19th Ave New York, NY 95822, USA

# 统计代写|时间序列分析代写Time Series Analysis代考|STAT3040

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

## 统计代写|时间序列分析代写Time Series Analysis代考|TS and Seasonal Dummies

Suppose that we are using the $T S$ approach. Without seasonality we would have:
$$X_t=\alpha+\mu t+Y_t .$$
Suppose there are $S$ is the number of periods in one year. For quarterly data then $S=4$ while for monthly data $S=12$. One strategy for dealing with seasonality is to replace the intercept $\alpha$ with $S$ dummy variables
$$d_{1 t}, d_{2 t}, \ldots d_{s t}$$
so that:
$$X_t=\sum_{j=1}^S \alpha_j d_{j t}+\mu t+Y_t .$$
To obtain $Y_t$, the cycle, would then run least squares on $X_t$ with $S$ seasonal dummies and a time trend and take $Y_t$ as the least squares residual.

For example with quarterly data (or $S=4$ ) one would have four dummy variables so that:
$$X_t=\alpha_1 d_{1 t}+\alpha_2 d_{2 t}+\alpha_3 d_{3 t}+\alpha_4 d_{4 t}+\mu t+Y_t$$
where:
\begin{aligned} d_{i t} & =1, \text { if } t \text { is in quarter } i, d_{i t}=0 \text { otherwise } \ i & =1,2,3,4 . \end{aligned}
With consumption data we would expect $\alpha_4>\alpha_1$, reflecting the Christmas effect on consumption.

## 统计代写|时间序列分析代写Time Series Analysis代考|DS with Seasonal Dummies

For the $D S$ model with seasonality a reasonable assumption is that the growth rate varies according to the period we are in. Thus instead of:
$$\Delta X_t=\mu+Y_t$$
we would have:
$$\Delta X_t=\sum_{j=1}^S \mu_j d_{j t}+Y_t .$$
To obtain the cycle $Y_t$ one would therefore regress $\Delta X_t$ on the $S$ seasonal dummies and obtain $Y_t$ as the least squares residual.
For example with quarterly data we would have:
$$\Delta X_t=\mu_1 d_{1 t}+\mu_2 d_{2 t}+\mu_3 d_{3 t}+\mu_4 d_{4 t}+Y_t$$
so that to obtain the cycle $Y_t$ one would regress $\Delta X_t$ on four seasonal dummies and obtain $Y_t$ as the least squares residual.

Another approach to seasonality which was made popular by Box and Jenkins is to seasonally difference. Here instead of (1.14) the trend takes the form:
$$T_t=W_{t-s} e^{\mu t} .$$
$$X_t-X_{t-s}=\mu+Y_t$$
so that instead of differencing 1 period as we normally do for $D S$ models, we instead difference say $S$ periods.
For example with quarterly data instead of regressing:
$$X_t-X_{t-1}=\mu+Y_t$$
we would run the regression:
$$X_t-X_{t-4}=\mu+Y_t$$
and obtain $Y_t$ as the least squares residual.

## 统计代写|时间序列分析代写Time Series Analysis代考|TS and Seasonal Dummies

$$X_t=\alpha+\mu t+Y_t .$$

$$d_{1 t}, d_{2 t}, \ldots d_{s t}$$

$$X_t=\sum_{j=1}^S \alpha_j d_{j t}+\mu t+Y_t .$$

$$X_t=\alpha_1 d_{1 t}+\alpha_2 d_{2 t}+\alpha_3 d_{3 t}+\alpha_4 d_{4 t}+\mu t+Y_t$$

\begin{aligned} d_{i t} & =1, \text { if } t \text { is in quarter } i, d_{i t}=0 \text { otherwise } \ i & =1,2,3,4 . \end{aligned}

## 统计代写|时间序列分析代写Time Series Analysis代考|DS with Seasonal Dummies

$$\Delta X_t=\mu+Y_t$$

$$\Delta X_t=\sum_{j=1}^S \mu_j d_{j t}+Y_t .$$

$$\Delta X_t=\mu_1 d_{1 t}+\mu_2 d_{2 t}+\mu_3 d_{3 t}+\mu_4 d_{4 t}+Y_t$$

$$T_t=W_{t-s} e^{\mu t} .$$

$$X_t-X_{t-s}=\mu+Y_t$$

$$X_t-X_{t-1}=\mu+Y_t$$

$$X_t-X_{t-4}=\mu+Y_t$$

## 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。