## 统计代写|时间序列分析代写Time-Series Analysis代考|540-FS2022

statistics-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|Multivariate time series outliers

In time series analysis, it is important to examine the possible outliers and do some proper adjustments because outliers can lead to inaccurate parameter estimation, model misspecification, and poor forecasts. Outlier detection has been studied extensively for univariate time series, including Fox (1972), Abraham and Box (1979), Martin (1980), Hillmer et al. (1983), Chang et al. (1988), Tsay (1986, 1988), Chen and Liu (1993), Lee and Wei (1995), Wang et al. (1995), Sanchez and Pena (2003), and many others. We normally classify outliers in four categories, additive outliers, innovational outliers, level shifts, and temporal changes. For MTS, a natural approach is first to use univariate techniques to the individual component and remove outliers, then treat the adjusted series as outlier-free and model them jointly. However, there are several disadvantages of this approach. First, in MTS an outlier of its univariate component may be induced by an outlier from other component within the multivariate series. Overlooking this situation may lead to overspecification of the number of outliers. Second, an outlier impacting all the components may not be detected by using the univariate outlier detection methods because they do not use the joint information from all time series components in the system at the same time.

To overcome the difficulties, Tsay et al. (2000) extended four types of outliers for univariate time series to MTS and their detections, and Galeano et al. (2006) further proposed a detection method based on projection pursuit, which sometime is more powerful than testing the multivariate series directly. Other references on MTS outliers include Helbing and Cleroux (2009), Martinez-Alvarez et al. (2011), and Cucina et al. (2014), among others.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Outlier detection through projection pursuit

Galeano et al. (2006) proposed a method that first projects the MTS into a univariate time series, and then detects outliers within the derived or projected univariate time series. They also suggested an algorithm that finds optimal projection directions by using kurtosis coefficients. This approach has two main advantages. First, it is simple because no multivariate model has to be prespecified. Second, an appropriate projection direction can lead to a test statistic that is more powerful.

To illustrate the method, we use projection of the VARMA model as an example. A linear combination of $m$ multiple time series that follow a VARMA model is a univariate ARMA model. Specifically, let $\mathbf{A}^{\prime}$ be a vector contains the weights of the linear combination and assume $\mathbf{X}{t}$ is a $m$-dimensional VARMA $(p, q)$ process. Then, Lütkepohl $(1984,1987)$ showed that $x{t}=\mathbf{A}^{\prime} \mathbf{X}{t}$ follows a $\operatorname{ARMA}\left(p^{}, q^{}\right)$ process with $p^{} \leq m p$ and $q^{} \leq(m-1) p+q$. Thus, $x{t}$ has the following representation
$$\phi(B) x_{t}=c+\theta(B) e_{t},$$
where $\phi(B)=|\boldsymbol{\Phi}(B)|, c=\mathbf{A}^{\prime} \boldsymbol{\Phi}(1)^{} \boldsymbol{\Theta}{0}$, and $\mathbf{A}^{\prime} \boldsymbol{\Phi}(B)^{} \boldsymbol{\Theta}(B) \mathbf{a}{t}=\theta(B) e_{t}, \boldsymbol{\Phi}(B)^{*}$ is the adjoint matrix of $\boldsymbol{\Phi}(B)$, and $e_{t}$ is a univariate white noise process with mean 0 and constant variance $\sigma^{2}$.
Suppose we observe a time series $\mathbf{Z}{t}$ that is affected by an outlier as shown in Eq. (2.84), the projected time series $z{t}=\mathbf{A}^{\prime} \mathbf{Z}{t}$ can be represented as $$z{t}=x_{t}+\mathbf{A}^{\prime} \boldsymbol{\alpha}(B) \boldsymbol{\omega} I_{t}^{(h)} .$$
Particularly, if $\mathbf{Z}{t}$ is affected by MAO, then the projected time series is $$z{\mathrm{t}}=x_{t}+\boldsymbol{\beta} I_{t}^{(h)},$$
so that it has an additive outlier of size $\boldsymbol{\beta}=\mathbf{A}^{\prime} \boldsymbol{\omega}$ at $t=h$. Similarly, if $\mathbf{Z}{t}$ is affected by an MLS, then its corresponding projected time series will have a level shift with size $\boldsymbol{\beta}=\mathbf{A}^{\prime} \boldsymbol{\omega}$ at $t=h$. The same argument can also be made in the case when we have MTC. Thus, we can formulate the following hypothesis $$H{0}: \boldsymbol{\beta}=\mathbf{0} \text { v.s. } H_{A}: \boldsymbol{\beta} \neq \mathbf{0},$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Outlier detection through projection pursuit

$$\phi(B) x_{t}=c+\theta(B) e_{t}$$

$$z t=x_{t}+\mathbf{A}^{\prime} \boldsymbol{\alpha}(B) \boldsymbol{\omega} I_{t}^{(h)} .$$

$$z \mathrm{t}=x_{t}+\boldsymbol{\beta} I_{t}^{(h)},$$

$$H 0: \boldsymbol{\beta}=\mathbf{0} \text { v.s. } H_{A}: \boldsymbol{\beta} \neq \mathbf{0},$$

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|DSC425

statistics-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|Granger causality

One of the interesting problems in studying a vector time series is that we often want to know whether there are any causal effects among these variables. Specifically, in a VAR $(p)$ model
$$\boldsymbol{\Phi}{p}(B) \mathbf{Z}{t}=\boldsymbol{\theta}{0}+\mathbf{a}{t},$$
we can partition the vector $\mathbf{Z}{t}$ into two components, $\mathbf{Z}{t}=\left[\mathbf{Z}{1, t}^{\prime}, \mathbf{Z}{2, t}^{\prime}\right]^{\prime}$ so that
$$\left[\begin{array}{cc} \boldsymbol{\Phi}{11}(\boldsymbol{B}) & \boldsymbol{\Phi}{12}(\boldsymbol{B}) \ \boldsymbol{\Phi}{21}(\boldsymbol{B}) & \boldsymbol{\Phi}{22}(\boldsymbol{B}) \end{array}\right]\left[\begin{array}{l} \mathbf{Z}{1, t} \ \mathbf{Z}{2, t} \end{array}\right]=\left[\begin{array}{l} \boldsymbol{\theta}{1} \ \boldsymbol{\theta}{2} \end{array}\right]+\left[\begin{array}{l} \mathbf{a}{1, t} \ \mathbf{a}{2, t} \end{array}\right]$$
When $\boldsymbol{\Phi}{12}(B)=\mathbf{0}$, Eq. (2.40) becomes $$\left{\begin{array}{l} \boldsymbol{\Phi}{11}(\boldsymbol{B}) \mathbf{Z}{1, t}=\boldsymbol{\theta}{1}+\mathbf{a}{1, t}, \ \boldsymbol{\Phi}{22}(B) \mathbf{Z}{2, t}=\boldsymbol{\theta}{2}+\boldsymbol{\Phi}{21}(B) \mathbf{Z}{1, t}+\mathbf{a}{2, t} . \end{array}\right.$$ The future values of $\mathbf{Z}{2, t}$ are influenced not only by its own past but also by the past of $\mathbf{Z}{1, t}$, while the future values of $\mathbf{Z}{1, t}$ are influenced only by its own past. In other words, we say that variables in $\mathbf{Z}{1, t}$ cause $\mathbf{Z}{2, t}$, but variables in $\mathbf{Z}{2, t}$ do not cause $\mathbf{Z}{1, r}$. This concept is often known as the Granger causality, because it is thought to have been Granger who first introduced the notion in 1969. For more discussion about causality and its tests, we refer readers to Granger (1969), Hawkes (1971a, b), Pierce and Haugh (1977), Eichler et al. (2017), and Zhang and Yang (2017), among others.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Cointegration in vector time series

It is well known that any stationary VARMA model can be approximated by a VAR model. Moreover, because of its easier interpretation, a VAR model is often used in practice. It should be noted that for a given vector time series $\mathbf{Z}{t}$, it could occur that each component series $Z{i, t}$ is nonstationary but its linear combination $\mathbf{Y}{t}=\boldsymbol{\beta}^{\prime} \mathbf{Z}{t}$ is stationary for some $\boldsymbol{\beta}^{\prime}$. In such a case, one should use its error-correction representation
$$\Delta \mathbf{Z}{t}=\boldsymbol{\theta}{0}+\boldsymbol{\gamma} \mathbf{Z}{t-1}+\boldsymbol{\alpha}{1} \Delta \mathbf{Z}{t-1}+\cdots+\boldsymbol{\alpha}{p-1} \Delta \mathbf{Z}{t-p+1}+\mathbf{a}{t}$$
where $\boldsymbol{\gamma}$ is related to $\boldsymbol{\beta}^{\prime}$ and $\boldsymbol{\gamma} \mathbf{Z}_{t-1}$ is a stationary error-correction term. For more details, we refer readers to Engle and Granger (1987), Granger (1986), Wei (2006, chapter 17), Ghysels and Miller (2015), Miller and Wang (2016), and Wagner and Wied (2017).

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

$$\boldsymbol{\Phi} p(B) \mathbf{Z} t=\boldsymbol{\theta} 0+\mathbf{a} t$$

\boldsymbol{\Phi} 11(\boldsymbol{B}) \mathbf{Z} 1, t=\boldsymbol{\theta} 1+\mathbf{a} 1, t, \boldsymbol{\Phi} 22(B) \mathbf{Z} 2, t=\boldsymbol{\theta} 2+\boldsymbol{\Phi} 21(B) \mathbf{Z} 1, t+\mathbf{a} 2, t .
$$、正确的。 \ \$$ 的末来价值 $\mathbf{Z} 2, t$ 不仅受到自己过去的影响，还受到过去的影响 $\mathbf{Z} 1, t$ ，而末来的价值 $\mathbf{Z} 1, t$ 只受自己 过去的影响。换句话说，我们说变量在 $\mathbf{Z} 1, t$ 原因 $\mathbf{Z} 2, t$, 但变量在 $\mathbf{Z} 2, t$ 不引起 $\mathbf{Z} 1, r$. 这个概念通常被称为格兰杰 因果关系，因为它被认为是格兰杰在 1969 年首次引入这个概念。关于因果关系及其检验的更多讨论，我们将读 者推荐给格兰杰 (1969)、霍克斯 (1971a， b)，Pierce 和 Haugh (1977), Eichler 等人。(2017 年) 以及张和杨 (2017 年) 等。

## 统计代写|时间序列分析代写Time-Series Analysis代考|Cointegration in vector time series

$$\Delta \mathbf{Z} t=\theta 0+\gamma \mathbf{Z} t-1+\boldsymbol{\alpha} 1 \Delta \mathbf{Z} t-1+\cdots+\boldsymbol{\alpha} p-1 \Delta \mathbf{Z} t-p+1+\mathbf{a} t$$

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT758

statistics-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|Fundamental concepts and issues

In studying a phenomenon, we often encounter many variables, $Z_{i, t}$, where $i=1,2, \ldots, m$, and the observations are taken according to the order of time, $t$. For convenience we use a vector, $\mathbf{Z}{t}=\left[Z{1, t}, Z_{2, t}, \ldots, Z_{m, l}\right]^{\prime}$, to denote the set of these variables, where $Z_{i, t}$ is the $i$ th component variable at time $t$ and it is a random variable for each $i$ and $t$. The time $t$ in $\mathbf{Z}{t}$ can be continuous and any value in an interval, such as the time series of electric signals and voltages, or discrete and be a specific time point, such as the daily closing price of various stocks or the total monthly sales of various products at the end of each month. In practice, even for a continuous time series, we take observations only at digitized discrete time points for analysis. Hence, we will consider only discrete time series in this book, and with no loss of generalizability, we will consider $Z{i, t}$, for $i=1,2, \ldots, m, t=0, \pm 1, \pm 2, \ldots$, and hence $\mathbf{Z}{t}=\left[Z{1, t}, Z_{2, t}, \ldots, Z_{m, t}\right]^{\prime}, t=0, \pm 1, \pm 2, \ldots$
We call $\mathbf{Z}{t}=\left[Z{1, t}, Z_{2, t}, \ldots, Z_{m, t}\right]^{\prime}$ a multivariate time series or a vector time series, where the first subscript refers to a component and the second subscript refers to the time. The fundamental characteristic of a multivariate time series is that its observations depend not only on component $i$ but also time $t$. The observations between $Z_{i, s}$ and $Z_{j, t}$ can be correlated when $i \neq j$,

regardless of whether the times $s$ and $t$ are the same or not. They are vector-valued random variables. Most standard statistical theory and methods based on random samples are not applicable, and different methods are clearly needed. The body of statistical theory and methods for analyzing these multivariate or vector time series is referred to as multivariate time series analysis.

Many issues are involved in multivariate time series analysis. They are different from standard statistical theory and methods based on a random sample that assumes independence and constant variance. In multivariate time series, $\mathbf{Z}{t}=\left[Z{1, t}, Z_{2, t}, \ldots, Z_{m, l}\right]^{\prime}$, a fundamental phenomenon is that dependence exists not only in terms of $i$ but also in terms of $t$. In addition, we have the following important issues to consider:

## 统计代写|时间序列分析代写Time-Series Analysis代考|High dimension problem in multivariate time series

Because of high-speed internet and the power and speed of the new generation of computers, a researcher now faces some very challenging phenomena. First, he/she must deal with an ever-increasing amount of data. To find useful information and hidden patterns underlying the data, a researcher may use various data-mining methods and techniques. Adding a time dimension to these large databases certainly introduces new aspects and challenges. In multivariate time series analysis, a very natural issue is the high dimension problem where the number of parameters may exceed the length of the time series. For example, a simple second order vector autoregressive VAR(2) model for the 50 states in the USA will involve more than 5000 parameters, and the length of the time series may be much shorter. For example, the length of the monthly observations for 20 years is only 240 . Traditional time series methods are not designed to deal with these kinds of high-dimensional variables. Even with today’s computer power and speed, there are many difficult problems that remain unsolved. As most statistical methods are developed for a random sample, the use of highly correlated time series data certainly introduces a new set of complications and challenges, especially for a high-dimensional data set.

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|540-FS2022

statistics-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|Reading data from CSVs and other

In this recipe, you will use the pandas . read_csv () function, which offers a large set of parameters that you will explore to ensure the data is properly read into a time series DataFrame. In addition, you will learn how to specify an index column, parse the index to be of the type DatetimeIndex, and parse string columns that contain dates into datetime objects.
Generally, using Python, data read from a CSV file will be in string format (text). When using the read_csv method in pandas, it will try and infer the appropriate data types (dtype), and, in most cases, it does a great job at that. However, there are situations where you will need to explicitly indicate which columns to cast to a specific data type. For example, you will specify which column(s) to parse as dates using the parse_dates parameter in this recipe.

You will be reading a CSV file that contains hypothetical box office numbers for a movie. The file is provided in the GitHub repository for this book. The data file is in datasets/ Ch2/movieboxoffice. csv.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Reading data from an Excel file

To read data from an Excel file, you will need to use a different reader function from pandas. Generally, working with Excel files can be a challenge since the file can contain formatted multi-line headers, merged header cells, and images. They may also contain multiple worksheets with custom names (labels). Therefore, it is vital that you always inspect the Excel file first. The most common scenario is reading from an Excel file that contains data partitioned into multiple sheets, which is the focus of this recipe.

In this recipe, you will be using the pandas . read_excel () function and examining the various parameters available to ensure the data is read properly as a DataFrame with a DatetimeIndex for time series analysis. In addition, you will explore different options to read Excel files with multiple sheets.

To use pandas. read_excel (), you will need to install an additional library for reading and writing Excel files. In the read_excel () function, you will use the engine parameter to specify which library (engine) to use for processing an Excel file. Depending on the Excel file extension you are working with (for example, . $\mathrm{xl}$ s or . $\mathrm{xl} \mathrm{sx}$ ), you may need to specify a different engine that may require installing an additional library.

The supported libraries (engines) for reading and writing Excel include $x l r d$, openpy $x 1$, odf, and pyxlsb. When working with Excel files, the two most common libraries are usually $x l r d$ and openpyxl.

The $\mathrm{xl}$ rd library only supports . $\mathrm{xl}$ s files. So, if you are working with an older Excel format, such as . $x l s$, then $x l r d$ will do just fine. For newer Excel formats, such as . $x$ lsx, we will need a different engine, and in this case, openpyxl would be the recommendation to go with.

## 有限元方法代写

tatistics-lab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。

## 英国补考|时间序列分析代写Time-Series Analysis代考|DSC 425

statistics-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

## 英国补考|时间序列分析代写Time-Series Analysis代考|Installing JupyterLab and JupyterLab extensions

Throughout this book, you can follow along using your favorite Python IDE (for example, PyCharm or Spyder) or text editor (for example, Visual Studio Code, Atom, or Sublime). There is another option based on the concept of notebooks that allows interactive learning through a web interface. More specifically, Jupyter Notebook or JupyterLab are the preferred methods for learning, experimenting, and following along with the recipes in this book. Interestingly, the name Jupyter is derived from the three programming languages: Julia, Python, and R. Alternatively, you can use Google’s Colab or Kaggle Notebooks. For more information, refer to the See also section from the Development environment setup recipe of this chapter. If you are not familiar with Jupyter Notebooks, you can get more information here: https : / jupyter. org/.

In this recipe, you will install Jupyter Notebook, JupyterLab, and additional JupyterLab extensions.

Additionally, you will learn how to install individual packages as opposed to the bulk approach we tackled in earlier recipes.

## 英国补考|时间序列分析代写Time-Series Analysis代考|Reading Time Series Data from Files

In this chapter, we will use pandas, a popular Python library with a rich set of I/O tools, data wrangling, and date/time functionality to streamline working with time series data. In addition, you will explore several reader functions available in pandas to ingest data from different file types, such as Comma-Separated Value (CSV), Excel, and SAS. You will explore reading from files, whether they are stored locally on your drive or remotely on the cloud, such as an AWS $\mathbf{S} 3$ bucket.

Time series data is complex and can be in different shapes and formats. Conveniently, the pandas reader functions offer a vast number of arguments (parameters) to help handle such variety in the data.

The pandas library provides two fundamental data structures, Series and DataFrame, implemented as classes. The DataFrame class is a distinct data structure for working with tabular data (think rows and columns in a spreadsheet). The main difference between the two data structures is that a Series is one-dimensional (single column), and a DataFrame is two-dimensional (multiple columns). The relationship between the two is that you get a Series when you slice out a column from a DataFrame. You can think of a DataFrame as a side-by-side concatenation of two or more Series objects.

A particular feature of the Series and DataFrames data structures is that they both have a labeled axis called index. A specific type of index that you will often see with time series data is the DatetimeIndex which you will explore further in this chapter. Generally, the index makes slicing and dicing operations very intuitive. For example, to make a DataFrame ready for time series analysis, you will learn how to create DataFrames with an index of type DatetimeIndex.

## 英国补考|时间序列分析代写Time-Series Analysis代考|Reading Time Series Data from Files

pandas 库提供了两个基本数据结构，Series 和 DataFrame，实现为类。DataFrame 类是一种独特的数据结构，用于处理表格数据（想想电子表格中的行和列）。两种数据结构的主要区别在于Series是一维的（单列），而DataFrame是二维的（多列）。两者之间的关系是，当您从 DataFrame 中切出一列时，您会得到一个 Series。您可以将 DataFrame 视为两个或多个 Series 对象的并排连接。

Series 和 DataFrames 数据结构的一个特殊特性是它们都有一个称为索引的标记轴。您将在时间序列数据中经常看到的一种特定类型的索引是 DatetimeIndex，您将在本章中进一步探讨。通常，索引使切片和切块操作非常直观。例如，要使 DataFrame 为时间序列分析做好准备，您将学习如何使用 DatetimeIndex 类型的索引创建 DataFrame。

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT 758

statistics-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|Getting Started with Time Series Analysis

When embarking on a journey to learn coding in Python, you will often find yourself following instructions to install packages and import libraries, followed by a flow of a code-along stream. Yet an often-neglected part of any data analysis or data science process is ensure that the right development environment is in place. Therefore, it is critical to have the proper foundation from the beginning to avoid any future hassles, such as an overcluttered implementation or package conflicts and dependency crisis. Having the right environment setup will serve you in the long run when you complete your project, ensuring you are ready to package your deliverable in a reproducible and production-ready manner.

Such a topic may not be as fun and may feel administratively heavy as opposed to diving into the core topic or the project at hand. But it is this foundation that differentiates a seasoned developer from the pack. Like any project, whether it is a machine learning project, a data visualization project, or a data integration project, it all starts with planning and ensuring all the required pieces are in place before you even begin with the core development.

In this chapter, you will learn how to set up a Python virtual environment, and we will introduce you to two common approaches for doing so. These steps will cover commonly used environment management and package management tools. This chapter is designed to be hands-on so that you avoid too much jargon and can dive into creating your virtual environments in an iterative and fun way.
As we progress throughout this book, there will be several new Python libraries that you will need to install specific to time series analysis, time series visualization, machine learning, and deep learning on time series data. It is advised that you don’t skip this chapter, regardless of the temptation to do so, as it will help you establish the proper foundation for any code development that follows. By the end of this chapter, you will have mastered the necessary skills to create and manage your Python virtual environments using either conda or venv.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Development environment setup

As we dive into the various recipes provided in this book, you will be creating different Python virtual environments to install all your dependencies without impacting other Python projects.

You can think of a virtual environment as isolated buckets or folders, each with a Python interpreter and associated libraries. The following diagram illustrates the concept behind isolated, self-contained virtual environments, each with a different Python interpreter and different versions of packages and libraries installed:

These environments are typically stored and contained in separate folders inside the envs subfolder within the main Anaconda folder installation. For example, on macOS, you can find the envs folder under Users//opt/anaconda3/ envs/. On Windows OS, it may look more like C: $\backslash$ Users $\backslash<$ yourusername $>\backslash$ anaconda3 \envs.
Each environment (folder) contains a Python interpreter, as specified during the creation of the environment, such as a Python $2.7 .18$ or Python $3.9$ interpreter.
Generally speaking, upgrading your Python version or packages can lead to many undesired side effects if testing is not part of your strategy. A common practice is to replicate your current Python environment to perform the desired upgrades for testing purposes before deciding whether to move forward with the upgrades. This is the value that environment managers (conda or venv) and package managers (conda or pip) bring to your development and production deployment process.

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT4025

statistics-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|Quasi-Biennial Oscillation

The Quasi-Biennial Oscillation will be discussed here at $\Delta t=1$ month. The time series used for this example is $\mathrm{QBO}$ at the atmospheric pressure level $20 \mathrm{hPa}$, which corresponds to the altitude of about $26 \mathrm{~km}$ above mean sea level (Fig. $6.5 \mathrm{a}$ and $# 2$ in Appendix). The spectral density estimate is shown in Fig. $6.5 \mathrm{~b}$ with the frequency axis given in a linear scale.

At the time when this text was being written, monthly observations of QBO were available from January 1953 through April of 2019 . The test extrapolation for the entire 2018 and the next six months of 2019, from May through November, which have been added in December 2019, is based upon the part of the time series that ends in December $2017(N=780)$.

The optimal, according to three of the five order selection criteria used here, is the AR model of order $p=10$ :
$$x_{t}=\varphi_{1} x_{t-1}+\varphi_{2} x_{t-2}+\cdots+\varphi_{10} x_{t-10}+a_{t} .$$
It means that the extrapolation equation is
$$\hat{x}{t}(\tau)=\varphi{1} \hat{x}{t}(\tau-1)+\varphi{2} \hat{x}{t}(\tau-2)+\cdots+\varphi{10} \hat{x}{t}(\tau-10)$$ The white noise variance corresponding to the $\operatorname{AR}(10)$ model is $\sigma{a}^{2} \approx 21(\mathrm{~m} / \mathrm{s})^{2}$ while the total variance of wind speed at $20 \mathrm{hPa}$ is $\sigma_{x}^{2} \approx 389(\mathrm{~m} / \mathrm{s})^{2}$. Therefore, the predictability criterion $\rho(1) \approx 0.05$ and the correlation coefficient $(6.13)$ between the unknown true and predicted values of wind speed at lead time $\tau=1$ month is $0.97$. As seen from Fig. 6.6, the statistical predictability of $\mathrm{QBO}$ at the $20 \mathrm{hPa}$ level described with the predictability criteria $r_{e}(\tau)$ and $\rho(\tau)$ is quite high.

The results of prediction test with the initial time in December 2017 (Fig. 6.7a) show that the AR method of extrapolation is working quite well with this time series: 19 of the 20 monthly forecasts stay within the $90 \%$ confidence limits. More predictions are given from December 2018 through January 2021 for future verification (Fig. 6.7b). The data used for the AR models were from January 1953 through December 2017 and through December 2018 , respectively. By the time when the book was ready for the publisher, more observations became available and they are included into Fig. 6.7b. The quality of extrapolation seems to be high, but one should have in mind that the $90 \%$ confidence intervals shown in the figure are wide.

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

Predicting the behavior of the oceanic ENSO component-sea surface temperature in equatorial Pacific-is regarded as a very important task in climatology and oceanography (e.g., #3 and #4 in Appendix). Attempts to predict ENSO’s atmospheric component-the Southern Oscillation Index-do not seem to be numerous (e.g., Kepenne and Ghil 1992). In this section, both tasks will be treated within the KWT framework.

At the annual sampling rate, the ENSO components behave similar to white noise (Chap. 5); their predictions through any probabilistic method would be practically useless. In the current example, the statistical forecasts of sea surface temperature in the ENSO area NINO3 $\left(5^{\circ} \mathrm{N}-5^{\circ} \mathrm{S}, 150^{\circ} \mathrm{W}-90^{\circ} \mathrm{W}\right)$ and the Southern Oscillation Index are executed at a monthly sampling rate using the data from January 1854 through February 2019 and from 1876 through February 2019 , respectively. The data are available at websites #5 and #6 given in Appendix below. The NINO3 time series is shown in Fig. 6.8a. It can be treated as a sample of a stationary process.
The autoregressive analysis of this time series showed an AR(5) model as optimal. Its spectral density estimates are shown in Fig. $6.8 \mathrm{~b}$. The low-frequency part of the spectrum up to $0.5$ cpy contains about $70 \%$ of the NINO3 variance and the ratio of the white noise RMS to the NINO3 RMS is 0.39. In contrast to the annual global

temperature with the trend present, the predictability of NINO3 diminishes quite fast, but, as seen from Fig. 6.9, it still extends to several months.

A KWT prediction from the end of 2017 through January 2019 is given in Fig. $6.10 \mathrm{a}$. The result of the test turned out to be satisfactory but one has to remember that the $90 \%$ confidence limits for the extrapolated values are rather wide. Only the first four or five predicted values lie within the relatively narrow interval not exceeding $\pm \sigma_{x}$

This data set is taken from site #7 in Appendix below. As mentioned in Chap. 5 , the components of MJO regarded as samples of scalar processes may possess relatively high statistical predictability. At the unit lead time (one day), the statistical predictability criterion $\rho$ (1) for the RMM1 component equals to about $0.18$ and the process should be studied in more detail. The predictability of the RMM1 time series decreases rather fast (Fig. 6.12), but it stays acceptable up to 6 days. The RMM2 component behaves in the same way.

Prediction examples (Fig. 6.13) turned out to be rather successful even for longer lead times, but the confidence bounds are rather wide. The cycles with periods close to 50 days cannot be reliably reproduced by the extrapolation trajectory at lead times close to the period of the cycle.

If the sampling rate is increased from 1 day to 10 days, the resulting time series becomes poorly predictable even at the unit lead time, that is, at 10 days. As both the original time series RMM1 and RMM2 and the time series with $\Delta t=10$ days are Gaussian or close to Gaussian, one can say that the Madden-Julian Oscillation is practically unpredictable at that sampling rate in spite of the presence of a significant spectral maximum.

The examples in this chapter include five rather typical and at the same time dissimilar cases with the sampling rates of one year, one month, and one day; they can be summed up in the following way:

• the global surface temperature that has some predictability due to the dominant role of low-frequency variations even when the linear trend is deleted.
• highly predictable Quasi-Biennial Oscillation whose spectrum contains a powerful peak at the low-frequency part of the spectrum,
• SOI-the atmospheric component of ENSO-which contains a statistically significant spectral maximum and still has low predictability because of the low dynamic range of its spectrum.
• MJO, with its smooth spectral maximum and acceptable forecasts at several lead times.

In conclusion, it has been shown here that the use of a forecasting method which agrees with the Kolmogorov-Wiener theory of extrapolation produces satisfactory results if the spectrum of the time series is concentrated within a relatively narrow frequency band. If the spectrum is spread more or less evenly over frequency, the time series is practically unpredictable. In all cases, even when the latest and previously unknown values of the time series lie close to the predicted trajectory, one should keep in mind the width of the confidence interval as a function of lead time. It is the quantity that defines the usefulness of forecasts.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Quasi-Biennial Oscillation

X吨=披1X吨−1+披2X吨−2+⋯+披10X吨−10+一个吨.

X^吨(τ)=披1X^吨(τ−1)+披2X^吨(τ−2)+⋯+披10X^吨(τ−10)白噪声方差对应于和⁡(10)模型是σ一个2≈21( 米/s)2而风速的总方差为20H磷一个是σX2≈389( 米/s)2. 因此，可预测性准则ρ(1)≈0.05和相关系数(6.13)在提前期风速的未知真实值和预测值之间τ=1月份是0.97. 从图 6.6 可以看出，问乙○在20H磷一个用可预测性标准描述的水平r和(τ)和ρ(τ)相当高。

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

• 由于低频变化的主导作用，即使在线性趋势被删除的情况下，全球地表温度也具有一定的可预测性。
• 高度可预测的准两年振荡，其频谱在频谱的低频部分包含一个强大的峰值，
• SOI——ENSO 的大气成分——包含一个统计上显着的光谱最大值，并且由于其光谱的低动态范围而仍然具有低的可预测性。
• MJO，具有平滑的光谱最大值和在几个前置时间可接受的预测。

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|QBUS3850

statistics-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|General Remarks

Forecasting geophysical processes is probably the most desired goal in Earth and related solar sciences. Reliable predictions are needed at time scales from hours and days (meteorology, hydrology, etc.) to decades and centuries (climatology and related sciences). With one exception, all geophysical processes in the atmosphereocean-land-cryosphere system are random, which means that none of them can be predicted at any lead time without an error. The exception is tides-a deterministic process which exists in the oceans, atmosphere, and in the solid body of the planet. The knowledge of tides is especially important for the oceans, and tides in the open ocean can be predicted almost precisely. Along the shorelines where tides play an important role, sealevel variations can generally be predicted with sufficient accuracy as well, but there may be some cases when random disturbances should also be taken into account (Munk and Cartwright 1966).

The behavior of another astronomically caused process – the seasonal trend-is so irregular that one cannot even say for sure whether the next summer (or any other season) will be warmer or cooler than the current one.

The atmospheric, oceanic, terrestrial, and cryospheric processes and their interactions can be described with fluid dynamics equations; however, the equations are complicated, numerous, and cannot be solved analytically. Getting reliable numerical solutions encounters serious physical and computational problems, which cannot be discussed in this book. However, there is at least one important example of successful numerical solution of prediction problems – the weather forecasting. The forecasts given by meteorologists are reliable and rarely contain serious errors at lead times at least up to about a week. These forecasts are obtained by uploading information about the current (initial) state of processes involved in weather generation into a numerical computational scheme having discrete temporal and spatial resolution and then running the scheme forward in time and space to obtain forecasts. As the knowledge of the initial conditions cannot be ideal, the forecasts contain errors. Besides, the computational grid is discrete so that the processes whose scales are smaller than the distance between the grid nodes and shorter than the unit time step cannot be directly taken into account. The errors in the initial and other conditions grow with the forecast lead time, and eventually, the variance of the forecast errors becomes equal to the variance of the process that is being forecasted. The forecast becomes unusable. It means that the process has a predictability limit; the limit should be defined quantitatively through the ratio of the forecast error variance as a function of lead time to the variance of the process. These issues have been discussed in a number of classical works by Lorenz (1963, 1975, 1995).

## 统计代写|时间序列分析代写Time-Series Analysis代考|Method of Extrapolation

In both scalar and multivariate cases, the extrapolation means a forecast of the time series on the basis of its behavior in the past. The method of extrapolation used in this book to predict the behavior of stationary geophysical time series is based upon the autoregressive modeling (Box et al. 2015). It is discussed in this chapter for the case of scalar time series $x_{t}$ known over a finite time interval from $t=\Delta t$ through $t=N \Delta t$. The sampling interval $\Delta t$ is the unit time step, which can be a minute, hour, month, year, or whatever the data prescribes. Here, $\Delta t=1$. The only

assumption made about the time series $x_{t}$ is that it presents a sample record of a stationary random process.

The first stage of extrapolation procedure is to approximate the scalar time series with an AR model of a properly selected order $p$. The result of approximation is
$$x_{t}=\varphi_{1} x_{t-1}+\cdots+\varphi_{p} x_{t-p}+a_{t},$$
where $\varphi_{j}, j=1, \ldots, p$ are the AR coefficients and $a_{t}$ is a zero mean innovation sequence (white noise) with the variance $\sigma_{a}^{2}$.

Equation (6.1) describes the time series as a function of its behavior in the past, that is, exactly what is required for time series extrapolation. The unknown true value of the time series at lead time $\tau$ is
$$x_{t+\tau}=\varphi_{1} x_{t+\tau-1}+\cdots+\varphi_{p} x_{t+\tau-p}+a_{t+\tau}$$
so that at the lead time $\tau=1$
$$x_{t+1}=\varphi_{1} x_{t}+\cdots+\varphi_{p} x_{t-p+1}+a_{t+1}$$
At time $t$, all terms in the right-hand side of this equation, with the exception of $a_{t+1}$, are known because they belong to the observed initial time series. Therefore, the extrapolated (predicted, forecasted) value of the time series at the unit lead time is
$$\hat{x}{t}(1)=\varphi{1} x_{t}+\cdots+\varphi_{p} x_{t-p+1} .$$
As the extrapolation error at the unit lead time is $a_{t+1}$, its variance is $\sigma_{a}^{2}$. For $\tau=2$, one has
$$\hat{x}{t}(2)=\varphi{1} \hat{x}{t}(1)+\cdots+\varphi{p} x_{t-p+2}$$
so that the extrapolation error will be the sum of $\sigma_{a}^{2}$ with the error at $\tau=1$ (that is, $\sigma_{a}^{2}$ ) multiplied by the autoregression coefficient $\varphi_{1}$. The general solution for the extrapolation of an $\operatorname{AR}(p)$ sequence at the lead time $\tau$ is
$$\hat{x}{t}(\tau)=\varphi{1} \hat{x}{t}(\tau-1)+\cdots+\varphi{p} \hat{x}_{t}(\tau-p)$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Global Annual Temperature

According to Table 5.2, the higher predictability occurs for the annual surface temperature averaged over very large areas, up to the entire surface of the planet. This happens because respective time series contain most of their energy within the low-frequency part of the spectrum.

The global annual temperature (notated here as GLOBE) from 1850 (#1 in Appendix below and Fig. 6.1a) shows two intervals with a definite positive trend; the trend is longer and slightly faster during the latest several decades. Similar to the earlier interval from 1911 through 1944 , the trend that happened during the years from 1974 through 2010 (the initial year for our extrapolation test below) may have been caused by natural factors (Privalsky and Fortus 2011) so that its higher predictability could have been the result of regular variations of climate. As for the higher frequencies, the spectral density estimate for the detrended time series (Fig. 6.1b) proves

that detrending the time series does not affect the spectrum at frequencies above $0.02$ cpy (at time scales 50 years and shorter).

The goal of this test is to get an idea of extrapolation efficiency for the original and detrended time series. With year 2010 as the initial time for extrapolation, one has eight observed values of temperature anomalies that can be compared with predictions for 2011-2018.

The entire time series of GLOBE from 1850 through 2018 can be regarded as a sample of a stationary random process and extrapolated in accordance with its best fitting AR model. The second approach regards the time series as nonstationary: the sum of a stationary process plus trend (linear, in our case). The first version means that the trend is a part of the low-frequency variations caused by the natural climate variability; in the second version, the climate variability is regarded as stationary while the trend is caused by some external factors, including possible anthropogenic effects.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Method of Extrapolation

X吨=披1X吨−1+⋯+披pX吨−p+一个吨,

X吨+τ=披1X吨+τ−1+⋯+披pX吨+τ−p+一个吨+τ

X吨+1=披1X吨+⋯+披pX吨−p+1+一个吨+1

X^吨(1)=披1X吨+⋯+披pX吨−p+1.

X^吨(2)=披1X^吨(1)+⋯+披pX吨−p+2

X^吨(τ)=披1X^吨(τ−1)+⋯+披pX^吨(τ−p)

## 统计代写|时间序列分析代写Time-Series Analysis代考|Global Annual Temperature

1850 年以来的全球年温度（此处记为 GLOBE）（下面附录中的#1 和图 6.1a）显示了两个具有明确正趋势的区间；在最近的几十年中，这一趋势更长，速度略快。与 1911 年到 1944 年的早期区间类似，1974 年到 2010 年（我们下面外推测试的第一年）发生的趋势可能是由自然因素引起的（Privalsky 和 ​​Fortus 2011），因此其较高的可预测性可以是气候规律变化的结果。至于更高的频率，去趋势时间序列的谱密度估计（图 6.1b）证明

GLOBE 从 1850 年到 2018 年的整个时间序列可以看作是一个平稳随机过程的样本，并根据其最佳拟合 AR 模型进行外推。第二种方法将时间序列视为非平稳的：平稳过程加上趋势的总和（在我们的例子中是线性的）。第一个版本意味着趋势是自然气候变率引起的低频变化的一部分；在第二个版本中，气候变率被认为是静止的，而趋势是由一些外部因素引起的，包括可能的人为影响。

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|Math5845

statistics-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|Properties of Time Series of Spatially Averaged Surface Temperature

With the exception of ENSO-related phenomena, the results of analysis of geophysical time series listed in Table $5.1$ do not contradict the hypothesis of the Markovian behavior of climate (Hasselmann 1976). Out of the 13 time series in Table 5.1, seven have orders not higher than 1 , which can be regarded as a confirmation of the hypothesis. The other six samples have low predictability, which does not differ much from predictability of the remaining seven time series. The predictability of AMO is better than in all other cases, and it may be high enough for practical applications. The AMO time series differs from other time series in the table in the sense that it is obtained by averaging SST over a large area of the North Atlantic; therefore, one can assume that the comparatively high rate of spectral density decrease and the higher predictability criterion $r_{e}(1) \approx 0.62$ for AMO could be the result of that averaging.

The global climate is better characterized with data obtained by averaging over large parts of the globe. The AMO time series is just a specific example of such averaging, but we have nine time series that show the surface temperature over the entire globe, its hemispheres, and oceanic and terrestrial parts. Those time series have been analyzed in Privalsky and Yushkov (2018) and found to have a more complicated structure and a higher predictability than the other time series studied in that work.

The data used in the above publication include the complete time series given by the University of East Anglia; most of the time series begin in 1850. The authors of the data files show that the degree of coverage during the XIX Century was poor. Following the example given in Dobrovolski (2000), we will study the same time series starting from 1920 , when the coverage with observations generally increases to $50 \%$ and higher for the global, hemispheric and oceanic data.

The results given in Table $5.2$ confirm one of the previous conclusions: the annual surface temperature averaged over large parts of the globe is best described with relatively complicated models having AR orders $p=3$ or $p=4$ and a relatively high statistical predictability. The results for the southern hemisphere as a whole and for its land follow a Markov model and have lower statistical predictability; they agree with our results obtained from the data given by the Goddard Institute of Space Studies (GISS). According to the GISS data for the southern hemisphere (#14 in Appendix), the autoregressive order $p=1$ and the criterion $r_{e}(1) \approx 0.55$.

The data sets show that spatial averaging on the global scale and over the northern hemisphere including its oceans and land produces time series whose properties differ quite significantly from what is shown in Table $5.1$ for individual climate indices. The optimal AR orders increase up to four, and the predictability criterion grows up to $0.82$ for the north hemispheric ocean. The reason for the behavior of temperature over the southern hemisphere for the time series which begin in 1920 is not clear, but it may be related to the change is statistical properties of the trivariate system consisting of the time series of global, land, and terrestrial time series. For example, the predictability criterion $r_{e}$ (1) for the entire time series is $0.74$ (Privalsky and Yushkov 2018 ) and $0.44$ for the time series that begins in 1920 . A more detailed description of the change is given in Chap. 14 .

## 统计代写|时间序列分析代写Time-Series Analysis代考|Quasi-Biennial Oscillation

The “rule of no significant sharp peaks” in climate spectra has at least one exception which is supported with decades of direct observations. At least one atmospheric process-the Quasi-Biennial Oscillation, or QBO-does not follow this rule. The QBO phenomenon exists in the equatorial stratosphere at altitudes from about 16 $\mathrm{km}$ to $50 \mathrm{~km}$, and it is characterized with quasi-periodic variations of the westerly and easterly wind speed. The period of oscillations is about 28 months, which corresponds to the frequency of about $0.43$ cpy. It has been discovered in the 1950 ‘s and investigated in a number of publications, in particular, in Holton and Lindzen (1972) who proposed a physical model for QBO. In the review of QBO research by Baldwin et al (2001), QBO is called “a fascinating example of a coherent, oscillating mean flow that is driven with propagating waves with periods unrelated to the resulting oscillation.” Some effects of QBO upon climate are discussed by Anstey and Shepherd $(2014)$.

The statistical properties of QBO such as its spectra and statistical predictability do not seem to have been analyzed within the framework of theory of random processes; this section (along with Chaps. 6 and 10) is supposed to fill this gap in the part related to $\mathrm{QBO}$ as a scalar and bivariate (Chap. 10) phenomenon. It will be analyzed here using the set of monthly observational data provided by the Institute of Meteorology of the Free University of Berlin for the time interval from 1953 through December 2018 (see #15 in Appendix and Naujokat 1986). The set includes monthly wind speed data in the equatorial stratosphere at seven atmospheric pressure levels, from 10 to $70 \mathrm{hPa}$; these levels correspond to altitudes from $31 \mathrm{~km}$ to $18 \mathrm{~km}$.

If the goal of the study were to analyze $\mathrm{QBO}$ as a scalar random process, the data could have been taken at the sampling interval $\Delta t=6$ months or even 1 year. As QBO’s statistical predictability at a monthly sampling rate will also be studied in Chap. 6, the sampling interval $\Delta t=1$ month is taken in this section as well. Examples of $\mathrm{QBO}$ variations are shown in Fig. 5.3.

The basic statistical characteristics of $\mathrm{QBO}$ are shown in Table 5.3. The average wind speed is easterly (negative), and it decreases below the $20 \mathrm{hPa}$ level turning eastward at the lowest level. The variance increases from the $10 \mathrm{hPa}$ level by about $10 \%$ to $15 \mathrm{hPa}$ and $20 \mathrm{hPa}$ and then gradually decreases downward by an order of magnitude. These facts are well known (e.g., Baldwin et al. 2001). The optimal AR models have orders from $p=11$ to $p=29$; such orders are too high for individual time domain analysis.

The typical shape of the spectrum shows an almost periodic random function of time at $f \approx 0.43$ cpy (Fig. 5.4a). The maximum is very narrow and completely dominates the spectrum so that a more detailed picture can only be seen when the scale is logarithmic along both axes (Fig. 5.4b). This seems to be an absolutely unique phenomenon at climatic time scales. At higher frequencies, the spectral density diminishes rather quickly with all other peaks being statistically insignificant. Having this in mind, the spectra will be shown in what follows at frequencies not exceeding 1 cpy.

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

The Madden-Julian Oscillation (MJO) is another unusual phenomenon both because it is not firmly fixed geographically and because it presents an oscillatory system not related to tides or to a seasonal trend. A review of MJO can be found in Zhang (2005).
Strictly speaking, the MJO phenomenon is a vector process and its spectra should be estimated in agreement with the approach discussed in Thomson and Emery (2014, Chap. 5). However, having in mind the methodological goals of the book, the MJO components will be treated here as either two scalar time series (this chapter and Chap. 6) or as a bivariate process (Chap. 8).

The MJO data used here consist of daily MJO indices RMM1 and RMM2 from January 1, 1979 through April 30, $2017(N=14000, \Delta t=1$ day). Thus, MJO is a bivariate random process. The source of the data is the Australian Bureau of Meteorology, site #16 in Appendix. The graph of the time series is shown in Fig. 5.6a. The hypothesis of stationarity can be accepted through visual assessment, but it is also confirmed by using the method described in Chap. 4. The spectral densities of the time series components are very similar and contain a single wide peak at the frequency close to $0.02 \mathrm{cpd}$. The spectral estimates are shown in Fig. $5.6 \mathrm{~b}$ for the part of the frequency axis up to $0.05 \mathrm{cpd}$; at higher frequencies, the spectrum is monotonically decreasing. The confidence limits are not shown because they almost coincide with the spectra due to the high reliability of estimates obtained with these long time series. The contribution of higher frequencies is negligibly small. Thus, the Madden-Julian Oscillation presents a good example of an oscillatory system. The statistical predictability criterion $r_{e}(1)$ given with Eq. (3.7) amounts to about $0.98$, meaning that both components possess high statistical predictability at the unit lead time, that is, at 1 day.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Quasi-Biennial Oscillation

QBO 的统计特性，如光谱和统计可预测性，似乎没有在随机过程理论的框架内进行分析；本节（连同第 6 章和第 10 章）应该填补与问乙○作为标量和双变量（第 10 章）现象。此处将使用柏林自由大学气象研究所提供的 1953 年至 2018 年 12 月期间的月度观测数据集进行分析（见附录中的 #15 和 Naujokat 1986）。该集合包括赤道平流层在七个大气压水平下的每月风速数据，从 10 到70H磷一个; 这些级别对应于从31 ķ米至18 ķ米.

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

Madden-Julian 振荡 (MJO) 是另一个不寻常的现象，既因为它在地理上没有牢固固定，也因为它呈现出与潮汐或季节性趋势无关的振荡系统。可以在 Zhang (2005) 中找到对 MJO 的评论。

## 有限元方法代写

tatistics-lab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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT4102

statistics-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|Frequency Resolution of Autoregressive Spectral Analysis

The AR (or MEM) spectral estimation provides an analytical formula for the estimated spectrum. It means that the spectral resolution in the formula is such that the value of spectral density can be calculated at any frequency. This is true, but the actual resolution is defined by the AR order: the number of extrema and inflection points in the spectral curve corresponding to an $\operatorname{AR}(p)$ model cannot be higher than $p$ (see Sect. 4.3). Therefore, a high resolution requires a high AR order, but a high-order model cannot be obtained with a short time series.

By definition, a linearly regular random process does not contain any strictly periodic components. This feature may cause some doubts about the ability of parametric time series analysis designed for regular processes to detect sharp peaks at frequencies which are close to each other, for example, when the data contain harmonic oscillations. Actually, the ability of autoregressive spectral analysis in this respect is very high under just one condition: getting accurate results requires having enough data for analysis. (Certainly, this requirement holds for all nonparametric method of spectral analysis such as Blackman and Tukey’s, MTM, Welch’s, etc.)

A unique case of harmonic oscillations with perfectly known frequencies within the Earth system is tides. The frequencies of tidal constituents are known precisely from astronomy; the amplitudes are determined from observations. The autoregressive analysis in the frequency domain provides a convenient tool for estimating frequencies of harmonic oscillations that are contained in time series of tidal phenomena. If the frequencies are determined correctly in sea level observations, one may hope that they will also be determined correctly in any other stationary data.
The example below is designed to verify how accurately the maximum entropy spectral analysis can determine the frequencies of tidal constituents by analyzing the time series of sea level at station 9414317 , Pier $221 / 2$, San Francisco, USA, using $10^{5}$ hourly sea level observations starting from January 28,2000 . The data source is $# 3$ in Appendix. A part of the record (about 50 days) is shown in Fig. 4.7. The tides obviously dominate the record.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Example of AR Analysis in Time and Frequency Domains

Consider the entire process of time series analysis using as an example the annual values of Tripole Index (TPI) for the Interdecadal Pacific Oscillation (Henley et al. 2015). The time series shown in Fig. $4.9$ extends from 1854 through $2018(N=165)$; it is closely related to other El Niño-Southern Oscillation indices but differs from them in some respects. The data source is taken from the Web site #5 in Appendix to this chapter. The time series does not contain any statistically significant trend, and its behavior allows one to assume, without any further analysis, that it can be treated as a sample of a stationary random process. The test for Gaussianity showed that the probability density function of this time series can be regarded as normal.

The time series has been analyzed in the time domain by fitting to it $\mathrm{AR}(p)$ models of orders from $p=0$ through $p=16$ (one-tenth of the time series length). Three of the five order selection criteria used in this book have chosen the order $p=3$ :
$$x_{t} \approx 0.46 x_{t-1}-0.29 x_{t-2}+0.15 x_{t-3}+a_{t}$$
The RMS error of all estimated AR coefficients equals to approximately $0.08$ so that the coefficients are statistically significant at the confidence level $0.9$ used in this book.

The estimates of the mean value and standard deviation are $\bar{x} \approx-0.15$ and $\hat{\sigma}_{x} \approx 0.61$. The respective confidence intervals for the mean value and variance estimates obtained for the TPI time series expressed with model (4.11) are [ $-0.25$,

$-0.04]$ and $[0.55,0.68]$. These confidence intervals are determined in accordance with Eqs. (4.1) -(4.4) using estimates of the numbers of independent observations $\bar{N}=93$ and $\hat{N}=130$ obtained for the AR(3) model (4.11). These values are calculated through the correlation function estimate under the assumption that the correlation function $r(k)$ at lags $k=1,2,3$ coincides with the sample estimates while its further values behave in the maximum entropy mode. This correlation function obtained according to Eq. (4.5) diminishes very fast so that the numbers of independent observations $\bar{N}$ and $\hat{N}$ do not differ drastically from the total number of observations $N$.

The innovation sequence variance $\sigma_{a}^{2} \approx 0.31$ and the predictability (persistence) criterion $r_{e}(1)=\sqrt{1-\sigma_{a}^{2} / \sigma_{x}^{2}}$ equals $0.17$ meaning that the unpredictable innovation sequence $a_{t}$ plays a dominant role in the time series of Tripole Index. This time series is quite close to a white noise sequence, and the variance of its prediction errors will be high.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Properties of Climate Indices

At climatic time scales, the basic statistical properties of a large number of geophysical time series-about 3000 -has been summarized in the fundamental work by Dobrovolski $(2000)$ dealing with stochastic models of scalar climatic data. The time series in that book include surface temperature, atmospheric pressure, precipitation, sea level, and some other geophysical variables observed at individual stations; the data set includes 195 time series of sea surface temperature averaged within $5^{\circ} \times 5^{\circ}$ squares. Most of those time series are best approximated with either a white noise or a Markov process (Dobrovolski 2000 , p. 135). The white noise model AR(0) can be justly regarded as a specific case of the $\mathrm{AR}(1)$ model. The prevalence of the $\mathrm{AR}(1)$ model for climatic time series obtained without large-scale spatial averaging has been noted recently in Privalsky and Yushkov (2018), but the results given in Dobrovolski $(2000)$ are based upon a much larger observation base.

In this section, we will complement the available information by studying first a number of geophysical time series that are often used as climate indicators or indices; their names usually contain the term “oscillation” or “index.” The list is given in Table 5.1, and the data sources are shown in the Appendix to this chapter. In all cases, the value of $\Delta t$ is one year. Along with the optimal AR orders $p$ for the time series, the table contains the values of statistical predictability criterion (3.7): $r_{e}(1)=\sqrt{1-\sigma_{a}^{2} / \sigma_{x}^{2}}$, where $\sigma_{x}^{2}$ and $\sigma_{a}^{2}$ are the time series variance and the variance of its innovation sequence.

The sources of data listed in the table are given in Appendix to this chapter: the numbers in the first column of the table coincide with the numbers in the Appendix.
Two characteristic features are common for the time series in Table 5.1: all of them can be regarded as Gaussian, and, with one exception, all of them have low statistical predictability. This means that they present sample records of random processes similar to a white noise; that is, their behavior in the time domain is very irregular, and, consequently, none of them contains oscillations as the term is understood in physics. The exception is the relatively high predictability of the Atlantic Multidecadal Oscillation. Thus, judging by the low optimal AR orders and the low predictability, one may say that though the optimal model for most of these time series is not AR(1) their behavior does not contradict the assumption of the Markov character of climate variability and that the value of the autoregressive coefficient is significantly smaller than one.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Frequency Resolution of Autoregressive Spectral Analysis

AR（或 MEM）谱估计为估计的谱提供了一个分析公式。这意味着公式中的光谱分辨率使得光谱密度的值可以在任何频率下计算。这是真的，但实际分辨率由 AR 阶定义：光谱曲线中极值和拐点的数量对应于和⁡(p)型号不能高于p（见第 4.3 节）。因此，高分辨率需要高AR阶数，而时间序列短却无法得到高阶模型。

## 统计代写|时间序列分析代写Time-Series Analysis代考|Example of AR Analysis in Time and Frequency Domains

X吨≈0.46X吨−1−0.29X吨−2+0.15X吨−3+一个吨

−0.04]和[0.55,0.68]. 这些置信区间是根据方程式确定的。(4.1) -(4.4) 使用独立观察次数的估计ñ¯=93和ñ^=130为 AR(3) 模型 (4.11) 获得。这些值是在相关函数的假设下通过相关函数估计计算得出的r(ķ)在滞后ķ=1,2,3与样本估计值一致，而其进一步的值表现为最大熵模式。该相关函数根据方程式获得。(4.5) 减少得非常快，因此独立观察的数量ñ¯和ñ^与观察总数没有太大差异ñ.

## 有限元方法代写

tatistics-lab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。