### 金融代写|金融计量经济学代写Financial Econometrics代考|ECMT6006

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|金融计量经济学Financial Econometrics代考|ARIMA

An important aspect of the time series is that time series data is often used for the forecasting. Based on the information of the past and present states of the variable, the future states of the variable are forecasted. The ARIMA models are introduced by the Box-Jenkins in the year 1976. The ARIMA stands for the “Auto Regressive Integrated Moving Average”. Thereafter, ARIMA models are widely used in finance for forecasting the stationary time series. The ARIMA models are useful for modelling both the univariate and multivariate time series. Commonly, time series is generated using the following: AR (Autoregressive) or MA (Moving average) or both (ARMA) or ARIMA processes.

AR (Autoregressive) Process
The AR (Autoregressive) process considers the past values of the time series for modelling. The first order AR (Autoregressive) model is represented by following Eq. $6.3$.
$$R_{I}=\Phi_{l} R_{t-1}+\mathbf{u}{t}$$ Where $R{t}$ represents the present value of the variable at time $t$
$R_{t-1}$ represents the past value of the variable at time $t-1$
$\Phi_{t}$ represents the proportion at time $t$
$\mathrm{u}{t}$ represents the white noise error term The above Eq. (6.3) represents that the present value of the variable $(R)$ at time $(t)$ is equal to the some proportion $\left(\Phi{t}\right)$ of the past value of the variable $(R)$ at time $(t-1)$ plus the white noise error term $\left(\mathrm{u}{t}\right)$. Likewise, $\mathrm{nth}$ order AR (Autoregressive) process or $\mathrm{AR}(\mathrm{n})$ can be represented as Eq. (6.4). The $\mathrm{AR}(\mathrm{n})$ model as shown in $(6.4)$ includes only the current and previous values of the variable $R$. $$R{t}=\Phi_{1} R_{t-1}+\Phi_{2} R_{t-2}+\ldots+\Phi_{n} R_{t-n}+\mathrm{u}_{t}$$
Basic properties of the $\mathrm{AR}$ (Autoregressive) process are as follows:

• Mean of the $R_{t}$ for $\mathrm{AR}$ (1) model is zero
• Variance of $R_{t}$ for $\mathrm{AR}$ (1) model is represented by the Eq. (6.5)
$$\frac{\sigma_{u}^{2}}{\left(1-\Phi_{1}^{2}\right)}$$
• Covariance between $R_{t}$ and $R_{t-1}$ is represented by the Eq. (6.6)
$$\frac{\Phi_{1} \sigma_{u}^{2}}{\left(1-\Phi_{1}^{2}\right)}$$
Similarly for lag $(\mathrm{n})$ the expression is shown below
$$\frac{\Phi_{1}^{n} \sigma_{u}^{2}}{\left(1-\Phi_{1}^{2}\right)}$$

## 金融代写|金融计量经济学Financial Econometrics代考|ARCH & GARCH

The ARMA models are good in explaining the serial correlation but not efficient in capturing the conditional heteroskedasticity or volatility clustering. Thus, for forecasting the time series accurately, there is need for more sophisticated techniques. The ARCH (see Engle, 1982, 1983) and GARCH (see Bollerslev, 1986) techniques are used widely for modelling the volatility or volatility clustering of the time series. An ARCH model can be estimated from the best fitting autoregressive (AR) model using the OLS. Then perform the ARCH test to check whether ARCH effect is present in the residuals obtained from the autoregressive (AR) regression. The best fitting autoregressive (AR) model can be represented by the Eq. (6.13).

$$Y_{I}=\alpha_{0}+\alpha_{1} Y_{t-1}+\alpha_{2} Y_{t-2}+\ldots+\alpha_{n} Y_{t-n}+\mathrm{u}{t}$$ Next, estimate the squares of the error term $\left(\hat{\mathrm{u}}{t}^{2}\right) \hat{\epsilon}^{2}$ by running a regression on the lagged value of the squares of the error term $\left(\hat{\mathrm{u}}{t}^{2}\right) \hat{\epsilon}^{2}$. $$\hat{\mathbf{u}}{t}^{2}=\alpha_{0}+\sum_{i=1}^{p} \alpha_{i} \hat{\mathbf{u}}{t-i}^{2} u$$ In the above Eq. (6.14), $p$ represents the length of The ARCH lags. The null hypothesis of the $\mathrm{ARCH}$ test assumes that there is no $\mathrm{ARCH}$ effect present in the time series. The GARCH model considers the lagged conditional variance term in addition to the lagged value of the squares of the error term $\hat{\epsilon}^{2}$. The generalized GARCH $(p, q)$ model can be represented mathematically as shown in the Eq. (6.15). $$\hat{\mathrm{u}}{t}^{2}=\alpha_{0}+\sum_{i=1}^{p} \alpha_{i} \hat{\mathrm{u}}{t-i}^{2}+\sum{i=1}^{q} \beta_{i} \sigma_{t-i}^{2}$$
Where
P represents the lags length of the lagged value of the squares of the error term $\hat{\epsilon}^{2}$
$Q$ represents the lags length of the lagged conditional variance terms.

## 金融代写|金融计量经济学Financial Econometrics代考|VAR

The VAR stands for the “Vector Autoregressive”. The VAR models are introduced by Christopher A. Sim in the year 1960. VAR models are useful specially on dealing with the multivariate time series over time. The VAR model structure of a variable includes linear function of the lagged values of the variable and all other variables included in the VAR model. Let’s characterize a VAR model for examining the variations in the $\mathrm{X}$ and $\mathrm{Y}$ variables. Mathematically, the above VAR model can be represented as Eq. (6.16 and 6.17).
\begin{aligned} &X_{t}=\alpha_{1}+\sum_{i=1}^{p} \beta_{i} X_{t-i}+\sum_{i=1}^{p} \gamma_{i} Y_{t-i}+\mathrm{u}{1 t} \ &Y{t}=\alpha_{2}+\sum_{i=1}^{p} \theta_{i} X_{t-i}+\sum_{i=1}^{p} \lambda_{i} Y_{t-i}+\mathrm{u}_{2 t} \end{aligned} The above two Eqs. (6.16 and 6.17) represent the VAR $(p)$ model. Where, $p$ represents the length of the lags. The VAR models assume that the variables are stationary. However, if the variables are not stationary but cointegrated, then VECM (Vector Error Correction Model) may be useful. The regression analysis expresses the dependency of one variable on the other. But it does not express the causality among the variables. The Granger Causality Test estimates provide detailed information on the causality among the variables. The VAR models are likewise useful to estimate the impulse response analysis and variance decomposition.

## 金融代写|金融计量经济学Financial Econometrics代考|ARIMA

AR（自回归）过程
AR（自回归）过程考虑时间序列的过去值进行建模。一阶 AR（自回归）模型由以下等式表示。6.3.

R我=披lR吨−1+在吨在哪里R吨表示变量在时间的现值吨
R吨−1表示变量在某个时间的过去值吨−1

R吨=披1R吨−1+披2R吨−2+…+披nR吨−n+在吨

• 的平均值R吨为了一个R(1) 模型为零
• 方差R吨为了一个R(1) 模型由方程式表示。(6.5)
σ在2(1−披12)
• 之间的协方差R吨和R吨−1由方程式表示。(6.6)
披1σ在2(1−披12)
同样对于滞后(n)表达式如下所示
披1nσ在2(1−披12)

## 金融代写|金融计量经济学Financial Econometrics代考|ARCH & GARCH

ARMA 模型能很好地解释序列相关性，但不能有效地捕捉条件异方差或波动率聚类。因此，为了准确地预测时间序列，需要更复杂的技术。ARCH（参见 Engle, 1982, 1983）和 GARCH（参见 Bollerslev, 1986）技术被广泛用于时间序列的波动率或波动率聚类建模。可以使用 OLS 从最佳拟合自回归 (AR) 模型估计 ARCH 模型。然后执行 ARCH 测试以检查从自回归 (AR) 回归获得的残差中是否存在 ARCH 效应。最佳拟合自回归 (AR) 模型可以由方程式表示。(6.13)。

P 表示误差项平方的滞后值的滞后长度ε^2

## 金融代写|金融计量经济学Financial Econometrics代考|VAR

VAR 代表“向量自回归”。VAR 模型由 Christopher A. Sim 在 1960 年引入。VAR 模型特别适用于处理随时间变化的多元时间序列。变量的 VAR 模型结构包括变量滞后值和 VAR 模型中包含的所有其他变量的线性函数。让我们描述一个 VAR 模型来检查X和是变量。在数学上，上述 VAR 模型可以表示为等式。（6.16 和 6.17）。
\begin{aligned} &X_{t}=\alpha_{1}+\sum_{i=1}^{p} \beta_{i} X_{ti}+\sum_{i=1}^{p} \gamma_{i} Y_{ti}+\mathrm{u} {1 t} \ &Y {t}=\alpha_{2}+\sum_{i=1}^{p} \theta_{i} X_{ti }+\sum_{i=1}^{p} \lambda_{i} Y_{ti}+\mathrm{u}_{2 t} \end{aligned} 以上两个方程。(6.16 和 6.17) 代表 VAR(p)模型。在哪里，p表示滞后的长度。VAR 模型假设变量是平稳的。但是，如果变量不是平稳的而是协整的，那么 VECM（矢量误差校正模型）可能会很有用。回归分析表达了一个变量对另一个变量的依赖性。但它并没有表达变量之间的因果关系。格兰杰因果检验估计提供了变量间因果关系的详细信息。VAR 模型同样可用于估计脉冲响应分析和方差分解。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。