求数学和英语的大大帮忙翻译下面这些东西，在下跪谢了

虽然单变量GARCH模型被证明在捕捉资产波动性上有很强的优势，但是对于估计资产收益之间的相关性上不如多变量GARCH模型（MGARCH）模型。MGARCH模型中应用较多且相对简单的模型是Bollerslev（1990）提出的静态条件相关模型（Constant Conditional Correlation），该模型将条件方差和条件协方差矩阵定义为：


(3.10)
其中， 是条件方差取对角项所形成的n*n的对角矩阵，R是固定的条件相关系数矩阵，Rii=1，Rij =（ρij）。

(3.11)
相对于其他MGARCH模型，DCC模型最大的不同时将条件相关系数的估计分为对一般GARCH模型的参数α、β和无条件相关系数 两部分来进行：

(2.12)

其中， 是标准化残差序列Zi,tZj,t构造的无条件相关系数，α，β分别为MGARCH模型中前期标准化残差平方项的系数和前期条件异方差项的系数，满足α≥0，β≥0并且α+β‹1
DCC模型则可以统一如下：











(3.13)
其中， 代表t-1时刻所有的信息集，


进一步采用最大似然估计法，如果 作为Dt的参数， 作为Rt的参数，则对数似然函数可以表示为：

(3.14)
当忽略常数项nlog2π的情况下，（3.14）  可以表示为：

(3.15)
为了简化，将其分为两步进行：


(3.16)
这样，似然函数就可以分为波动性（2.18）式和相关性（2.19）式两部分：

(3.17)

(3.18)
因此
（3.19）
由此，Dcc模型将分为两阶段来估计时变条件相关系数矩阵：一、求得使似然函数波动性部分（3.17）式最大化的参数 ；二，将 代入（3.18）式中求使相关性部分最大化参数 。

自己动手 丰衣足食。。。

Although the univariate GARCH model is that volatility in the capture of assets have a strong advantage, but to estimate the correlation between asset returns not as good as multivariate GARCH model (MGARCH) model. MGARCH model used more often and relatively simple model is Bollerslev (1990) proposed a static conditional correlation model (Constant Conditional Correlation), the model terms and conditions of the variance covariance matrix is defined as:


(3.10)
Which is the conditional variance to take the diagonal entries of the n * n formed by the diagonal matrix, R is the fixed conditional correlation coefficient matrix, Rii = 1, Rij = (ρij).

(3.11)
Compared to other MGARCH models, DCC model is not the greatest conditions while the estimated correlation coefficient is divided into the average GARCH model parameters α, β and unconditional correlation coefficients for the two parts:

(2.12)
Where is the standardized residual sequence Zi, tZj, t structure unconditional correlation coefficient, α, β, respectively MGARCH model pre-standardized residuals squared coefficients and initial conditions of the coefficients of items Heteroscedasticity meet α ≥ 0, β ≥ 0 and α + β <1
DCC model can unity as follows:











(3.13)
Which, on behalf of all time t-1 information set,


Further use of maximum likelihood estimation, if, as the parameters Dt, as the parameters Rt, then the logarithmic likelihood function can be expressed as:

(3.14)
When ignoring the case of constant nlog2π, (3.14) can be expressed as:

(3.15)
To simplify, divided into two steps:


(3.16)
This likelihood function can be divided into two waves (2.18) type and the correlation (2.19) type of two parts:

(3.17)

(3.18)
Therefore
(3.19)
Thus, Dcc model will be divided into two stages to estimate the time-varying conditional correlation coefficient matrix: First, obtain the likelihood function part of the volatility (3.17) where the parameters of maximum; Second, the substitution (3.18) where seeking to maximize the relevance of some parameters.

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强人就是多啊。。。

顶一下楼上的。。。。。。。。。。。。

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