volatility spillovers from australia's major trading partners across the gfc

8/11/2019 Volatility Spillovers from Australia's Major Trading Partners Across the GFC

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yit = ln(pit) ln(pit1)


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i

j, j =i n i = 1,....,N.

xt = xt1+ t

xt = (x1t, x2t) x

xt = (L)t

(L) = (1 L)1

xt = A(L)ut

A(L) = (L)Q1

t u

t = Q

tt,E(u

tu

t) = I, Q1

t

t.


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xt+1,t = xt,

et+1,t = xt+1 xt+1,t= A0ut+1 =

a0,11 a0,12a0,21 a0,22

u1,t+1u2,t+1

E

et+1,te

t+1,t

= A0A

0

x1,t a20,11+ a

20,12

x2,t a20,21 + a

20,22

xi xj

i, j = 1, 2 i =j.

S=a20,12+ a

22,1

trace(A0A0

100

S=

H1h=0

Ni,j=1

i=j

a2h,ij

H1h=0 trace(AhA

h)


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yt = Et1(yt)+t, Et1(yt) yt t 1 t

t =

htt , t N(0, 1)

ht = +

pj=1

2tj+

qj=1

jhtj

> 0, j 0 j 0 ht 0. j , j j +j

j+ j 1


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r

i=1

i +s

i=1

i < 1

E(2t )< 1+ 12

+ 1 < 1.

E(log(1+ 1I(t)2t + 1))< 0.

t

ut = xt+

pi=1

irti

qi=1

iati

xt k m p q

yt = E(yt | Ft1) + t

t = Dtt

yt = (y1t, .....,ymt)

, t = (it,......,mt)

Ft t Dt = diag(h1/2

1 , ......., h1/2

m ), m


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t = 1,....,n.

hit, i = 1, ...., m,

hit = +r

j=1

ij2i,tj+

sj=1

ijhi.tj

ij i

ij i

rj=1

ij+

sj=1

ij .

= E(t

t | Ft1) = E(t

t), = {it} i, j = 1, ...., m. t

t = Dtt

tDt, Dt = (diagQt)1/2

E(t

t | Ft1) =Qt = DtDt, Qt = D

1t QtD

1t

m

rt = t+t


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rt = (SPRETLt, ASXRETt, H ANGSRETt)

=

0.000210.00026

0.00022

. 12

3

=

0.01240.0163

0.0154

.=

1.00 0.25095 0.229330.25095 1.00 0.65536

0.22933 0.65536 1.00

.

Q3(1) = 1205.43335, Q3(4) = 1280.38447, andQ3(8) = 1440.30046,

r1t = 0.00056169(0.00009224) + 0.0577rt1(0.00531397) +a1t h1t =0.00000158(0.000) + 0.0862(0.000) + 0.8987h1,t1(0.000) + e1t

rUSRETL,t = C1 P3USRETLt1+ a1trAUSRET,t= C2+ P21USRETLt1 P22AUSRETt1+ a2t

rHANGSENGRET,t= C3+ P31USRETLt1 P33HANGSENGRETt1+ a3t


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a1t, a2t, a3t

g11,t= A0+ A1b21,t1+ A2g11,t1

q21,t= T0+ T1q21,t1 T2a2,t1g22,t= B0+ B1b

22,t1+ B2g22,t1

q31,t= U0+ U1q31,t1+ U2a3,t1q32,t= W0+ W1q31,t1+ W2a2,t1

g33,t= D0+ D1b23,t1+ D2g33,t1+ D5g22,t1

b1t = a1t, b2t= a2t q21,tb1t, b3,t= a3,t q31,tb1t, q32,tb2t C3,D0,T2,U0,W0, W1, W2,

C1

P3

C2

P21

P22

C3

P31

P33

A0

A1

A2

B0

B1

B2

D0

D1

D2

D5

T0

T1

T2

U0

U1

U2

W0

W1

W2


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volatility spillovers from australia's major trading partners across the gfc

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