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|Time Series and Their Features

1.1 As stated in the Introduction, time series are indeed ubiquitous, appearing in almost every research field where data are analyzed. However, their formal study requires special statistical concepts and techniques without which erroneous inferences and conclusions may all too readily be drawn, a problem that statisticians have found necessary to confront since at least Udny Yule’s Presidential Address to the Royal Statistical Society in 1925, provocatively titled “Why do we sometimes get nonsense-correlations between time series? A study in sampling and the nature of time series.”
1.2 In general, a time series on some variable $x$ will be denoted as $x_t$, where the subscript $t$ represents time, with $t=1$ being the first observation available on $x$ and $t=T$ being the last. The complete set of times $t=1,2, \ldots, T$ will often be referred to as the observation period. The observations are typically measured at equally spaced intervals, say every minute, hour, or day, etc., so the order in which observations arrive is paramount. This is unlike, say, data on a cross section of a population taken at a given point in time, where the ordering of the data is usually irrelevant unless some form of spatial dependence exists between observations. ${ }^2$
1.3 Time series display a wide variety of features and an appreciation of these is essential for understanding both their properties and their evolution, including calculating future forecasts and, therefore, unknown values of $x_t$ at, say, times $T+1, T+2, \ldots, T+h$, where $h$ is referred to as the forecast horizon.

Fig. $1.1$ shows monthly observations of an index of the North Atlantic Oscillation (NAO) between 1950 and 2017. The NAO is a weather phenomenon in the North Atlantic Ocean and measures fluctuations in the difference of atmospheric pressure at sea level between two stable air pressure areas, the Subpolar low and the Subtropical (Azores) high. Strong positive phases of the $\mathrm{N} \Lambda \mathrm{O}$ tend to be associated with above normal temperatures in eastern United States and across northern Europe and with below-normal temperatures in Greenland and across southern Europe and the Middle East. These positive phases are also associated with above-normal precipitation over northern Europe and Scandinavia and with below-normal precipitation over southern and central Europe. Opposite patterns of temperature and precipitation anomalies are typically observed during strong negative phases of the NAO (see Hurrell et al., 2003).

Clearly, being able to identify recurring patterns in the NAO would be very useful for medium- to long-range weather forecasting, but, as Fig. $1.1$ illustrates, no readily discernible patterns seem to exist.

统计代写|时间序列分析代写Time-Series Analysis代考|AUTOCORRELATION AND PERIODIC MOVEMENTS

1.4 Such a conclusion may, however, be premature for there might well be internal correlations within the index that could be useful for identifying interesting periodic movements and for forecasting future values of the index. These are typically referred to as the autocorrelations between a current value, $x_t$, and previous, or lagged, values, $x_{t-k}$, for $k=1,2, \ldots$. The lag-k (sample) autocorrelation is defined as
$$r_k=\frac{\sum_{t=k+1}^T\left(x_t-\bar{x}\right)\left(x_{t k}-\bar{x}\right)}{T s^2}$$

where
$$\bar{x}=T^{-1} \sum_{t=1}^T x_t$$
and
$$s^2=T^{-1} \sum_{t=1}^T\left(x_t-\bar{x}\right)^2$$
are the sample mean and variance of $x_t$, respectively. The set of sample autocorrelations for various values of $k$ is known as the sample autocorrelation function (SACF) and plays a key role in time series analysis. An examination of the SACF of the NAO index is provided in Example 3.1.
1.5 A second physical time series that has a much more pronounced periodic movement is the annual sunspot number from 1700 to 2017 as shown in Fig. 1.2. As has been well-documented, sunspots display a periodic cycle (the elapsed time from one minimum (maximum) to the next) of approximately 11 years; see, for example, Hathaway (2010). The SACF can be used to calculate an estimate of the length of this cycle, as is done in Example 3.3.

统计代写|时间序列分析代写Time-Series Analysis代考|Time Series and Their Features

1.1 如引言中所述，时间序列确实无处不在，几乎出现在每个分析数据的研究领域。然而，他们的正式研究需要特殊的统计概念和技术，否则很容易得出错误的推论和结论，至少从 Udny Yule 于 1925 年向皇家统计学会发表总统讲话（标题为“为什么我们有时会在时间序列之间得到无意义的相关性？一项关于抽样和时间序列性质的研究。”
1.2 一般来说，关于某个变量的时间序列X将表示为X吨, 其中下标吨代表时间，用吨=1是第一个可用的观察X和吨=吨成为最后一个。全套时间吨=1,2,…,吨通常称为观察期。观测值通常以等间隔测量，例如每分钟、每小时或每天等，因此观测值到达的顺序至关重要。这与在给定时间点获取的人口横截面数据不同，其中数据的排序通常是无关紧要的，除非观察之间存在某种形式的空间依赖性。2
1.3 时间序列显示出各种各样的特征，理解这些特征对于理解它们的性质和演变至关重要，包括计算未来的预测，因此，未知的价值X吨在，比如说，时间吨+1,吨+2,…,吨+H， 在哪里H被称为预测范围。

统计代写|时间序列分析代写Time-Series Analysis代考|AUTOCORRELATION AND PERIODIC MOVEMENTS

$1.4$ 然而，这样的结论可能为时过早，因为指数内部很可能存在内部相关性，这可能有助于识别有趣的周期性变动 和预测指数的末来价值。这些通常被称为当前值之间的自相关， $x_t$ ，以及以前的或滞后的值, $x_{t-k} ，$ 为了 $k=1,2, \ldots$ lag-k (样本) 自相关定义为
$$r_k=\frac{\sum_{t=k+1}^T\left(x_t-\bar{x}\right)\left(x_{t k}-\bar{x}\right)}{T s^2}$$

$$\bar{x}=T^{-1} \sum_{t=1}^T x_t$$

$$s^2=T^{-1} \sum_{t=1}^T\left(x_t-\bar{x}\right)^2$$

$1.5$ 第二个具有更明显周期性运动的物理时间序列是从 1700 年到 2017 年的年度太阳黑子数，如图 $1.2$ 所示。正 如已充分证明的那样，太阳黑子显示出大约 11 年的周期性周期 (从一个最小值（最大值) 到下一个所经过的时 间) ；例如，参见 Hathaway (2010)。SACF 可用于计算此循环长度的估计值，如示例 $3.3$ 中所做的那样。

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。