhding)lstrungbnhcngca1 nhmnhtnhccmccadysctnhbngcchlnltloidnccmc u, ng thi, thm vo cc mc tip theo, sao cho tng s lng cc mc tham gia tnh s trung bnh khng thay i.Gi s c dy thi gian y1 ,y2 ,y3, . . . yn-1 ,ynNu tnh trung bnh trt cho nhm 3 mc , ta s c:1 2 3 2( ) / 3 y y y y = + + Su tm bi: www.daihoc.com.vn 962 3 4 3( ) / 3 y y y y = + +3 4 5 2( ) / 3 y y y y = + +. . 2 2 1 1( ) / 3n n ny y y y = + +T , ta c 1 dy s mi gm cc s trung bnh trt l 2 3 1, ,...,ny y y T v d (*), tnh s trung bnh trt cho nhm 3 mc , ta c : ThngSn lngS trung bnhThngSn lngS trung bnh trt yitrt yi 140,4740,844,7236,839,3844,845,0 340,638,5949,447,7 438,040,31048,948,2 542,242,91146,445,8 648,543,81242,2Bng 5.7 Trung bnh trt cng c tnh t nhiu mc th cng c tc dng san bngnh hng ca cc nhn t ngu nhin. Nhngmt khc b lm gim s lng ccmc ca dy trung bnh trt.5.3.3. Phng php hi quy Trncsdysthigian,ngitatmmthms(gilphngtrnhhiquy) phn nh s bin ng ca hin tng qua thi gian c dng tng qut nh sau:Trong :a0, a1, . . . . ., an : cc tham s.t: th t thi gian.lachnngndngcaphngtrnhhiquyihiphidavosphn tch c im bin ng ca hin tng qua thi gian, ng thi kt hp vi mt s phng phpnginkhc(nhdavoth,davotng(gim)tuyti,davotc Su tm bi: www.daihoc.com.vn 97pht trin, . . . .)Ccthamsai(i=1,2,3,...,n)thngcxcnhbngphngphpbnh phng nh nht. Tc l:2( ) minLT TTy y = Sau y l 1 s dng phng trnh hi quy n gin thng c s dng: _ Phng trnh ng thng: y = a0 + a1tPhngtrnhngthngcsdngkhcclngtng(hocgim)tuyti lin hon (cn gi l sai phn bc 1) xp s nhau. xc nh a0 v a1: ta p dng phng php bnh phng nh nht. T a0 va1 c xc nh bi h phng trnh sau:0 11 120 11 1 1(*)n ni in n ni i iy na a tyt a t a t= == = == += + V d: C s liu v doanh thu ca mt n v sn xut qua cc nm nh sau:Nm19981999200020012002 Doanh thu (T ng)3032313433 tnh a0 v a1 cho v d ny, ta lp bng sau: Nmytt2tyyLTt 1998301130 30,4 1999 32246431,2 2000 31399332,0 2001 3441613632,8 2002 3352516533,6 1601555488 Su tm bi: www.daihoc.com.vn 98Th cc gi tr tng ng trong bng vo h phng trnh trn (*) ta c: 0 10 1160 5 15488 15 55a aa a= + = + T y ta tnh c a0 = 29,6 v a1 = 0,8. Th cc gi tr t ln lt t 1 n 5 tng ng vi thi gian t nm 1998 n nm 2002 ta tnh c cc gi tr doanh thu theo ng hi quy l thuyt y= a0 + a1t l cc gi tr trong ct yLTt.Ta nhn thy rng: bin t l bin th t thi gian, ta c th thay t bng t' (nhng vn m bo tnh th t), sao cho ,t= 0 th vic tnh ton s n gin hn. C 2 trng hp:1.Nuthtthigianlslthlythigiannggiabng0,ccthigian ng trc l -1, -2, -3 v t ng sau l 1, 2, 3.2. Nu th t thi gian l s chn th ly hai thi gian ng gia l -1 v 1, cc thi gian ng trc ln lt l -3, -5, . . . v ng sau ln lt l 3, 5, . . .Vi 't=0 th h phng trnh trn s l:y = na0=> a0 =y /n 't y= 21a t => a1 = 't y/' 2t Khi :yLT = a'0 +a'1t'Vi cch chn 't = 0, ta lp bng sau:Nmyt't'2t'yyLTt 199830-24-6030,4 199932-11-3231,2 20003100032,0 200134113432,8 200233246633,6 1600108 Bng 5.8 a0 = 160 / 5 = 32;a1 = 8 /10 = 0,8 yT =32 + 0,8t' (*)Su tm bi: www.daihoc.com.vn 99 d on sn lng cho nm 2003 th t = 3 vo phng trnh(*) ta c y = 32+0,8*3= 34,4 (t ng)Vi hai cch chnt # 0vt = 0, ta thy kt qu vn nh nhau.5.3.4. Phng php biu hin bin ng thi v S bin ng ca mt s hin tng trong kinh t x hi thng c tnh thi v, ngha l hng nm trong tng thi gian nht nh, s bin ng c lp i lp li.Nghin cu bin ng thi v nhm ra nhng ch trng bin php ph hp, kp thi, hn ch nhng nh hng ca bin ng thi v i vi sn xut v sinh hot ca x hi.Nhimvcanghincuthngkldavosliucanhiunm(tnhtlba nm) xc nh tnh cht v mc ca bin ng thi v. Phng php ny thng c s dng tnh cc ch s thi v.Ch s thi v c tnh theo cng thc: ( )0/ 100(%)i iI y y x =Trong : Iis thi v ca thi gian i. iy : S bnh qun ca cc mc cng thi gian i. 0y : S bnh qun ca tt c cc mc trong dy s. V d: C s liu v sn lng in thoi ng di ca mt n v Bu in qua cc nm nh sau:Su tm bi: www.daihoc.com.vn 100 Sn lng in thoi ng di (cuc) Thng 199719981999 Cng cc thng cng tn (iy ) Bnh qun cc thng cng tn (iy ) Ch s thi vIi = (yi /iy )x100 A1234567 1137.139184.326241.892563.357187.78572.38361.937 2130.009213.218270.682613.909204.63678.88394.415 3159.241234.3350.684744.255248.07595.62478.158 4147.674222.667338.037708.378236.12591.02455.108 5148.589236.26353.488738.337246.11294.87474.356 6162.643229.976368.601761.22253.7497.81489.058 7160.598235.483376.304772.385257.46199.25496.231 8172.235246.789383.399802.423267.474103.1515.529 9180.119249.628410.292840.039280.013107.9539.696 10181.161254.651421.905857.717285.905110.2551.054 11185.552246.818415.502847.872282.624108.94544.729 12197.785259.143632.2331089.16363.053139.95699.748 Cng9.339.023 Bng 5.9 9.339.0231.037.66936y = =(cuc) Qua kt qu trnh by bng trn ta thy sn lng in thoi ng di trong nctngcaonhtnhngthngcuinm(gntt)vgimthpnhtthnggingvthng hai.Giskhochsnlnginthoichonm2000l6000000cucthtad on sn lng ca tng thng ca nm 2000 s l: cc sn lng trong ct (7) Su tm bi: www.daihoc.com.vn