SỬ DỤNG MÔ HÌNH ARIMA TRONG PHÂN TÍCH CHUỔI THỜI GIAN

8/3/2019 S DNG M HNH ARIMA TRONG PHN TCH CHUI THI GIAN

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S DUNG MO HNHARIMA

TRONG D BAO CHUOI THI G

CAO HAO THI

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NOI DUNGGii thieu xay dng Mo Hnh ARIMA(Auto -Regressive Integrated Moving

Average )T Hoi Qui Ket Hp Trung Bnh Trt

ng dung d bao gia ca song tai Tp. HC


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GII THIEU

Mo hnh nhan qua

Mo hnh chuoi thi gian

Hai loai mo hnh d bao chnh:

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oi vi cac chuoi thi gianARIMA thng c s dung e d ba

Theo mo hnh ARIMA, gia tr d bao se ph

thuoc vao cac gia tr qua kh va tong ctrong so cac nhieu ngau nhien hien hanhva cac nhieu ngau nhien co o tre


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MO HNH ARIMA

Tnh dng (Stationary)Tnh mua vu (Seasonality)Nguyen ly Box-JenkinNhan dang mo hnh ARIMAXac nh thong so mo hnh ARIMAKiem nh ve mo hnh ARIMA

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TNH DNG

Trung bnh: E(Yt ) = const

Phng sai: Var (Yt ) =2

= constong phng sai: Covar (Yt , Yt-k) = 0

Mot qua trnh ngau nhien Yt c xem la dngneu


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o th Yt = f(t)Ham t tng quan mau(SAC Sample Auto Correllation)

Nhan biet:

Neu SAC = f(t) giam nhanh va tat dan ve 0 thchuoi co tnh dng

)()(

])[(

),()()(

))([(

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t t

t o

k t t k t t

k t t k

o

k k

Y Var n

Y Y Y Y E

Y Y Cov n

Y Y Y Y Y Y Y Y E

SAC

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Kiem nh Dickey-Fullerxac nh xem chuoi thi gian co phai la Bc Ngau Nh(Random Walk); ngha la

Y t = 1*Y t-1 + etNeu chuoi la Bc Ngau Nhien th khong co tnh d

BIEN OI CHUOI KHONG DNG THANH CHUOI DLay sai phan bac 1 hoac bac 2 th se c mot chuoi kequa co tnh dngChuoi goc: YtChuoi sai phan bac 1: Wt = Yt Yt-1Chuoi sai phan bac 2: Vt = Wt Wt-1


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TNH MUA VU

Tnh mua vu la hanh vi co tnh chu ky cua chuoithi gian tren c s nam lch

Tnh mua vu co the c nhan ra da vao o thSAC = f(t). Neu c sau m thi oan th SAC lai cogia tr cao th ay la dau hieu cua tnh mua vu

Chuoi thi gian co ton tai tnh mua vu se khong cotnh dngPhng phap n gian nhat e kh tnh mua vu lalay sai phan th m

m t t tY Y Z

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MO HNH ARIMA

Theo Box- Jenkin moi qua trnh ngaunhienco tnh dng eu co the bieudien bang mo hnh ARIMA


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Mo Hnh AR(p)Qua trnh phu thuoc vao tong co trong so cua cac gia

qua kh va so hang nhieu ngau nhien

Mo Hnh MA(q)Qua trnh c mo ta bang tong co trong so cua cac nnhien hien hanh co o tre

Mo Hnh ARIMA(p,d,q)Phng trnh tong quat cua ARIMA

t p t p t t t Y Y Y Y e...2211

q tq t t t tY e...2211

q tq t t p t p t t Y Y Y e...... 1111

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NHAN DANG MO HNHTm cac gia tr thch hp cua p, d, q. Vi

d la bac sai phan cua chuoi c khao satp va q se phu thuoc vaoSPAC = f(t) va SAC = f(t)

Chon mo hnh AR(p) neu SPAC co gia tr cao tai otre 1, 2, ..., p va giam nhieu sau p va dang ham SACgiam dan

Chon mo hnh MA(q) neu o th SAC co gia tr cao to tre 1, 2, ..., q va giam nhieu sau q va dang hamSPAC giam dan


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Mo hnh SAC = f(t) SPAC = f(t)AR (p) Giam dan Co nh p

MA(q) Co nh q Giam dan

ARMA(p,q) Giam dan Giam dan

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THONG SO CUA ARIMA (p,dCac thong so i va j cua ARIMA se cxac nh theo phng phap bnh phng toithieu (OLS-Ordinary Least Square) sao cho:

MinY Y t t

2)

(

Vi)

( t t t Y Y


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KIEM TRA CHAN OAN MO

Kiem nh xem so hanget cua mo hnh cophai la mot nhieu tra ng (white noise, nhieungau nhien thuan tuy) hay khong.et c tao ra bi qua trnh nhieu trang neu:

Viec kiem nh tnh nhieu trang se da treno th SAC cua chuoiet .

),0(~ 2e N t0)( t E e

constVar t

2)(e

0),( k t t k Cov e

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D BAOD bao iem

Khoang tin cay

tY

)(

)(

t t t t tkY Y kY e


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S DUNG MO HNH ARIMATRONG D BAO GIA

Chuoi gia ca song tai Tp.HCM gom 111 dlieu thang t 1/1990 en 3/1999 va phanmem EVIEWS e d bao gia tr thang 4/1999

Cac d lieu qua kh cua gia ca song at ten la RFISH va chuoi sai phan bac 1

c at ten la DRFISH.

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Chuoi RFISH va DRFISH khong co tnh dngdo d lieu co tnh mua vu

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

90 91 92 93 94 95 96 97 98

RFISH

-12000

-8000

-4000

0

4000

8000

12000

90 91 92 93 94 95 96 97 98

DRFISH


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S dung phan mem EVIEW e kh tnh muavu va tien hanh th nghiem cho nhieu mohnh ARIMA

Mo hnh toi u co dang ARIMA(2,1,2) vi thoan kh tnh muavu lam=12

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Ket qua ve cac thong so i va j c trnhbay trong bang sau:Dependent Variable:D(RFISH)Method: Least SquaresDate: 2/3/2002 Time: 18:17Sample(adjusted): 1991:04 1999:03Included observations:96 after adjusting endpointsConvergence achieved after 50 iterations

C -283.3601 1010.997 -0.280278 0.7799

AR(2) 0.413278 0.135466 3.050799 0.0030

SAR(12) 0.963121 0.044544 21.62164 0.0000MA(2) -0.846851 0.118603 -7.140218 0.0000

R-squared 0.614807 Mean dependent var 203.1250

Adjusted R-squared 0.597875 S.D. dependent var 3545.923

S.E. of regression 2248.588 Akaike info criterion 18.32467

Sum squared resid 4.60E+08 Schwarz criterion 18.45823

Log likelihood -874.5842 F-statistic 36.31124

Backcast: 1990:02 1991:03Variable Coefficient Std. Error t-Statistic Prob.

SMA(12) -0.781433 0.078476 -9.957634 0.0000

Durbin-Watson stat 1.718345 Prob(F-statistic) 0.000000


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THAM NH TNH NHIEU TRCUAet

o th SAC cua chuoi et. cho thay et co tnhnhieu trang va c trnh bay nh sau:

OHT #1

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O TH CUARFISH VARFISHF


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KET QUAD bao iem la = 26267

Khoang tin cay 95% la[ 21742 , 30792 ]Gia tr thc thang 4/1999 la Yt = 26000 Gia tr nay nam trong khoang tin cay 95% vaxap x vi giatr d bao iemSai so d bao la ( -Yt)/ Yt *100 = 1,03%

tY

tY

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KET LUANo th RFISHF bam rat sat o th RFISHGia tr d bao xap x vi gia tr tren thc te (sai so d bao nho) va khoang tin cay 95% cung cha giatr thc o tin cay cua mo hnh d bao

a ap dung mo hnh ARIMA e d bao cho hn 20loai mat hang tai Tp.HCM theo qui trnh tng t vacung at c cac ket qua d bao vi o tin cay ca

TOM LAI, MO HNH ARIMA LA MOT MO HNTIN CAY OI VI D BAO NGAN HAN


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TAI LIEU THAM KHAOBowerman B.L., and O

Connell R.T., 1993. Forecasting and Time Series . 3 rd ed., Wadsworth, Inc.

Cao Ha o Thi va Ca c Co ng S 1998. Ba n Dch Kinh Te L ng C S (Basic Econometrics cu a Gujarati D.N.).Ch ng Tr nh Fulbright ve Gia ng Da y Kinh Te ta i Vie tNam.

EVIEWS, 2000. Quantitative Micro Software.

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TAI LIEU THAM KHAOPindyck R.S., and Rubinfeld D.L., 1991. Econometric Models

and Economic Forecast. 3rd ed., McGraw-Hill.

Ramanathan R., 2001. Introductory Econometrics with

Applications. 5th ed., Harcourt College Publishers

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SỬ DỤNG MÔ HÌNH ARIMA TRONG PHÂN TÍCH CHUỔI THỜI GIAN