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8/2/2019 MT S PHNG PHP KHAI PH D LIU QUAN H TRONG TI CHNH V CHNG KHON (M HNH ARIMA)

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I HC QUC GIA H NI

TRNG I HC CNG NGH

Nguyn Ngc Thip

MT S PHNG PHP KHAI PH DLIU QUAN

H TRONG TI CHNH V CHNG KHON

(M HNH ARIMA)

KHA LUN TT NGHIP I HC H CHNH QUY

Ngnh : Cng ngh thng tin

H NI - 2010


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I HC QUC GIA H NI

TRNG I HC CNG NGH

Nguyn Ngc Thip

MT S PHNG PHP KHAI PH DLIU QUAN

H TRONG TI CHNH V CHNG KHON(M HNH ARIMA)

KHA LUN TT NGHIP I HC H CHNH QUY

Ngnh : Cng ngh thng tin

Cn b hng dn : PGS-TS H Quang Thy

Cn bng hng dn : Th.s Nguyn Th Oanh.

H NI - 2010


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LI CM N

Li u tin, em xin by t long bit n ti cc thy, c gio trong

trng i hc Cng Ngh - i hc Quc Gia H ni. Cc thy c dy bo, ch

dn em v lun to iu kin tt nht cho chng em hc tp trong sut qu trnh hc

i hc c bit l trong thi gian lm kha lun tt nghip.

Em xin by t lng bit n su sc ti thy gio PGS.TS H Quang Thy

cng c gio ThS Trn Th Oanh, v cc anh ch trong phng LAB 102 hng

dn em tn tnh trong nm hc va qua.

Ti cng xin cm n nhng ngi bn ca mnh, cc bn lun bn ti,

gip v cho ti nhng kin ng gp qu bu trong hc tp cng nh trong

cuc sng.Cui cng con xin gi ti b m v ton th gia nh lng bit n v tnh

cm yu thng nht.

H Ni, ngy 10/05/2010

Nguyn Ngc Thip


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MU

Bi ton d bo ti chnh ngy cng c nhiu ngi quan tm trongbi cnh pht trin kinh t x hi. u t vo th trng chng khon i hi nhiukinh nghim v hiu bit ca cc nh u t. Cc k thut khai ph d liu c p

dng nhm d bo s ln xung ca th trng l mt gi gip cc nh u t cth ra quyt nh giao dch.

M hnh ARIMA c xy dng vi chc nng nhn dng m hnh, clng cc tham s v a ra kt qu d bo da trn cc tham sc lng cla chn mt cch ti u.

Kha lun nghin cu, thi hnh m hnh ARIMA (t cc nghin cu ca Box-Jenkins) v ng dng vo bi ton khai ph d liu chui thi gian trong d bo tichnh, chng khon. Kha lun thc nghim trn d liu vnIndex v thu ckt qu bc u.

Vi ni dung trnh by nhng l thuyt cbn v m hnh ARIMA chod liu thi gian thc (time series) v cch p dng vo bi ton thc t - d bo sln xung ca th trng chng khon. Kha lun c t chc theo cu trc nhsau :

Chng 1. GII THIU CHUNG gii thiu s lc v khai ph dliu ni chung v bi ton d bo ang c quan tm trong khai ph d liu . Biton d bo c p dng di khia cnh s dng m hnh ARIMA cho chui thigian thc.

Chng 2. M HNH ARIMA V PHN MM EVIEW trnh bymt s ni sung c s l thuyt v m hnh ARIMA, cng nh nhng cng c sc p dng vo trong m hnh m kha lun cp : Hm t tng quan ACF,hm t tng quan ring phn PACFCc bc pht trin m hnh : xc nh mhnh, c lng cc tham s, kim nh chnh xc v d bo. M hnh ARIMA lmt qu tnh th v sai : khi mt kim nh no khng tha mn, phi xc nhli m hnh. Tip n gii thiu qua v phn mm Eviews 5.1 cho qu trnh thi hnh.

Chng 3. P DNG M HNH ARIMA VO BI TON TICHNH, CHNG KHON trnh by thc nghim m hnh ARIMA cho d liu ti

chnh, chng khon. Cc bc trong qu trnh thi hnh chng trnh vi phn mmEviews 5.1, a ra kt qu v nh gi vi thc t.

Phn Kt lun tng kt kt qu ca kha lun v phng hng nghincu tip theo.


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MC LC

MU............................................................................................................................................ 4

Chng 1. GII THIU CHUNG..................................................................................................... 7

1.1. Bi ton dbo 7

1.2. Dliu chui thi gian 9

1.2.1. Khi nim chui thi gian thc............................................................................... 10

1.2.2. Thnh phn xu hng di hn................................................................................. 10

1.2.3. Thnh phn ma...................................................................................................... 11

1.2.4. Thnh phn chu k.................................................................................................. 11

1.2.5. Thnh phn bt thng............................................................................................ 12

CHNG 2. M HNH ARIMA V PHN MM EVIEWS....................................................... 13

2.1. M hnh ARIMA 13

2.1.1. Hm t tng quan ACF.......................................................................................... 13

2.1.2. Hm t tng quan tng phn PACF...................................................................... 14

2.1.3. M hnh AR(p)........................................................................................................ 17

2.1.4. M hnh MA(q)....................................................................................................... 17

2.1.5. Sai phn I(d)............................................................................................................. 18

2.1.6. M hnh ARIMA...................................................................................................... 18

2.1.7.Cc bc pht trin m hnh ARIMA....................................................................... 22

2.2. Phn mm ng dng Eviews 22

2.2.1. Gii thiu Eviews.................................................................................................... 22

2.2.2.pdngEviewsthihnhccbcmhnhARIMA............................................. 27Tm tt chng 2 29

Chng 3. P DNG M HNH ARIMA VO BI TON TI CHNH, CHNG KHON...30

3.1. M hnh ARIMA cho d bo ti chnh, chng khon 30

3.1.1. D liu ti chnh...................................................................................................... 30

3.1.2. M hnh ARIMA cho bi ton d bo ti chnh..................................................... 30


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3.1.3. Thit k m hnh ARIMA cho d liu................................................................... 31

3.2. p dng 33

3.2.1. Mi trng thc nghim........................................................................................ 33

3.2.2.Dliu....................................................................................................................... 33

3.2.3.Kim tra tnh dng ca chui chng khon AAM............................................... 34

3.2.4.Nhn dng m hnh................................................................................................. 35

3.2.5.c lng v kim nh vi m hnh ARIMA..................................................... 37

3.2.6Thc hin d bo........................................................................................................ 38

KT LUN...................................................................................................................................... 41


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Chng 1. GII THIU CHUNG

1.1. Bi ton dbo

S pht trin ca cng ngh thng tin v vic ng dng cng ngh thng tin

trong nhiu lnh vc ca i sng, kinh t x hi trong nhiu nm qua cng ng ngha

vi lng d liu c cc cquan thu thp v lu tr ngy mt tch ly nhiu ln.H lu tr cc d liu ny v cho rng trong n n cha nhng gi tr nht nh no .

Tuy nhin, theo thng k th ch c mt lng nh ca nhng d liu ny (khong t

5% n 10% ) l lun c phn tch, s cn li h khng bit s phi lm g hoc c

th lm g vi chng nhng h vn tip tc thu thp rt tn km vi nghlo srng

s c ci g quan trng b b qua sau ny c lc cn n n. Mt khc, trong mi

trng cnh tranh, ngi ta ngy cng cn c nhiu thng tin vi tc nhanh tr

gip vic ra quyt nh v ngy cng c nhiu cu hi mang tnh cht nh tnh cn

phi tr li da trn mt khi lng d liu khng l c. Vi nhng l do nh vy,cc phng php qun tr v khai thc csd liu truyn thng ngy cng khng p

ng c thc t lm pht trin mt khuynh hng k thut mi l k thut pht

hin tri thc v khai ph d liu (KDD Knowledge Discovery and Data Mining).

K thut pht hin tri thc v khai ph d liu v ang c nghin cu, ng

dng trong nhiu lnh vc khc nhau cc nc trn th gii, ti Vit Nam k thut

ny tng i cn mi m tuy nhin cng ang c nghin cu v dn a vo ng

dng.

T tha xa xa, nhng nh tin tri gi mt v tr quan trng trong cng ng.

Khi vn minh nhn loi pht trin lm gia tng cc mi quan h phc tp ca cc

giai on trong cuc sng, con ngi c nhu cu quan tm n tng lai ca h.

Nh trnh by trong [2, 3], k thut d bo hnh thnh t th k th 19, tuy

nhin d bo c nh hng mnh m khi cng ngh thng tin pht trin v bn cht m

phng ca cc phng php d bo rt cn thit s h tr ca my tnh. n nm

nhng 1950, cc l thuyt v d bo cng vi cc phng php lun c xy dng v

pht trin c h thng.

D bo l mt nhu cu khng th thiu cho nhng hot ng ca con ngi trong

bi cnh bng n thng tin. D bo s cung cp nhng cscn thit cho cc hochnh, v c th ni rng nu khng c khoa hc d bo th nhng dnh tng lai ca

con ngi vch ra s khng c s thuyt phc ng k.

Trong cng tc phn tch d bo, vn quan trng hng u cn t ra l vic

nm bt ti a thng tin v lnh vc d bo. Thng tin y c th hiu mt cch c


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th gm : (1) cc s liu qu kh ca lnh vc d bo, (2) din bin tnh hnh hin

trng cng nhng thi pht trin ca lnh vc d bo v (3) nh gi mt cch y

nht cc nhn tnh hng c vnh lng ln nh tnh.

Cn c vo ni dung phng php v mc ch ca d bo, ngi ta chia d bo

thnh hai loi: Phng php nh tnh v phng php nh lng.Phng php nh tnh thng ph thuc rt nhiu vo kinh nghim ca mt hay

nhiu chuyn gia trong lnh vc lin quan. Phng php ny thng c p dng, kt

qu d bo sc cc chuyn gian trong lnh vc lin quan nhn xt, nh gi v a

ra kt lun cui.

Phng php nh lng s dng nhng d liu qu kh theo thi gian, da trn

d liu lch s pht hin chiu hng vn ng ca i tng ph hp vi mt m

hnh ton hc no v ng thi s dng m hnh lm m hnh c lng. Tip

cn nh lng da trn ginh rng gi tr tng lai ca bin s d bo s ph thuc

vo xu th vn ng ca i tng trong qu kh. Phng php d bo theo chui

thi gian l mt phng php nh lng.

Phng php chui thi gian s da trn vic phn tch chui quan st ca mt

bin duy nht theo bin sc lp l thi gian. Ginh ch yu l bin s d bo s

gi nguyn chiu hng pht trin xy ra trong qu kh v hin ti.

Kha lun tp trung nghin cu m hnh ARIMA thc hin phn tch d liu

chng khon hng ti vic d bo chng khon. M hnh ARIMA (AutoRegressive

Integrate Moving Average) do Box-Jenkins ngh nm 1976 [6, 11, 13], da trn m

hnh t hi quy AR v m hnh trung bnh ng MA. ARIMA l m hnh d bo nhlng theo thi gian, gi tr tng lai ca bin s d bo s ph thuc vo xu th vn

ng ca i tng trong qu kh. M hnh ARIMA phn tch tnh tng quan gia

cc d liu quan st a ra m hnh d bo thng qua cc giai on nhn dng m

hnh, c lng cc tham s t d liu quan st v kim tra cc tham sc lng

tm ra m hnh thch hp. M hnh kt qu ca qu trnh trn gm cc tham s th hin

mc tng quan trn d liu, v c chn d bo gi tr tng lai. Gii hn

tin cy ca d bo c tnh da trn phng sai ca sai s d bo.


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1.2. Dliu chui thi gianTrong cc bi ton d bo ni chung v cc bi ton d bo ti chnh v chng

khon ni ring, d liu thng c biu din di dng chui thi gian. Trong cc

dng d liu c phn tch th d liu chui thi gian lun thuc tp u v tnh

ph bin. Cc bng thng k thm d v cc kiu d liu c phn tch trong 4 nm2005-20081 (Hnh 1) l mt minh chng viu ny.

http://www.kdnuggets.com/polls/2008/data-types-analyzed-data-mined.htm

http://www.kdnuggets.com/polls/2007/data_types_analyzed.htm

http://www.kdnuggets.com/polls/2006/types_data_analyzed_mined.htm

http://www.kdnuggets.com/polls/2005/data_types.htm

Hnh 1. Chui thi gian l kiu d liu c phn tch ph bin

1http://www.kdnuggets.com/


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1.2.1. Khi nim chui thi gian thc

Theo [13, 16], d liu thi gian thc hay chui thi gian l mt chui cc gi tr

ca mt i lng no c ghi nhn l thi gian.

V d : S lng hng ha c bn ra trong 12 thng nm 2009 ca mt cng

ty.Cc gi tr ca chui thi gian ca i lng X c k hiu l X1, X2, X3,,

Xt, , Xn viX l gi tr ca X ti thi im t.

Cc thnh phn ca dliu chui thi gian thc

Cc nh thng k thng chia chui theo thi gian thnh 4 thnh phn:

Thnh phn xu hng di hn (long term trend component)

Thnh phn ma (seasional component)

Thnh phn chu k (cyclical component)

Thnh phn bt thng (irregular component)

1.2.2. Thnh phn xu hng di hn

Thnh phn ny dng ch xu hng tng hay gim ca i lng X trong thi

gian di. V mt th thnh phn ny c th biu din bi mt ng thng hay mt

ng cong trn.

Hnh 1a. Xu hng tng theo thi gian [16]


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1.2.3. Thnh phn ma

Thnh phn ny dng ch xu hng tng hay gim ca i lng X tnh theo

ma trong nm (c th tnh theo thng trong nm)

V d : Lng tiu th cht t s tng vo ma ng v gim vo ma h,

ngc li, lng tiu th xng s tng vo ma h v gim vo ma ng.

Lng tiu th dng hc tp s tng vo ma khai trng

Hnh 2. Thnh phn ma [1]

1.2.4. Thnh phn chu k

Thnh phn ny ch s thay i ca i lng X theo chu k. Thnh phn ny

khc thnh phn ma ch chu k ca i lng X ko di hn 1 nm. nh gi

thnh phn ny cc gi tr ca chui thi gian c quan st hng nm.

V d, Lng dng chy n h Tr An t nm 1959 1985

Hnh 3. Thnh phn chu k [1]

Tha i theoXuhng tng theo

m3/s

t


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1.2.5. Thnh phn bt thng

Thnh phn ny dng ch s thay i bt thng ca cc gi tr trong chui

thi gian. S thay i ny khng th don bng cc s liu kinh nghim trong qu

kh, v mt bn cht thnh phn ny khng c tnh chu k.


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CHNG 2. M HNH ARIMA V PHN MM EVIEWS

2.1. M hnh ARIMA

2.1.1. Hm ttng quan ACF

Hm t tng quan o lng ph thuc tuyn tnh gia cc cp quan sty(t) v y(t+k), ng vi thi on k = 1, 2, (k cn gi l tr). Vi mi tr k,

hm t tng quan ti tr kc xc nh qua lch gia cc bin ngu nhin

Yt. Yt+kso vi cc gi tr trung bnh, v c chun ha qua phng sai.

Di y, gi thit rng cc bin ngu nhin trong chui dng thay i

quanh gi tr trung bnh vi phng sai hng s2. Hm t tng quan ti cc tr khc nhau s c gi tr khc nhau.

Trong thc t, ta c thc lng hm t tng quan ti tr th k qua

php bin i trung bnh ca tt c cc cp quan st, phn bit bng cc tr k, vigi tr trung bnh mu l , c chun ha bi phng sai 2.Chng hn, cho michui N im, gi tr rkca hm t tng quan ti tr th kc tnh nh sau :

rk=

(1.1)

vi

(1.2)

yt : chui thi gian dng ti thi im t

yt+k: chui thi gian dng ti thi im t +k

^ : gi tr trung bnh ca chui dng

rk: gi tr tng quan gia yt v yt+k ti tr k

rk= 0 th khng c hin tng t tng quan

V mt l thuyt, chui dng khi tt c cc rk= 0 hay ch vi rkkhc khng. Do

chng ta xem xt hm t tng quan mu, do sai s mu s xut hin v vy, hintng t tng quan khi rk= 0 theo ngha thng k.

Khi hm t tng quan ACF gim t ngt, c ngha rkrt ln tr 1, 2 v

c ngha thng k (|t| >2). Nhng rkny c xem l nhng nh v ta ni rng


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hm t tng quan ACF gim t ngt sau tr k nu khng c nhng nh

tr k ln hn k. Hu ht hm t tng quan ACF s gim t ngt sau tr 1, 2.

Nu hm t tng quan ACF ca chui thi gian khng dng khng gim t

ngt m tri li gim nhanh nhng u : khng c nh, ta gi chiu hng ny l

tt dn. Xem minh ha trong hnh 4, hm t tng quan ACF c th tt dntrong vi dng sau :

Dng phn phi mu (hnh 4a v hnh 4b)

Dng sng sin (hnh 4c)

Kt hp c hai dng 1 v 2.

S khc nhau gia hin tng tt dn nhanh v tt dn chm u c

phn bit kh ty tin.

2.1.2. Hm ttng quan tng phn PACF

Song song vi vic xc nh hm t tng quan gia cc cp y(t) v y(t+k), ta

xc nh hm t tng quan tng phn cng c hiu lc trong vic can thip n cc

quan st y(t+1), ..., y(t+k-1). Hm t tng quan tng phn ti tr k Ckkc c

lng bng h s lin h y(t) trong mi kt hp tuyn tnh bn di. S kt hp

c tnh da trn tm nh hng ca y(t) v cc gi tr trung gian y(t+k).

y(t+k) = Ck1y(t+k-1) + Ck2y(t+k-2) + ... + Ckk-1y(t + 1) + Ckky(t) + e(t)

(1.3)

Gii phng trnh hi quy da trn bnh phng ti thiu v h s hi quy Ckj

phi c tnh mi tr k, vi j chy t 1 n k.

Gii php t tn km hn do Durbin [14] pht trin dng xp x quy h s

hi quy cho m hnh ARIMA chui dng, s dng gi tr hm t tng quan ti

tr k rkv h s hi quy ca tr trc. Di y l phng php Durbin s dng

cho 3 tru tin.

tr 1 : Khi to, gi tr ca hm t tng quan tng phn ti tr 1 c

cng gi tr vi hm t tng quan ti tr 1 v khng c trung gian gia cc quanst kt tip : C11 = r1

tr 2 : Hai gi tr C22 v C21c tnh da vo hm t tng quan r2 v r1,

cng vi hm t tng quan tng phn trc


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C22

C21 = C11 C22C11

tr 3 : Tng t, ba gi tr C33, C32, C31c tnh da vo cc hm t

tng quan trc r3,r2,r1 cng vi cc h sc tnh tr th 2 : C22 v C21.

C33=

C32 = C21-C33C22

C31 = C22- C33C21

Tng quan, hm t tng quan tng phn c tnh theo Durbin :

Ckk=,

, (1.4)

Trong :

rk: Hm t tng quan ti tr k

v : Phng sai

Ckj : Hm t tng quan tng phn cho tr k, loi b nhng nh hng ca

cc tr can thip.

Ckj = Ck-1,j (Ckk).C(k-1,k-j) k = 2,, j = 1,2,, k-1

C22 = (r2-r12)/(1-r1

2)

C11 = r1

Khi tr tng, s cc h s tng theo. Phng php ca Durbin cho php vic

tnh quy da vo vic s dng kt qu trc .

Tm li, hm t tng quan ACF v hm t tng quan tng phn PACF ca

chui thi gian c cc c tnh khc nhau. Hm t tng quan ACF o mc ph

thuc tuyn tnh gia cc cp quan st. Hm t tng quan tng phn PACF o mc

ph thuc tuyn tnh tng phn. ARIMA khai thc nhng im khc bit ny xc nh cu trc m hnh cho chui thi gian.

Xu hng vn ng ca hm t tng quan tng phn PACF c th gim t

ngt (thng sau tr 1 hoc 2) hay c th gim u. Cng nh hm t tng quan


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2.1.3. M hnh AR(p)

Theo [6, 11, 16], tng chnh ca m hnh AR(p) l hi quy trn chnh s

liu qu khnhng chu k trc.

Y(t) = a0 + a1y(t-1) + a2y(t-2) +apy(t-p) + e(t) (1.5)Trong :

y(t) : quan st dng hin ti

y(t-1), y(t-2), ... : quan st dng qu kh (thng s dng khng qu 2 bin

ny)

a0, a1, a2, : cc tham s phn tch hi quy.

et : sai s d bo ngu nhin ca giai on hin ti. Gi tr trung bnh c

mong i bng 0.Y(t) l mt hm tuyn tnh ca nhng quan st dng qu kh y(t-1). y(t-2),

Ni cch khc khi s dng phn tch hi quy y(t) theo cc gi tr chui thi gian

dng c tr, chng ta sc m hnh AR (yu t xu th c tch khi yu

t thi gian, chng ta s m hnh ha nhng yu t cn li l sai s).

S quan st dng qu kh s dng trong m hnh hm t tng quan l bc p

ca m hnh AR. Nu ta s dng hai quan st dng qu kh, ta c m hnh tng

quan bc hai AR(2).

iu kin dng l tng cc tham s phn tch hi quy nh hn 1 :

a1 + a2 + + ap < 1

M hnh AR(1) : y(t) = a0 + a1y(t-1) + e(t)

M hnh AR(2) : y(t) = a0 + a1y(t-1) + a2y(t-2) +e(t)

2.1.4. M hnh MA(q)

Quan st dng hin ti y(t) l mt hm tuyn tnh ph thuc cc bin sai s d

bo qu kh v hin ti. M hnh bnh qun di ng l mt trung bnh trng s ca

nhng sai s mi nht.

y(t) = b0 + e(t) +b1e(t-1) + b2e(t-2) + ... +bqe(t-q)

(1.6)

Trong :


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e(t) : sai s d bo ngu nhin, gi tr ca n khng c bit v gi tr trung

bnh ca n l 0.

e(t-1), e(t-2), ... : sai s d bo qu kh (thng thng m hnh s s dng

khng qu 2 bin ny)

b0, b1, b2, ... : gi tr trung bnh ca y(t) v cc h s bnh qun di ng.

q : sai s qu khc dng trong m hnh bnh qun di ng, nu ta s dng

hai sai s qu kh th s c m hnh bnh qun di ng bc 2 l MA(2).

iu kin cn l tng cc h s bnh qun di ng phi nh hn 1 :

b1 + b2 + ... + bq < 1

M hnh MA(1) : y(t) = b0 + e(t) + b1e(t-1)

M hnh MA(2) : y(t) = b0 + e(t) + b1e(t-1) + b2e(t-2)

2.1.5.Sai phn I(d)

Chui dng : Chui thi gian c coi l dng nu nh trung bnh vphng sai ca n khng i theo thi gian v gi tr ca ng phng sai gia haithi on ch ph thuc vo khong cch v tr v thi gian gia hai thi onny ch khng ph thuc vo thi im thc t m ng phng sai c tnh.

Sai phn ch s khc nhau gia gi tr hin ti v gi tr trc . Phn

tch sai phn nhm lm cho n nh gi tr trung bnh ca chui d liu, gip chovic chuyn i chui thnh mt chui dng.

Sai phn ln 1 (I(1)) : z(t) = y(t) y(t-1)

Sai phn ln 2 (I(2)) : h(t) = z(t) z(t-1)

2.1.6. M hnh ARIMA

M hnh ARMA(p,q) : l m hnh hn hp ca AR v MA. Hm tuyn tnh s

bao gm nhng quan st dng qu kh v nhng sai s d bo qu kh v hin ti :

y(t) = a0 + a1y(t-1) + a2y(t-2) +... + apy(t-p) + e(t)

+ b1e(t-1) +b2e(t-2) + ... + bqe(t-q)

(1.7)

Trong :


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y(t-p), v e(t-q) : quan st dng v sai s d bo qu kh.

a0, a1, a2, ..., b1, b2, ... : cc h s phn tch hi quy

V d : ARMA(1,2) l m hnh hn hp ca AR(1) v MA(2)i vi m hnh hn hp th dng (p,q) = (1,1) l ph bin. Tuy nhin, gi tr p

v q c xem l nhng tr cho ACF v PACF quan trng sau cng. C hai iu

kin bnh qun di ng v iu kin dng phi c tha mn trong m hnh hn

hp ARMA.

M hnh ARIMA(p,d,q) : Do m hnh Box-Jenkins ch m t chui dng

hoc nhng chui sai phn ha, nn m hnh ARIMA(p,d,q) th hin nhng chui

d liu khng dng, c sai phn (y, d ch mc sai phn).

Khi chui thi gian dng c la chn (hm t tng quan ACF gim tngt hoc gim u nhanh), chng ta c th ch ra mt m hnh dnh bng cch

nghin cu xu hng ca hm t tng quan ACF v hm t tng quan tng phn

PACF. Theo l thuyt, nu hm t tng quan ACF gim t bin v hm t tng

quan tng phn PACF gim mnh th chng ta c m hnh t tng quan. Nu hm

t tng quan ACF v hm t tng quan tng phn PACF u gim t ngt th

chng ta c m hnh hn hp.

V mt l thuyt, khng c trng hp hm t tng quan ACF v hm t

tng quan tng phn cng gim t ngt. Trong thc t, hm t tng quan ACFv hm t tng quan tng phn PACF gim t bin kh nhanh. Trong trng hp

ny, chng ta nn phn bit hm no gim t bin nhanh hn, hm cn li c

xem l gim u. Do i lc s c trng hp gim t bin ng thi khi quan st

biu hm t tng quan ACF v hm t tng quan tng phn PACF, bin php

khc phc l tm vi dng hm dnh khc nhau cho chui thi gian dng. Sau ,

kim tra chnh xc m hnh tt nht.

M hnh ARIMA (1, 1, 1) : y(t) y(t-1) = a0 + a1(y(t-1) y(t-2) + e(t) + b1e(t-

1))

Hoc z(t) = a0 + a1z(t-1) + e(t) + b1e(t-1),

Vi z(t) = y(t) y(t-1) sai phn u tin : d = 1.

Tng t ARIMA(1,2,1) : h(t) = a0 + a1z(t-1) + e(t) + b1e(t-1),


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Vi h(t) = z(t) z(t-1) sai phn th hai : d = 2.

Theo [6], trong thc hnh d ln hn 2 rt t c s dng.


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Hnh 5. S m phng m hnh Box-Jenkins [3].

Tnh cc hm ttngquan v ttng quan tngphn nhn dng mt mhnh d nh

Chn la mt m hnh

c lng cc gi tr chocc tham s m hnh

Kim tra chnh xcca m hnh

Sdng m hnh dbo

Kh


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2.1.7. Cc bc pht trin m hnh ARIMA

Theo [3, 6], phng php Box Jenkins bao gm cc bc chung:

Xc nh m hnh

c lng tham s

Kim nh chnh xc

D bo.

Xc nh m hnh : M hnh ARIMA chc p dng i vi chui dng

M hnh c th trnh by theo dng AR, MA hay ARMA. Phng php xc

nh m hnh thng c thc hin qua nghin cu chiu hng bin i ca

hm t tng quan ACF hay hm t tng quan tng phn PACF.

o Chui ARIMA khng dng : cn phi c chuyn i thnh chui

dng trc khi tnh c lng tham s bnh phng ti thiu. Vicchuyn i ny c thc hin bng cch tnh sai phn gia cc gi tr

quan st da vo ginh cc phn khc nhau ca cc chui thi gian

u c xem xt tng t, ngoi tr cc khc bit gi tr trung bnh.

Nu vic chuyn i ny khng thnh cng, s p dng tip cc kiu

chuyn i khc (chuyn i logarithm chng hn).

c lng tham s : tnh nhng c lng khi u cho cc tham s a0, a1,

, ap, b1, , bqca m hnh dnh. Sau xy dng nhng c lng sau

cng bng mt qu trnh lp. Kim nh chnh xc : Sau khi cc tham s ca m hnh tng qut xy

dng, ta kim tra mc chnh xc v ph hp ca m hnh vi d liu. Chng

ta kim nh phn d (Yt Y^t) v c ngha cng nh mi quan h cc tham

s. Nu bt c kim nh no khng tha mn, m hnh s nhn dng li cc

bc trn c thc hin li.

Dbo : Khi m hnh thch hp vi d liu tm c, ta s thc hin d bo

ti thi im tip theo t. Do , m hnh ARMA(p,q) :

y(t+1) = a0 + a1y(t) + + apy(t p + 1) + e(t+1) + b1e(t) + + bqe( t q + 1)

(X)

2.2. Phn mm ng dng Eviews

2.2.1. Gii thiu Eviews


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Eviews l mt gi phn mm thng k cho Windows, c s dng chnh vo

phn tch kinh t hng i tng chui thi gian. N do Quantitative Micro Software

(QMS) ph trin. Bn 1.0 c ra i vo thng 3 nm 1994 [].

Phng Thanh Bnh [5] gii thiu tng i c th v Eviews v cc tnh

hung s dng Eviews. Eviews cung cp cc cng c phn tch d liu phc tp, hiquy v d bo chy trn Windows. Vi Eviews, chng ta c th nhanh chng xy dng

mi quan h kinh t lng t d liu c sn v s dng mi quan h ny d bo cc

gi tr tng lai. Eviews c th hu ch trong tt c cc loi nghin cu nhnh gi

v phn tch d liu khoa hc, phn tch ti chnh, m phng v d bo vm, d bo

doanh s, v phn tch chi ph. c bit, Eviews l mt phn mm rt mnh cho phn

tch d liu thi gian.

Eview a ra nhiu cch nhp d liu rt thng dng v d s dng nh nhp

bng tay, t cc file c di dng excel hay text, d dng mrng file d liu c sn.

Eviews trnh by cc biu , kt qun tng v c th in trc tip hoc chuyn quan

cc loi nh dng vn bn khc nhau. Eviews gip ngi s dng d dng c lng

v kim nh cc m hnh kinh t lng. Ngoi ra, Eviews cn gip ngi nghin cu

c th xy dng cc file chng trnh cho d n nghin cu ca mnh.

Khi khi ng chng trnh c dng :

Hnh 6. Eviews 5 Users Guide.

To mt tp tin Eviews

Command

WorkStatus


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C nhiu cch to mt tp tin mi.

Eviews s to ra mt tp tin mi ta nhp d liu vo mt cch th cng t

bn phm hoc copy v paste

File/ New Workfilet thc n chnh mhp thoi Workfile

Create. gc bn tri m t cu trc cbn ca d liu. Ta c th chn giaDated-Regular Frequency, Unstructured, Balanced Panel. Vi d liu thi

gian ta chn Dated-Regular Frequency, nu d liu n gin ta chn

Balanced Panel, cc trng hp khc chn Unstructured.

Hnh 7. La chn cu trc cbn ca qu trnh to Workfile

Nu l d liu nm, th Frequency ta chn Annual; cc Start date v

Ende date ta nhp nm bt u v nm kt thc ca chui d liu. Nu d liu l qu,th Frequency ta chn Quarrterly

Mv c d liu t mt ngun bn ngoi (khng thuc nh dng ca Eviews)

nh Text, Excel, Stata

File/open/Foreign Data as Workfile,n hp thoi Open, chn

Files of type


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Hnh 8. Mmt file c sn vi Eviews 5

Sau khi to mt tp tin Eviews, ta lu li di nh dng Eviews bng

cch hn File/Save As hay File/Save...

Trnh by dliu

Trnh by dliu ca mt chui

xem ni dung ca mt bin no , v dgiadongcua trong tp tin. Ta

kch p vo.

Hnh 9. Miu t chui d liu

V th

C hai cch biu hin th dng Line ca bin. Th nht, t chui(ly

chui giadongcua lm v d) ta chn View/Graph/Line. Th 2, t ca s


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Workfile trn thanh Main menu ta chn Quick/Graph/Line Graph, ri nhp

tn bin giadongcua

Hnh 10: th ca chui GIADONGCUA

n gin copy th ra word ta ch cn Ctrl + C v paste sang word.

To mt bin mi

Eviews h trchuyn i to bin mi bng cch clickGenr ri g

hm chuyn i. Thng thng : loggiadongcua = log(giadongcua).

Bin tr, ti, sai phn v ma v

Bin tr , ti mt giai on (xt-1) : x(-1), (xt+1) : x(+1)

Bin tr k giai on (xt-k) : x(-k), (xt+k) : x(+k)

Sai phn bc mt (d(x) = xt xt-1)

Sai phn bck k (d(x,k) = xt xt-k)

Biu tng quan.

View/Correlogram


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Hnh 11. Biu hm t tng quan, t tng quan tng phn.

Hm v cc php ton trong Eviews

- Cc php ton s hc : +,-,*,/

- Cc php ton chui

Eviews cho php tnh ton hoc to mt chui mi t mt hoc nhiu

chui c sn bng cc ton t thng thng nh trn. V d :

2*y +3, x/y +z

-Cc hm chui : Hu ht cc hm Eviews u bt u bng k hiu @, vd @mean(y) : Gi tr trung bnh ca chui y

@abs(x) : Hm gi tr tuyt i

@sqrt(x) : Hm cn bc hai

2.2.2. p dng Eviews thi hnh cc bc m hnh ARIMA

2.2.2.1. Xc nh m hnh

a dliu vo : Do d liu trong qu trnh d bo s dng m hnh ARIMA

l ln, d liu u vo c xut : Mv c d liu t mt ngun bnngoi (khng thuc nh dng ca Eviews) nh Text, Excel, Stata

File/open/Foreign Data as Workfile,n hp thoi Open, chn

Files of type (xem thm 2.2.1)

Kim tra tnh dng ca chui dliu : kch p vo bin GiaDongCua,


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View/Graph/line : a ra tng v mt chui thi gian l dng hay

khng.

View/Correlogram : Xc nh cc thnh phn p,d,q ca m hnh.

2.2.2.2. c lng m hnh, kim tra m hnh

T biu tng quan, xc nh c cc thnh phn p,d,q cho m hnh. Tip

theo ta xy dng m hnh theo cc bc :

Chn Quick/estimate Equation g vo mc Equation Specification m hnh

c xc nh 2.2.2.1.

Type : giadongcua c ar(1) ma(2), giadongcua c ar(1), giadongcua c

ma(2) (Ty thuc vo m hnh c xc nh)

Hnh12. c lng m hnh.

Hnh 13. Kt qu qu trnh c lng

Chn View/Residual tests/correlogram-Q-Statistic : Dng xc nh tnh nhiutrng ca m hnh.


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M hnh c gi l nhiu trng(white noise) c trung bnh v phng sai khngi theo thi gian hay hm t tng quan v t tng quan ring phn dao ng quanhmt v tr trung bnh ca chui [17].

Khi mt mt m hnh c xc nh l nhiu trng, ta c th dng m hnh m khng cn n m hnh tip theo.

Cc tiu chun nh gi mt m hnh l tt nht [18] :

o BIC nh (Schwarz criterion c xc nh bi : n.Log(SEE) + K.Log(n))

o SEE nh

o R2 ln

o Q-statistics v th tng quan ch ra phn d l nhiu trng.

Sau c th th vi cc m hnh khc v so snh kt qu theo cc tiu chun nh

gi.

2.2.2.3. Dbo

Ti ca s Equation ca phng trnh, bm nt forecast

Hnh 14. Chn cc yu cu thch hp cho d bo

Tm tt chng 2

Chng ny nhm gii thiu v m hnh ARIMA: (1) hm t tng quanACF, (2) hm t tng quan tng phn PACF, (3) m hnh thnh phn AR(p), (4)m hnh MA(q), sai phn I(d), cc bc trong qu trnh xy dng m hnh ARIMA.Gii thiu sb v phn mm ng dng Eviews 5.1 phc v cho bi ton d bo

bng m hnh ARIMA.


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Chng 3. P DNG M HNH ARIMA VO BI TON TI CHNH,CHNG KHON

3.1. M hnh ARIMA cho dbo ti chnh, chng khon

3.1.1. Dliu ti chnh

D liu chng ta s dng l d liu chui thi gian. c im chnh phn

bit gia d liu c phi l thi gian thc hay khng chnh l s tn ti ca ct

thi gian c nh km trong i tng quan st. Ni cch khc, d liu thi gian

thc l mt chui cc gi tr quan st ca bin Y :

Y = {y1, y2, y3,, yt-1, yt, yt+1, , yn} vi yt l gi tr ca bin Y ti thi imt.

Mc ch chnh ca vic phn tch chui thi gian thc l thu c mt m

hnh da trn cc gi tr trong qu kh ca bin quan st y1, y2, y3,, yt-1, yt cho

php ta don c gi tr ca bin Y trong tng lai, tc l c th don c

cc gi tr yt+1, yt+2,yn.

Trong bi ton ca chng ta, d liu chng khon c bit ti nh mt chui

thi gian a dng bi c nhiu thuc tnh cng c ghi ti mt thi im no .

Vi d liu ang xt, cc thuc tnh l : Open, High, Low, Close, Volume

Open : Gi c phiu ti thi im mca trong ngy.

High : Gi c phiu cao nht trong ngy

Low : Gi c phiu thp nht trong ngy

Close : Gi c phiu c nim yt ti thi im ng ca sn giao dch

Volume : Khi lng giao dch c phiu (bn, mua) trong ngy.

3.1.2. M hnh ARIMA cho bi ton dbo ti chnh

Da vo trnh t cbn ca phng php lun (phn 1.7) cng cu trc v hot

ng ca m hnh ARIMA trong chng 2. p dng m hnh ARIMA vo bi

ton d bo ti chnh, ta xy dng m hnh d bo.

M hnh gm 3 qu trnh chnh :


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Xc nh m hnh : Vi u vo l tp d liu chui thi gian trong ti chnh

gip cho vic xc nh ban u cc thnh phn trong m hnh p, d, q, S.

c lng, kim tra : M hnh ARIMA l phng php lp, sau khi xc nh

cc thnh phn, m hnh sc lng cc tham s, sau th kim tra chnh

xc ca m hnh : Nu hp l, tip bc sau, nu khng hp l, quay tr libc xc nh

D bo : Sau khi xc nh cc tham s, m hnh sa ra d bo cho ngy

tip theo.

3.1.3. Thit k m hnh ARIMA cho dliu

Vic thit k thnh cng m hnh ARIMA ph thuc vo s hiu bit r

rng v vn , v m hnh, c th da vo kinh nghim ca cc chuyn gia d

bo

Trong qu trnh tm hiu, kha lun sa ra cc bc xy dng mt

m hnh nh sau :

1. Chn tham bin

2. Chun b d liu

Xc nh tnh dng ca chui d liu

Xc nh yu t ma v

Xc nh yu t xu th

3. Xc nh cc thnh phn p, q trong m hnh ARMA4. c lng cc tham s v chn on m hnh ph hp nht

5. D bo ngn hn

3.1.3.1 Chn tham bin

Hng tip cn ph bin trong d liu ti chnh l tp trung xy dng m hnh

d bo gi c phiu ng ca sau khi kt thc mi phin giao dch (Close).

3.1.3.2 Chun b dliu

Xc nh tnh dng ca chui d liu : Da vo th ca chui v th cahm t tng quan.

Nu th ca chui Y = f(t) mt cch trc quan nu chui c coi l dng

khi th ca chui cho trung bnh hoc phng sai khng i theo thi gian

(chui dao ng quanh gi tr trung bnh ca chui)


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Da vo th ca hm t tng quan ACF nu th cho ta mt chui gim

mnh v tt dn v 0 sau q tr.

Xc nh yu t ma v cho chui d liu : Da vo th ca chui d liu Y

= f(t). (Xem phn chng 1.1)

Xc nh yu t xu th cho chui d liu : Xem li phn 2.1.2 (Trong gii hnca kha lun)

3.1.3.3 Xc nh thnh phn p, q trong m hnh ARMA

Sau khi loi b cc thnh phn : Xu th, ma v, tnh dng th d liu tr

thnh dng thun c th p dng m hnh ARMA cho qu trnh d bo. Vic xc

nh 2 thnh phn p v q.

Chn m hnh AR(p) nu th PACF c gi tr cao ti tr 1, 2, , p v

gim nhiu sau p v dng hm ACF gim dn

Chn m hnh MA(q) nu th ACF c gi tr cao ti tr 1, 2, , q v gim

nhiu sau q v dng hm PACF gim dn.

3.1.3.4 c lng cc thng s ca m hnh v kim nh m hnh ph hp nhtC nhiu phng php khc nhau c lng. y, kha lun tp trung

vo : Khi chn c m hnh, cc h s ca m hnh sc c lng theo

phng php ti thiu tng bnh phng cc sai s. Kim nh cc h s a, b ca m

hnh bng thng k t. c lng sai s bnh phng trung bnh ca phn d S2 :

S2 =

=

^

Trong : et = Yt Y^t = phn d ti thi im t

n = s phn d

r = tng s h sc lng

Tuy nhin : cng thc cha ra tham kho...Hin nay phng php clng c hu ht trong cc phn mm thng k : ET, MICRO TSP va SHAZAM,

Eviews...

Nu phn d l nhiu trng th c th dng v dng m hnh d bo.

3.1.3.5. Kim tra m hnh ph hp nhtDa vo cc kim nh nh


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BIC nh (Schwarz criterion c xc nh bi : n.Log(SEE) + K.Log(n))[]

SEE nh [19]

R2 ln : R-squared = (TSS-RSS)/TSS [19]

,

3.1.3.6 Dbo ngn hn m hnhDa vo m hnh c chn l tt nht, vi d liu qu kh ti thi im t, ta

s dng d bo cho thi im k tip t+1.

3.2. p dng

ng dng m hnh ARIMA vo bi ton d bo chng khon ca ca Cng ty

cphn Thy sn Mekong(M CK : AAM)

S dng Phn mm EVIEWS 5.1 don (ng dng ca m hnh ARIMA

cho bi ton don chui thi gian).

Quy trnh thc nghim c tin hnh nh m t2.2.2.

3.2.1. Mi trng thc nghim

Mi trng thc nghim Eview 5.1 chy trn hiu hnh Window XP SP2,my tnh tc 2*2.0 GHz, b nh1GB RAM.

3.2.2. DliuChn loi d liu d bo: D liu c ly t

http://www.cophieu68.com/datametastock.php

Trong ta chn C phiu c m MMA don, v s dng ring Gi ng

ca.

D liu u vo l file.CSV or .dat c ly t website xung.

D liu y c dng nh sau :

MaCK Ngay GiaDongCua

AAM 5/14/2010 33.4


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AAM 5/13/2010 33.2

AAM 5/12/2010 33.2

AAM 5/11/2010 34.4

AAM 5/10/2010 34.9

AAM 5/7/2010 36.5

Bng 1. D liu u vo

D liu cho qu trnh d bo c bt u t ngy 24/9/2009 n ngy

14/5/2010. y kha lun ch tp trung vo GiaDongCua, v qu trnh d bo s

gip ta xc nh c Gi ng ca ca ngy k tip ngay sau .

Hnh 15. Chn GIADONGCUA lm mc tiu d bo

3.2.3. Kim tra tnh dng ca chui chng khon AAM


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Hnh 16. Biu ng ca

3.2.4. Nhn dng m hnhXc nh cc tham s p, d, q trong ARIMA

Hnh 17. xc nh d = 0,1,2 ?


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Hnh 18. Biu ca SAC v SPAC ca chui GIATHAMCHIEU

Nhn vo hnh 3.7, ta thy biu hm t tng quan ACF gim dn mt ccht t v 0. Chui cha dng, ta phi sai phn ln 1.

Kim tra th Correlogram ca chui sai phn bc 1.

Hnh 19. Biu ca SPAC v SAC ng vi d=1

Nh vy sau khi ly sai phn bc 1 chui dng: d=1, ACF tt nhanh v 0

sau 1 trq=1, PAC gim nhanh v 0 sau 1 tr: p=1


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3.2.5. c lng v kim nh vi m hnh ARIMAXy dng m hnh ARIMA(1,1,1)

Chn Quick/Estimate Equation, sau g"dgiathamchieu car(1) ma(1)",

Hnh 20. c lng m hnh ARIMA(1,1,1)

Click OK, kt qu l :

Hnh 21. Kt qu m hnh ARIMA(1,1,1)

Chn View/Residual tests/Correlogram-Q- Statistic

Hnh 22 : Kim tra phn d c nhiu trng


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Nh vy, sai s ca m hnh ARIMA(1,1,1) l mt chui dng v n c phn

phi chun. Sai s ny l nhiu trng.

Ta c bng xc nh cc tiu chun nh gi sau khi th vi mt vi m

hnh khc nhau :

M hnh ARIMA BIC Adjusted R2 SEE

ARIMA(1,0,0) 4.24 0.97 1.967

ARIMA(2,1,1) 4.26 0.004 1.96

ARIMA(1,1,1) 4.20 0.57 1.909

ARIMA(4,2,1) 4.26 0.44 1.957

Bng 2 : Tiu chun nh gi cc m hnh ARIMA

3.2.6 Thc hin dbo

Ti ca s Equation n nt Forecast

Hnh 23. D bo

Ti Forecast sample : ta chnh ngy d bo : 14/5/2010 20/5/2010

Kt qu l :


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Hnh 24. Kt qu ca bng thng k d bo.

Ta c kt qu d bo ca 3 ngy 14/5/2010 20/5/2010Ngy Gi thc t Gi dbo nh gi

17/05/2010 33.5 32.94174 -0.55826

18/05/2010 33.2 32.89932 -0.30068

19/05/2010 32.5 32.86322 0.36322

20/05/2010 33.2 32.83250 -0.3675

Bng 3. nh gi d bo

Qua thc nghim d bo c 4 ngy t ngy 17/05 20/05/2010, chng ta

nhn thy kt qu a ra kh chnh xc so vi gi thc t ca m chng khon

AAM.

Tuy s lng ngy d bo th nghim cha nhiu song c th nhn nh rng

m hnh ARIMA(1,1,1) l kh ph hp d bo m CK AAM.

Tm tt chng 3

Chng 3 gii thiu v mi trng thc nghim phn mm, d liu u vo l

gi chng khon ca cng ty vi m AAM (chn GiaDongCua lm bin d bo).

Kha lun tin hnh tng bc qu trnh thi hnh d bo twf d liu nh nu


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chng 2. nh gi sb thnh cng ca m hnh c chn : M hnh c chn

d bo kh chnh xc.


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KT LUN

Qua thi gian nghin cu thc hin kha lun tt nghip, em nm c

quy trnh xy dng m hnh ARIMA cho d liu ti chnh v p dng m hnh ny

vo bi ton thc t - bi ton d bo ti chnh. Nhng kt qu chnh m kha lun

t c c th tng kt nh sau :

Nghin cu mt s ni dung l thuyt cbn v chui thi gian, v m hnh

ARIMA, v cng c Eviews c th p dng c Eviews thi hnh m hnh

ARIMA trong d bo ti chnh, chng khon.

Nm c quy trnh dng phn mm Eviews thi hnh m hnh ARIMA cho d

liu thi gian thc (vi 4 bc cbn) tnh ton gi tr d bo d liu ti chnh,

chng khon.

Thc hin quy trnh s dng phn mm Eviews thi hnh m hnh ARIMA cho

d liu m c phiu m CK AAM d bo ngn hn gi c phiu.

Bn cnh nhng kt qu t c, cn c nhng vn m thi im ny,

kha lun cha gii quyt c:

p dng vi chui d liu c tnh xu th.

Thut ton c lng cng nhnh gi cn nhiu hn ch.

y ch l m hnh phn tch kthut, cha th d bo mt cch chnh sch, bi

ch ph thuc vo mt bin Thi gian, trong khi qu trnh d bo ph thuc

vo nhiu yu t.

Nhng ni dung cn nghin cu pht trin tip tc ni dung kha lun:

Xy dng m hnh ARIMA a bin : ch s ca gi chng khon ph thuc vo

nhiu bin khc nhau.

Gii quyt yu t xu th cho chui d liu


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TI LIU THAM KHO

Ti liu tham kho ting Vit

[1].ng Th nh Tuyt. Tm hiu v ng dng mt s thut ton khai ph d liu

time series p dng trong bi ton dbo ti chnh. Kha lun tt nghip i hc

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