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# 统计代写|贝叶斯分析代考BAYESIAN ANALYSIS 代考|ERTH695 Basic Random Models

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## 统计代写|贝叶斯分析代考BAYESIAN ANALYSIS 代考|Introduction

Up to this point, two approaches for modeling time series have been discussed. As previously explained, the first is founded on the belief that there is a fixed seasonal pattern about a trend, such as the Air Passenger data and these two features can be delineated with the $\mathrm{R}$ decompose command. The second approach takes account of the seasonal pattern and trend to change over time. With mathematical time series, the difference between the fitted value and the observed value allows one to calculate the random error series. If the model includes various aspects of the deterministic characteristic of the series, then the residuals should exhibit as a realization of independent random variables, but this may not be the case. That is to say, the residuals may show some structure such as a trend or positive autocorrelation.

## 统计代写|贝叶斯分析代考BAYESIAN ANALYSIS 代考|White Noise

Because a good fit implies that the residuals are independent random variables, the model to be presented next will be with a foundation of white noise.
White noise is a time series
$${W(t), t=1,2, \ldots, n}$$
of variables $W(1), W(2), \ldots, W(n)$, which are independent and identically distributed with mean 0 , constant variance $\sigma^{2}$, and of course $\operatorname{cor}[W(i), W(j)]=0, i \neq j$. In addition, if $W(i) \sim N\left(0, \sigma^{2}\right)$, the noise is referred to Gaussian or normal white noise.
$\mathrm{R}$ is useful to simulate time series and this will be done for the basic stochastic models, such a white noise, random walks, and random walks with drift. Consider the scenario where a fitted time series can be used to simulate data. As has been seen throughout this book, simulation is used for a variety of reasons. In $\mathrm{R}$, simulation is a simple operation where most of the well-known distributions are simulated with a $\mathrm{R}$ function. For example, for a simulation of normal random variables, rnorm(100) generates 100 standard normal variables. Now consider, the code
RC 4.1.
set.seed(1)
$w<-\operatorname{rnorm}(100)$
time<-seq $(1,100,1)$
plot(time,w)
that generates 100 white noise values and the plot abscissa has a unit of one. One should check to see how well the random number generator simulates white noise. For example, the sample mean $(\mathrm{w})=.10887$, sample standard deviation sd $(\mathrm{w})=.8067$, and the lag one correlation is acf(w)\$acf[2]$=-.00365$, and finally, the lag two is given by acf$(w) \$a c f[3]=-.02707$. Of course, one should also use the command $\operatorname{acf}(w)$ to plot the autocorrelation function of the $\mathrm{w}$ series. The command hist( $\mathrm{w})$ generates the default histogram of the $\mathrm{w}$ purported white noise series and is valuable in detecting departures from a normal distribution. Such evaluations are necessarily subjective, in that another individual might detect different deviations from normality.

## 统计代写|贝叶斯分析代考BAYESIAN ANALYSIS 代考|White Noise

$$W(t), t=1,2, \ldots, n$$

R对于模拟时间序列很有用，这将用于基本随机模型，例如白噪声、随机游走和带有漂移 的随机游走。考虑可以使用拟合时间序列来模拟数据的场景。正如本书通篇所见，使用模 拟的原因有很多。在 $\mathrm{R}$, 模拟是一个简单的操作，其中大多数众所周知的分布都是用R功 能。例如，对于正态随机变量的模拟， $\operatorname{norm}(100)$ 生成 100 个标准正态变量。现在考虑 代码
RC 4.1.
set.seed (1)
$w<-\operatorname{rnorm}(100)$

plot(time,w)

## 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。