assignmentutor-lab™ 为您的留学生涯保驾护航 在代写时间序列分析Time-Series Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写时间序列分析Time-Series Analysis代写方面经验极为丰富，各种代写时间序列分析Time-Series Analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 统计代写|时间序列分析代写Time-Series Analysis代考|NONLINEAR STOCHASTIC MODELS

11.7 As discussed in $\S \mathbf{3 . 6}$, Wold’s decomposition theorem allows us to represent every weakly stationary, purely nondeterministic, stochastic process as a linear combination of a sequence of uncorrelated random variables, as in (3.2). A stochastic process can then be considered nonlinear if it does not satisfy the assumptions underlying the decomposition, for example, if the representation is:
$$x_t-\mu=f\left(a_t, a_{t-1}, a_{t-2}, \ldots\right)$$
where $f(\cdot)$ is some arbitrary nonlinear function. However, the “curse of dimensionality” means that this representation is of little practical use. Consequently, as an approximation to $f(\cdot)$, consider a Taylor expansion of (11.2) around zero:
$$x_t-\mu=f\left(0, a_{t-1}, a_{t-2}\right)+a_t f^{\prime}\left(0, a_{t-1}, a_{t-2}\right)+0.5 a_t^2 f^{\prime \prime}\left(0, a_{t-1}, a_{t-2}\right)+\cdots$$
where $f^{\prime}$ and $f^{\prime \prime}$ are the first and second derivatives of $f$ with respect to $a_t$. By dropping higher-order terms, we can express $x_t$ in terms of its conditional moments. For example, by keeping only the first two terms, $x_t$ can be expressed as a function of the conditional mean and variance, respectively. Simple forms of nonlinearity can also be obtained by assuming some loworder polynomial function for $f(\cdot)$ : for example, the first-order nonlinear moving average (see Robinson, 1977).
$$x_t=a_t+\psi_1 a_{t-1}^2$$
Polynomial functions of lagged $x_t$ can also be used (Jones, 1978), while another simple way of introducing nonlinearity is to allow $x_t$ to respond in a different manner to innovations depending on their sign.

## 统计代写|时间序列分析代写Time-Series Analysis代考|BILINEAR MODELS

11.9 An important class of nonlinear model is the bilinear, which takes the general form
$$\phi(B)\left(x_t-\mu\right)=\theta(B) \varepsilon_t+\sum_{i=1}^R \sum_{j=1}^S \gamma_{i j} x_{t-i} \varepsilon_{t-j}$$
Here $\varepsilon_t \sim S W N\left(0, \sigma_{\varepsilon}^2\right)$, where this notation is used to denote that the innovations $\varepsilon_t$ are strict white noise. The second term on the right hand side of (11.3) is a bilinear form in $\varepsilon_{t-j}$ and $x_{t-i}$, and this accounts for the nonlinear character of the model, for if all the $\gamma_{i j}$ are zero, (11.3) clearly reduces to the familiar ARMA model. The bilinear model can be thought of as a higherorder Taylor approximation to the unknown nonlinear function $f(\cdot)$ than that provided by the Wold decomposition.
11.10 Little analysis has been carried out on this general bilinear form, but Granger and Andersen (1978) have analyzed the properties of several simple bilinear forms, characterized as:
$$x_t=\varepsilon_t+\gamma_{i j} x_{t-i} \varepsilon_{t-j}$$
If $i>j$ the model is called super-diagonal, if $i=j$ it is diagonal, and if $i<j$, it is sub-diagonal. If we define $\lambda=\gamma_{i j} \sigma$ then, for super-diagonal models, $x_t$ has zero mean and variance $\sigma_{\varepsilon}^2 /\left(1-\lambda^2\right)$, so that $|\lambda|<1$ is a necessary condition for stability.

Conventional identification techniques using the SACF of $x_t$ would identify this series as white noise, but Granger and Andersen show that, in theory at least, the SACF of the squares of $x_t$ would identify $x_t^2$ as an ARMA $(i, j)$ process, so that we could distinguish between white noise and this bilinear model by analyzing $x_t^2$.

# 时间序列分析代考

## 统计代写|时间序列分析代写时间序列分析代考|非线性随机模型

$$x_t-\mu=f\left(a_t, a_{t-1}, a_{t-2}, \ldots\right)$$
，其中$f(\cdot)$是某个任意的非线性函数。然而，“维度的诅咒”意味着这种表示几乎没有实际用途。因此，作为$f(\cdot)$的近似值，考虑(11.2)在0附近的泰勒展开:
$$x_t-\mu=f\left(0, a_{t-1}, a_{t-2}\right)+a_t f^{\prime}\left(0, a_{t-1}, a_{t-2}\right)+0.5 a_t^2 f^{\prime \prime}\left(0, a_{t-1}, a_{t-2}\right)+\cdots$$
，其中$f^{\prime}$和$f^{\prime \prime}$是$f$对$a_t$的一阶和二阶导数。通过去掉高阶项，我们可以用条件矩来表示$x_t$。例如，通过只保留前两项，$x_t$可以分别表示为条件均值和方差的函数。非线性的简单形式也可以通过假设$f(\cdot)$的某个较低的多项式函数得到:例如，一阶非线性移动平均(见Robinson, 1977)。
$$x_t=a_t+\psi_1 a_{t-1}^2$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|双线性模型

11.9一类重要的非线性模型是双线性模型，它的一般形式是
$$\phi(B)\left(x_t-\mu\right)=\theta(B) \varepsilon_t+\sum_{i=1}^R \sum_{j=1}^S \gamma_{i j} x_{t-i} \varepsilon_{t-j}$$

$$x_t=\varepsilon_t+\gamma_{i j} x_{t-i} \varepsilon_{t-j}$$

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师