Civil Engineering Reference
In-Depth Information
3
Econometrics Models
In this paper, we used the dynamic copula-based GARCH models. The analysis
of copulas has two advantages. First, copulas provide a greater flexible method
of constructing multivariate distributions, given the marginal distributions and the
dependence structures separately. We can connect
k
(such as the normal distribution,
the marginal distribution of the lognormal distribution) through any copula function.
Second, linear correlation and Granger causality analysis method are the commonly
used correlation analysis method, but there are still many limitations, this kind of
method can only analyze linear situation of correlated variables, linear correlation
coefficient, and the corresponding elliptical distribution that can only describe the
linear correlation degree between variables and symmetrical correlation model.
When meeting the question which is nonlinear, it cannot get accurate results. We
briefly review the basic properties of a bivariate copula (
K
=
2) below.
3.1
The Marginal Distribution of the Model and the Joint
Distribution of Copula Model
The GARCH (1,1) model can be described as follows:
y
i
,
t
=
x
0
+
x
1
y
i
,
t
−
1
+
x
2
e
i
,
t
−
1
+
e
i
,
t
(1)
e
i
,
t
=
√
p
i
,
t
k
i
,
t
,
k
i
,
t
∼
SkT
(
k
i
|
η
i
,
λ
i
)
(2)
p
i
,
t
=
ω
i
,
t
+
α
i
e
2
i
,
t
−
1
+
β
i
p
i
,
t
−
1
e
i
,
t
(3)
x
1
captures the impact of nonsynchronous effects. When model the GARCH, it
needs to satisfy the condition is (1)
1. The error
term of
e
i
,
t
is assumed to be a skewed-
t
distribution, which can be used to capture the
possible asymmetric and heavy-tailed characteristics. The Hansen density function
(1994) is used in this research:
ω
i
>
0; (2)
α
i
,
β
i
≥
0; (3)
α
+
β
i
<
⎧
⎨
qc
1
2
−
(
η
+
1
)
/
2
2
qk
+
d
1
η
−
d
q
+
,
< −
k
−
λ
1
skewed
−
t
(
k
|
η
,
λ
)
.
(4)
qc
1
2
−
(
η
+
1
)
/
2
2
qk
+
d
⎩
1
η
−
d
q
+
,
k
≥−
1
+
λ
The value of
d
,
q
,and
c
are defined as
d
η
−
2
(
η
+
1
/
2
)
q
2
2
d
2
and
c
d
≡
4
λ
1
,
≡
1
+
2
λ
−
≡
π
(
η
−
(5)
η
−
2
)(
η
/
2
)
Search WWH ::
Custom Search