CÁC MÔ HÌNH ARCH GARCH VÀ DỰ BÁO RỦI RO

ĐẠI HỌC QUỐC GIA THÀNH PHỐ HỒ CHÍ MINH
ĐẠI HỌC QUỐC GIA THÀNH PHỐ HỒ CHÍ MINH
TRƯỜNG ĐẠI HỌC KINH TẾ - LUẬT
TRƯỜNG ĐẠI HỌC KINH TẾ - LUẬT
KHOA KINH TẾ
KHOA KINH TẾ
BÀI TIỂU LUẬN DỰ BÁO KINH TẾ
CÁC MÔ HÌNH ARCH/GARCH VÀ DỰ BÁO RỦI
CÁC MÔ HÌNH ARCH/GARCH VÀ DỰ BÁO RỦI
RO
RO
DANH SÁCH NHÓM 18
  
  
   !
"#$%&'( ! 
)*%'+(,-  .!
&' /0  .
MỤC LỤC
1
DANH MỤC BẢNG BIỂU
$'1: 234566627' 234#&8*7"09':*6;<&=>
<?*@%ABCDEEFEE>
DANH MỤC HÌNH VẼ, ĐỒ THỊ
G15@H'(I*JKJLM
G1?$@80M'N*(I*O
G1!PQ(L0M'7G6O6<R>
G1PQ(L0M'7G6O6<R>
G1DPQ(L0M'7G6O6<R>
G1S5N$7G6O6<R>
G15N$7G6O6<R>

G15N$7G6O6<R>
G1.T@$0U'6O2
2
G1T@$0U'6O2VC'@H"L
G1PQ(L0M'7G6O2<>
G15N$0Q(L0M'6O2<>
G1!5N$0Q(L0M'7G6O2<D>
G1W@HLX((Y(I*7G6O2<D>
G1D%JV5N$7G6O2<>6O2<D>
G1S$'Z
D
G1$'Z

D
G15N$0Q(L0M'?6O2<R>
G1.%J40['J*(I*6O2<D>?6O2<R>
G15N$0Q(L0M'?6O2<R>
G15N$0Q(L0M'?6O2<!R>
G15N$0Q(L0M'?6O2<R>
G1!$'6
D
G1$'6

D
G1D5N$0Q(L0M'?6O2F<R>
G1S5N$0Q(L0M'?6O2<!R>
Hình 3.1: Biến động của suất sinh lợi
Hình 3.2 Gin đ t tượng quan của R
Hình 3.3 Kết qu ước lượng mô hình ARMA(0,1)
Hình 3.4 Kết qu ước lượng mô hình ARMA(0,1)

Hình 3.5 Kết qu ước lượng mô hình ARMA(1,1)
3
Hình 3.6 Các chỉ số của mô hình ARMA(1,0)


 !"#$%#&'
()*+"#,'
()*+"#,'-(.'*/01%2
3 !"#$%#&'
45+*/%6!7
8 !"#$%#&'8
945+*/%6!78
:;<- !"=>8
 !"#$%#&'9
 !"#$%#&'8
 !"#$%#&'
3 !"#$%#&'?
3;<- !"8=>?
33 !"#$%#&'?
3 !"#$%#&'@?
4
CHƯƠNG I: GIỚI THIỆU TỔNG QUÁT
1. Giới thiệu tính cần thiết:
84"T\']+'(7'(+V5L0M'"%'L^8((_@`'QX
7GV/a4b_('c4(c'*V7'd'(eT]8f%
(I*d'@#0N*JKJLMV-'R(g]8f%"I"%fh'
(((if%40['J** @HLX((Y1&7G@'J$@`jL8(
0Q(L0M'JKJLMV-'(I*HJ$(+T<_]+(345(I*H(7'
 >\'QjJKJLMV-'@f*% 5k"I"%Xk'"I
"%4Xk'1

Q8(0a R((7GV5L0M']8f%@gl4$(eV$
C']8f%\(@H]*%@H'(I*(((j9'*12(7G]8f%0a
H(e((7G6O2<6%'"ZJJZ2%]%*LZZ"%JV]*J( >
(c'Jm@0M(@(a4@5"%'fTLa 1
"%'d'C'#@b R((7G6O2@`@0M('(\Jn
]+'@T0Q(L0M'((bk$0U'@5"I"%(I*((J$(_"
5
"09'(\'V%R"09''R"09']#R"09'fK@H'J$
"09'(*%(K4V(h('(K47'(%((N 5@V
]%*R@o(fXL"%'N$""I"%1
2. Mục tiêu:
+((I*fTLah'QX((7Gj"M(%X(]8f%"I
"%((f5JkV5(_(e@H]*%@H'(*%12(7G]8f%
V7'(g@[#L]8f%'""'fGd*(g5Q]8f%"I"%
(%((f5Jk 12+TL((7GJ*@b p
 7G6O21
 7G6O2<>1
 7G6O2<N>1
 7G?6O2<4RN>1
 7G?6O2F1
 7G?6O21
 q0U'((7G6O2U"H'<7Ge*bk$0U'@5
"I"%>1
3. Phạm vi:
f%(%Jm'QX((7G@eL7G6O2R?6O2?6O2
B@eJm@0*"*d']8f%a(_:(1"%'@eReJm@@5H_]+
8(5@TK "r[1
4. Kết cấu của báo cáo:
?4#LQp
 3'N*_(#54A(I*ff%(%1

 ?QXL_ 5Ra:sJ%J((7G1
 &'(\\']+'(I*X(]8f%1
 5La@:K7Gk01
6
CHƯƠNG II: TỔNG QUAN LÝ THUYẾT
1. Định nghĩa, khái niệm liên quan:
1.1 Hiện tượng phương sai thay đổi:
1.1.1 Định nghĩa:
;0['J** @3:$ "*V'$5f4Ap Var(U
i
) = σ
2
1'$5
40['J*J*Jk@f4AG7GN 'o4*X0M' 1
1.1.2 Nguyên nhân xảy ra hiện tượng phương sai thay đổi:
F%f$(KK@V51
F%V/aa4:nL_JkLX1
F2%'09"c@0M(V'XB"%'NV\1
F2e((N*J'%AL*<N*JV(fX"KJ%Q((N*JV(
"%'t>1
F7G@]A'J*RflJef5_(M4%C(]A''$_((I*LJ*1
1.1.3 Hậu quả của hiện tượng phương sai thay đổi
F2(0Q(L0M'fG40['lKuvL0Q(L0M' 5_V7'(X(
0'V7'XN$1
F2(0Q(L0M'(I*((40['J*L((0Q(L0M'(X(wxL'"(I*
k'VyKz'^*1
F2(f%0Q(L0M'VT@]8f%VJn]+'k'VyL
V7'@'(a 1
1.1.4 Phương pháp phát hiện: ;0['44@4#]0
n]+'(YVT@p

F T@;*"V1
FT@?LZ{JZ"1
FT@|LZ&%2"%JJZ"J<VT@|LZV7'L(}>1
;0['44@4#]0
F*N 7GN 'k(pY
i
= β
1
+ β
2
X
2
+β
3
X
3 +….+
β
k
X
k +
U
i

F*@0M(4#]0Z

1
7
Fm@4#]0Z
 
<Z



>@kQ=
 
<%o(Q~

"%'"09'M4N 
f5>1
&5@H"H'(I*fT@4#]0C'* '$V=C'G'$540['
J*h'Jk(eTV7'l*`1
T@;*"V
FW#RN 7G'k(@T@0M(4#]0Z

1
FPQ(L0M'7GN J*plne
i
2
= β
1
+ β
2
lnX
i
+ vi.
"09'M4(ef5'$_(G0Q(L0M'N  QB'f5'$
_(%o(Q~

1
FT@'$5


pu

w1&5'$5 ff(flG(eTV5LaJ8
A(I*X0M'40['J*J*Jk* @31
T@?LZ{JZ"
FW#R*(•'N 7G'k(@T@0M(4#]0Z

1
FN H"%'((7GJ*p
ǀ e
i
ǀ = β
1
+ β
2
X
i
+vi
ǀ e
i
ǀ = β
1
+ β
2
(1/Xi) +vi
ǀ e
i
ǀ = β
1
+ β

2
√X
i
+vi
ǀ e
i
ǀ = β
1
+ β2(1/√Xi) +vi
F0['80VT@;*"VR*(•'(eTVT@'$5

pu

w1
&5'$5 ff(flG(eTV5La(eX0['40['J*J*Jk*
@3
T@|LZ
FPQ(L0M'fh'€)1B@e@0M(((4#]0Z


FPQ(L0M'7GJ*p
ei2 = α1 + α2X2 + α3X3 +α4X22 + α5X32 + α6X2X3+vi
FQ

p40['J*(I*J*JkV7'@3R(eT(i"h'O(e4#:K4:i•<]‚>R
]‚fh'XJk(I*7GV7'VTXJk(o1
8
F&5OV7'0MN'"•<]‚>RG'$5V7'(e([JUff(fl1
"%'"09'M4'0M(LAG'$5ff(fl1
1.1.5 Phương pháp khắc phục:

&0(c'*@`f540['J*(I*J*Jk* @3L(%((0Q(L0M'V7'
(gXN$d*1G5fX44V}(4+(L5J\((#51X((d*(A
(CfX 4+H((I 5%LXƒ


@0M(f5* (0*1*4bfX
"09'M4p
 ƒ


@`f5
ƒ


@`

f5R(c'*(eT]]'V}(4+((CfX@efh'((Jn]+'
40['44fG40['lK(e"'Jk@`"Gf U"1
 ƒ


(0*f51
"%''(\V5X(f5"0Q(ƒ
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kJn]+'40['44fG40['lK(e"'JkG(c'*(#(e
d''$5K@ƒ
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Rf5@37G'k(J*%(%7G@`@0M(
f5@3 l*`'$540['J*(I*J*JkV7'@31;0['44fG
40['lKJm@0M(4]+'(%7G@`@0M(f5@30@`(i"*
"0Q(@b R40['44fG40['lK(e"'JkL40['44fG
40['lK4]+'(%a4JkLX@`@0M(f5@31
1.2 Số hạng nhiễup0Q(L0M'QtG(c'** VX
A'fh'VX4#]0
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1.3 Tính dừng :
dLX(I*fKV-(j9'*%@(eT@0M((%L@0M(A%"*BH
N"G'tHa4M4]dLX(+TR(eT@0M((%LHV5N$
<(fX>(I*N"G't@e1* e((V(R(eT:ZN"G't
L3'TV5N$LHt(I*3'T@e1H_(K(I*N
"G't@0M(((4b_((j9'*@o(fXN*b
:Z:sV/L0„'L_]B'1
9
1.3.1 Chuỗi thời gian “dừng” :
H(j9'*]B''((@o(@TJ*p
 dLX]*%@H':'N*H'""'fG(k@"%']A1
 dLX(e'"40['J*:(@V7'* @3Z%9'*1
 dLX(eH'$@80['N*Q((XJk80['N*Jm'$]#
V@H"C'L1
&5H(j]B'RG'""'fGR40['J*X440['J*<U((@H
"V(*>Jm'k'*fKVT*@*'@%L09'(c'A9@T%…@
 (e'^*L((@AL0M' V7'* @3Z%9'*1H(j]dLX
0a (e:0Q'"U'""'fGd']*%@H':'N*'
""'fG<d'f5(I*'"(j9'*:%* N*'"
"'fG>@0M(@%fh'40['J*JmL0*1
&5H(j9'*(e'""'fG* @3Z%9'*%o('"
40['J** @3Z%9'*%o(($*G@eL(j9'*V7'

]B'1
2j9'*]B'(e*"g"KN*"'1GZ%?{*"*<!>RH(j
9'*V7']B'G(i(eT'(\(I*e"%'V%$'9
'*@*'@0M(:Z:s1jHt]dLX9'**'HG5K
@(iTXd'(+T"%'HV%$'9'*:Z:sR]%
@eV7'TVNe*(%(('*@%A9'*V(1
Q+(@_(]8f%R(((j9'*V7']B'(eTJmV7'(e'"8(
1G"%']8f%(j9'*RL7'$@"h':0Q'a@H'(I*]d
LX"%'NV\XA@0M(] "G(%(('*@%A0['L*1&0a R
V7'T]8f%@'G(%0['L*50f$b]dLXL7* @31[
d*R@kQ4b_(N R5(j9'*V7']B'GK($((V5
N$@TG(I*H4b_(N  5_(3@TJmV7'(e'"(%
X(]8f%R@0M('LX0M'†N '$A%‡1a R@VX([f$K
(%X(]8f%H(j9'*L(j@e4$(e_]B'1
10
1.3.2 Chuỗi không dừng:
7'09'** 'o44$(((jV7']B']%f$(K(I*(j(e 5
k:5%o('t…@e]09'0Lf$(K(I*((f5V51
_]+(3@T(I*(jV7']B'L7Gf0Q('t1&5"09'
(\'V%%A@H'XN$7'(b:\'G'J$0'(3
45* ˆ'09'Z%7Gf0Q('t…\(L(jV7']B'1
1.3.3 Chuỗi dừng sai phân:
Hf0Q('tLH(jV7']B'0'J*4bfa((I*eLH
(j]B'1*'f0Q('t@eLH(j]B'J*4bfa(HRVzX
‰<>1&5H(j9'*V7']B'UJ*4bfa(H0']B'UJ*fa(
*RG'(j9'*@eL(j]B'J*4bfa(*RV_X‰<>1
3'NR(j]B'UJ*4bfa(]RVzXL‰<]>1H(j]B'(•'(eT
'L(j]B'J*4bfa(RV_X‰<>1Z%V'X(I*((]8f%
G]7'09'(*%K09'V7'0MN1
2. Giới thiệu mô hình dự báo:

2.1 Các mô hình ARCH:
2.1.1 Vấn đề về phương sai thay đổi:
"%'7GN €)(3@T* 7G6O‰6G40['"G(I*(c'
*L7@0M(4bL*4#RH4#L'""'fGH4#L(c
J%(V@0M(@A]Xfh'* *(g'L

17G€)G (#VG'


4$fh'R40['J*(I*

V7'@3

V7'80['N*12g7
G6O‰6G (#

4$]B'1$b

LH 5kN*"'"%'
7GN G_(K@A]X@o(fX(I*R40['J*(I*

@A]X
(%@HLX(fG40['(I*'"8('"N 1&5(j9'*(I*
(c'*LHf5iJKJLM* '(I*HL%AJ$G(bl@o"*L
L((%(c'*(eT]8f%"I"%(I*(j@e"%'V(c'*(e
T]8f%@0M('""'fG* e((V(LL((%(c'*(e
T]8f%@0M(40['J*(I*

1We(_LK@@`L6O2"*@9
'$N 51

2.1.2 Ý tưởng cơ bản của ARCH:
11
Š'LZL'09@#G"*7G6O21WT(eT]8f%@0M(40['J*
(I*

G7'@`@o"*'$@L40['J*(I*

L40['J*(e@VX
J8* @3(I*

@0M(7$fh'HN "%'@e40['J*(I*

<ƒ

w‹>4+H(%fG40[''"(("

 "%'NV\12c'*(e
40['"GJ*p
κ = α
0
+ α
1
u
2
t-1
+ α
2
u
2
t-2

+ … + α
k
u
2
t-k
+ ε
t
<.1>
B40['"G<.1>G(c'*%%(eT]8f%@0M('"40['
J*(I*B@e:(@@0M(\("I"%(I*f5@*':s1
2.1.3 Quy trình thực hiện ARCH:
, "G8(X6O2'((f0Q(([f$J*p
0Q(p]'6O‰6@T:(@40['"G"'fGkK1K
6O‰6]'@T]8f%4$l*`((@VX([f$Lz 5@`@(a41
;# @`@0M("Gf V^"%'(0['6O‰61
0Q(pJ*V(e@0M(7G]8f%'""'fGkKG(c'*5
L(LK (I*7GN 1*V(e(('"G(c'*
5VT@_6O21T@_6O2@0M(7$0J*p
2c'*0Q(L0M'40['"G<.1>p
 κ = α
0
+ α
1
u
2
t-1
+ α
2
u
2

t-2
+ … + α
k
u
2
t-k
+ ε
t

2c'*VT@'$ 5J*p
H
0
: α
1
= α
2
= … = α
n
= 0
H
1
: α
2
1 +
α
2
2
+ … + α
2
n

> 0
2c'*(e((@TVT@p
 2(p]'k'Vy
 2(p]'k'V(fG40['
0Q(!p*VVT@_6O25V7'(eX\'6O2G(c'*
]B'LAR5(eX\'6O2G(c'*5(A 7G6O2@T]8
f%"I"%1)c(@e(c'*Jm(eX*7G0J*p
Y
t
= c + + u
t
<.1>
κ = α
0
+ α
1
u
2
t-1
+ α
2
u
2
t-2
+ … + α
k
u
2
t-k
+ ε

t
<.1!>
"%'@e40['"G<.1>L40['"G0Q(L0M''""'fG
40['"G(gLA0Q(L0M''"40['J*(I*12c'*(eT]'
7G6O‰6@TG5f5(I*(c'*(e'"] K]'
40['44€)@T0Q(L0M'<.1!>("J*%(%7GL4M4K
@T((XJkN (ez'^*k'V1*VG@0M(40['"G<.1!>k
KG(c'*(eT5]8f%40['J*(I*7'N*40['
"G<.1>'""'fG7'N*40['"G<.1>1B@e(c'*(e
12
T]8f%@0M('""'fG(I*9@T54Z%J*JkQ\(z'^*
@`("0Q(1
2.1.4 Mô hình ARCH(1) :
7G6O2<>Jm7Ge*@'Q'""'fG40['J*(I*
H(j9'*Z%((@0M(:(@J*@b p
Y
t
= β
1
+β
2
X
t
+ u
t
<.1>
u
t
~ N(0, h
t

)
h
t
= γ
0
+ γ
1
u
2
t-1
<.1D>
Œ40['"G<.1>@0M('L40['"G0Q(L0M''""'fG
40['"G<.1D>@0M('L40['"G0Q(L0M''"40['J*1)0zR
@T@['$"%'X(TX(7'\((I*40['"'40['J*RB@b 
J*(c'*Jn]+'V_X

* (%ƒ


1
7G6O2<>(%"h'V(eH(cJk(LQ:$ "*U'*@%A•RG'"


<'" X@k%o(fG40['>(•'JmLQ[1&'^*LRV

F
LQEl
G40['J*(I*

(•'JmLQEl1XJk0Q(L0M'Ž


4$(e]K]0['G
40['J*L7]0['1
2.1.5 Mô hình ARCH(q):
8(5R40['J*(e@VX(eT4+H(V7'(iH@H"(g
@H""0Q(@ed*RGj"09'M4(eTA%"*HN "G6O2
V(*1
7G6O2<>Jm@0M(TX0J*p
Y
t
= β
1
+β
2
X
t
+ u
t

u
t
~ N(0, h
t
)
h
t
= γ
0
+ γ
1

u
2
t-1
+ γ
2
u
2
t-2

7G6O2<!>JmLp
Y
t
= β
1
+β
2
X
t
+ u
t

u
t
~ N(0, h
t
)
h
t
= γ
0

+ γ
1
u
2
t-1
+ γ
2
u
2
t-2
+ γ
3
u
2
t-3

7G6O2<N>Jm7Ge*@'9'""'fG40['J*(I*
H(jZ%((J*p
Y
t
= β
1
+β
2
X
t
+ u
t

13

u
t
~ N(0, h
t
)
h
t
= γ
0
+ u
2
t-j
2(XJk0Q(L0M'4$(e]K]0['G40['J*L7]0['1
2.1.6 Kiểm định ảnh hưởng ARCH:
"0Q(V0Q(L0M'((7G6O2<N>R@N*"'L(c'*(#VT
"*:Z(eA(($0U'6O2* V7'@Tf5((7G%(#0Q(
L0M'Z%40['440Q(L0M'6O2* GZ%40['440Q(L0M'
€)1T@$0U'6O2Jm@0M(8(XZ%N "G0J*p
0Q(pPQ(L0M'40['"G"'fGZ%40['44€)p
Yt = β
1
+ β
2
X
t
+ µ
t
2(f5'$_((eTf*%'((f5"(I*f54+H(((f5'$
_(V((e$0U'@5•


1&'%"*RV8(XQ]dLXtGA'
•

"%'7G@0M(@34#]0Z

1
0Q(pPQ(L0M'40['"GN 4+p
e
2
t
= γ
0
+ γe
2
t-1
+ γ
2
e
2
t-2
+ … + γ
q
e
2
t-q
+ w
t
=(@XJk:(@(I*7GN 4+R@oLO
*:


1
0Q(!p=(@'$5

0J*p
H
0
: γ
1
= γ
2
= … = γ
q
BV5N$N 4+R*_O
*:

‘RQLJkN*J(I*(j]dLX@*'
@0M(:Z:s1k'V JmZ%4b4k(•

QJkfa(8]%LJk@H"N
<]%Z


LH3'(I*N4#LK fG40['>1&5'"k'V•

_
%<O

‘>LQ['"•

"*f$'<Z%2‰‰&<’R]1‚1>"%'Z:(ZL>RG

(c'*f(fl'$5

R'0M(LA1&5f(fl'$5

RG*(eTV5
La"h'(j]dLX@*':s(e$0U'6O21
2.1.7 Ước lượng các mô hình ARCH trên Eviews:
Bảng 2.1 : số liệu về giá đóng cửacủa cổ phiếu Vnindex giai đoạn từ
04/01/2005 đến 07/11/2014
nguồn : hp://www.cophieu68.vn/export.php
mức ý ngĩa : α = 5%
"0Q(5*:Z:s]A']dLX(I*JKJLMO@T(]A'7G4
M4(%40['"GJKJLM"'fG1
0Q(pm@(I*OZ%9'*1
Hình 2.1 Biến động của suất sinh lợi
14
08
06
04
02
.00
.02
.04
.06
.08
05 06 07 08 09 10 11 12 13 14
R
&0a RJKJLMO(eTLH(j]B'(eT(e$0U'6O2G
((]*%@H'(I*ON*'"V7'@*1
0Q(pT@_]B'

Hình 2.2 Giản đồ tự tượng quan của R
15
&0a ROLH(j]B'A((@H"(%6O61*(eT0Q(L0M'
n!7GJ*@b @T:Z7G%4M4K(%X(0Q(L0M'JK
JLM"'fGp6O6<R>R6O6<R>R6O6<R>1
0Q(!p)8*(7G4M4(%JKJLM"'fG1
PQ(L0M'7G6O6<R>
"(n*J3ŠZ“J'rLX†)J"*<>‡
Hình 2.3 Ước lượng mô hình ARMA(0,1)
PQ(L0M'7G6O6<R>
"(n*J3ŠZ“J'rLX†)J"*"<>‡
Hình 2.4 Ước lượng mô hình ARMA(1,0)
16
PQ(L0M'7G6O6<R>
"(n*J3ŠZ“J'rLX†)J"*"<>*<>‡
Hình 2.5 Ước lượng mô hình ARMA(1,1)
17
Hình 2.6 Kết quả mô hình ARMA(1,1)
Hình 2.7 Kết quả mô hình ARMA(1,0)
Hình 2.8 Kết quả mô hình ARMA(0,1)
18
*K (((iJk(I*7G6O6<R>lK@b L7G4M4
K1
0Q(pT"*(eA$0U'6O2* V7'1
Hình 2.9 Kiểm định ảnh hưởng ARCH
Hình 2.10 Kiểm định ảnh hưởng ARCH khi tăng độ trễ lên 7
19
0Q(DpPQ(L0M'7G6O2<>
*V@`f5(e$0U'6O2RkK(c'*Jn]+'40['44
0Q(L0M'6O2* G40['44€)1

Hình 2.11 Ước lượng mô hình ARCH(1)
20
Hình 2.12 Kết quả ước lượng ARCH(1)
21
?"0Q(L0M'(I*XJkŽ

(e]K]0['"K(ez'^*k'VR@
(%K V5N$0Q(L0M'4M4QV5LaU4#VT@$0U'
6O21
‘WT0Q(L0M'H7G6O2fa((*%[R_]+6O2<D>R(c'*(•'8(
X0['80U7G6O2<>R0'* Ga4Jk%7†6O2‡Rfb
'9*a4JkD
Hình 2.13 Kết quả ước lượng mô hình ARCH(5)
Hình 2.14 Đồ thị độ lệch chu•n của mô hình ARCH(5)
22
.00
.01
.02
.03
.04
.05
05 06 07 08 09 10 11 12 13 14
Conditional standard deviation
Hình 2.15 So sánh kết quả mô hình ARCH(1) và ARCH(5)
2e”07G6O2<D>(%*0Q(L0M'40['J*•["r"'[
J%Q7G6O2<>1W 4#%(\'l7G6O2<D>4M4Q
]dLX[7G6O2<>1
Hình 2.16 Bảng e
5
23

Hình 2.17 Bảng e
2
5
2.2 Mô hình GARCH:
Z%Š'LZ< D>RH"%'d'A(5(I*7G6O2Le(e”'k'
]A'7G"'fG]@H'[L]A'7G8N <6O>1Ga RH
24
z0U'Q@0M(@:KL(c'*@0*((f5"(I*40['J*(e
@VX%40['"G40['J*Z%]A'8N 1q0U' ]%
%LLZ"JLZ@:KL#@#%C.S"A4(_–%"*L%‚Š(%%Z"(J
Q'†?ZZ"*LJZ]6%'"ZJJZ2%]%*LZZ"%JVZ]*J( ‡R5}L
7G?6O21&'%"*R5(($0U'6O2(eN@H"(eT$
0U'V5N$0Q(L0M']%'$@'VTJkfa(8]%"%'7GR@
(''"'@kQ(((j9'*'}R_]+'(((345QL0
""09'1(_Ga R7G?6O2(e:0Q'@0M(((]8
f%Jn]+'43f5[1
117G?6O2<4RN>
7G?6O2<4RN>(e]A'J*@b p
Y
t
= β
1
+β
2
X
t
+u
t
<.1S>
u

t
~ N(0,h
t
)
ht = γ
0
+ ∑δ
i
h
t-i
+ ∑γ
j
u
2
t-j
<.1>;0['
"G<.1>eL"h'40['J*

fb '94+H(%($'"NV\(I*
d'(cJk(R@A]XfU((f5"(I*A'fG40['R(('"
NV\(I*f$b

R@A]XfU((f5
F
1&54wR(e'^*Lfa((I*6O
fh'G7G?6O2<RN>@['$L7G?6O2<R>1;0['"G
40['J*(I*7G?6O2<R>@0M(TX0J*p
h
t
= γ

0
+ δ
1
h
t-1
+ γ
1
u
2
t-1
2.2.2 Mô hình GARCH(1,1) và ARCH(q) vô tận:
WTaK 7G?6O2<R>LfT]'(I*7G6O2<N>RQN
Vs%]7aR(c'*(#Hf5@31


wŽ

—˜
F
—Ž



F

wŽ

—˜<Ž

—˜

F
—˜



F
>—Ž



F
wŽ

—Ž



F
—˜Ž

—˜


F
—˜Ž—

F
wŽ

—Ž




F
—˜Ž

—˜<Ž

—˜
F!
—Ž



F!
>—˜Ž



F
wŽ

—Ž



F
—˜Ž

—˜


Ž

—˜
!

F!
—˜

Ž



F!
—˜Ž



F
™
wŽ

—˜Ž

—˜

Ž

—™™—˜
š

Ž

<.1>
Wo6wŽ

—˜Ž

—˜

Ž

—™11<.1.>
&5b*5(I*40['"G<.1.>(%˜*Jm(ep
˜6w˜Ž

—˜

Ž

—™1<.1>
25