TAI LIEU THAM KHAO
Hinh 2-7. Xac suat voã nqã trong mo hinh Merton-KMV
2.5. MO HINH CHUOI THOI GIAN
Van de quan trong trong dr bao chuoi thoi gian la c6 gang xay dung duqc cac mo hinh de du bao tot nhat xu huong van dong cua chu6i thai
(2.43)
gian. Cac mo hinh dr bao chuoi thai gian dugc xay dung dga tren vi@c khai thac cac m6i quan he n i tai cua dc)ng thai trong qua khtr cua n6. Nc)i dung muc nay gioi thieu mot s6 mo hinh dr bao chuoi thoi gian: Mo hinh san mil gian dan, Mo hinh Holt-Winter, Mo hinh ARMA (Autoregressive Moving Average Process), Mo hinh ARIMA (lnterrated ARM A), Mo hinh ECM (Error Corection Model) va mo hinh GARCH (Generalized Autoregressive Conditional Heteroscedasticity Models).
2.5.1.Mohinh san mii
a.Mohinh san mii gian don
Mo hinh san mu gian don (Single Exponential Smoothing) dra tren trung binh co trong so. Gia su athi ky t c6 t;, t;_,, ... , khi d6 cong thrc san mu cua chuoi co dang sau:
A A
Y, =aY, +(1-a)Y,_"O <a< I a la hang so san.
Mo hinh san mil gian don phu hop v&i chu6i khong c6 y~u t6 thai V\l va khong co xu the.
b. Mohinh Holt-Winters
•• MO hinh coyeu to xu the
Phan xu the o thi ky t, ky hieu T,, duoc xac dinh la chenh l@ch gira hai gia tri Y, va Y,,. Ta c6 cac phuang trinh:
f, =aY, +(d-a)O,, +T,).0<a< I, T, = /J(Y, - Y,_,)+(I -BT,,O</3 <I, va cong thrc dr bao thoi ky t+h: Y,,, = f, +hT, .
•• MO hinh coyeu to xu theva yuto ma vu
Khi chu6i co yeu to mua V\l F, thi mo hinh Holt-Winters dugc dieu chinh nhu sau:
(2.44)
(2.45)
T, = /J(Y, - Y,_1) + (I -/J)T,_"0</J < I, F, =r~ +(1-r)F,_.,O<r<l,
y '
I
(2.46)
va cong thre dr bao th'i ky t+k:
• Cong thrc dr bao mo hinh Holt-Winters d,;mg c(mg
~ {(Y, +hT,)+F;+h-k,h=l, ...,k
1, =
(Y, +hT,)+ Eh =k+1, ... ,2k
• Congthrc dr bao mo hinh Holt-Winters d,,mg nhan
~ {(Y, +hT,)F,+h-k'h= 1, ... ,k
1.,= - .
(Y,+hT,)F,+h-2k,h =k+1, ... ,2k
Mo hinh Holt-Winters la sv ma r9ng cua mo hinh san mu gian dan, cho phep san mu cua chu6i co yeu to xu the hay chu6i c6 ca yeu to xu the va yeu to muaVl,I.
2.5.2. Mo hinh ARIMA a. Mo '1i11'1 AR(p)
(2.4 7)
(2.48)
r, = ¢0 +I¢,I' r,_, +u,
i=I
(2.4_9) trong d6 Y,_, la tr~ b?c i cua Y,, u, la sai so ngau nhien othoi ky t, ¢,
la cac he so.
Mo hinh AR(p) cho bi€t sà ph1,1 tlm9c cua r tai thi diem t vao cac bien tre cua no.
b. Mo l,inl,MA(q)
1, = .+, + 2o, ,,
l=I
(2.50) trong d6 u, la sai so ngau nhien athai ky t, 0, la cac he so.
Mo hinh MA(q) cho bi€t thong tin cua r tc:ii thai di~m t ph1,1 thu(>c vao sai so ohien tai va sai so oqua khr.
c. Mo hi11'1 ARMA(p,q)
" ,,
1,-=4.+ 2ox. + 2o. +
l=I !=I
(2.51) d. Mo '1in'1 ARIMA(p,d,q)
Mo hinh ARMA(p,q) chi thvc hi~n khi chu6i Y, la chu6i dung, tuy nhien nhieu chuoi thai gian trong kinh te la chu6i khong dung. Do d6, truac
khi su dt,mg mo hinh ARMA chung ta can bin d i chuoi ban dau ve chuoi dung, thong thuc'mg nguai ta lay sai phan cua chu6i ban dftu. N~u m<)t chu6i dung a sai phan bjc d, ta ky hieu Id); mo hinh ARIMA duoc ky hieu la ARIMA(p,d,q).
De lra chon mo hinh ARIMA(p,d,q) nguai ta thuc'mg thrc hien qua m(>t s6 bu6c:
• Kiem dinh xem chu6i dfr li?u c6 la chu6i dung hay khong? Neu chu6i khong dung thi chung ta lay sai phan.
• Khi chuyen sang chu6i dirng, ti~p theo chung ta phai xac djnh p va q.
Ova tren cac ham tuang quan rieng (PACF) va ham tuang quan (ACF) de xac djnh cac gia tri p, q. Tuy nhien, neu co nhieu gia tri cua p, q thi ta kh6 xac djnh chinh xac bac cua AR va MA. Khi d6, chung ta dra tren cac tieu chu§n: AIC, SC, ... d~ Iva ch9n dugc mo hinh c6 sai so dr bao nho nh!t. Hi?n nay, v6ãi st,r h6 trqcua phftn m~m: Eviews, Stata, R, ... dt,ra tren nhfrng tieu chuan nay, chung ta de dang xac djnh dugc mo hinh ARIMA.
2.5.3.Mo hinhECM
Trong nhieu bai toan, chang han: xet tac dong cua thu nhp toi tieu dung, tac d(mg cua cac bien vi mo toi lai suat, ... khi d6 chung ta c6 th~ su dàng mo
hinh hoi quy de nghien cru. Neu nhr cac bien nay la cac bien khong dimg thi ket qua uoc luong bang mo hinh hoi quy tuyen tinh co the la giamao.
GiaSilchung ta mu6n nghien CLIUtac d(mg cua Xi t6i Y,, n~u nhux,, Y,
la cac bien Khong dmng, ma sai phan bac nhat AY,, AX, la cac chuoi dmg.
Chung ta co the hoi quy L1Y,ph1,1 thu(>c vao ,1Xi. Tuy nhien khi thvc hi~n nhu vay, ta co the bo m!t thong tin dai han ve quan he gira Y,vaX,. Xet mo hinh can bAng trang ngiin Iwn:
(2.52) trang d6 E,_, la phftn du khi h6i guy Y, pl11,1 thu(>c vaoX, va ~3E1_1 la phftn mfrt can bAng. Mo hinh (2.52) duqc g9i la mo hinh hieu chinh sai s6 (ECM).
2.5.4. Mo hinh d1_1ã bao di) dao di)ng
Trang cac mo hinh kinh te luong, thuang gia thiet phrong sai cua sai so ngau nhien la khong doi theo thai gian. Tuy nhien, cac chu6i dfr lieu ve kinh te, djc biet cac chu i dr lieu tai chinh co xu hun g dao dong cao vao m(>t s6 giai doan, dong thai cung c6 m(>t s6 giai doan it dao d(>ng han (hinh 2.7 minh h9a ve sr bien dong o cc giai doan cua chuoi lgi suat cua chi so
VNINDEX). Dieu do co the duge giai thich boi chuoi dr lieu theo thi gian chiu anh humg boi cac tin trc tot xau va hanh vi cua cc nha dau tu tren thj truang. Chinh vi vay. gia djnh phucmg sai khong d6i theo thai gian thuang khong phu hqp v&i dr lieu chuoi th i gian .
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