统计代写|时间序列分析作业代写time series analysis代考|Frequency Resolution of Autoregressive Spectral

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时间序列分析是分析在一个时间间隔内收集的一系列数据点的具体方式。在时间序列分析中,分析人员在设定的时间段内以一致的时间间隔记录数据点,而不仅仅是间歇性或随机地记录数据点。

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|时间序列分析作业代写time series analysis代考|Frequency Resolution of Autoregressive Spectral

统计代写|时间序列分析作业代写time series analysis代考|Frequency Resolution of Autoregressive Spectral

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.

The frequencies of the main tidal constituents were determined by conducting autoregressive spectral analysis of the entire time series of length $10^{5} \mathrm{~h}$, the AR order $p=10^{4}$, and the frequency resolution of the spectral estimate $10^{-6} \mathrm{cph}$. The results for the diurnal tides are shown in Fig. $4.8$ and in Table 4.2.

As seen from the table, the errors in estimates of the constituents’ periods do not exceed $0.022 \%$. The average error for the entire range of diurnal tides is $0.0077 \%$. This is not a misprint; it is a proof that the autoregressive spectral analysis does allow one to obtain very accurate estimates of periods of tidal constituents and, consequently, of any other periodic or quasi-periodic component. This statement is correct as long as there is a sufficient amount of reliable data. Good estimates can be obtained with shorter time series, for example, one year of hourly data, and the resolution will still be high but not as high as when the time series contains $10^{5}$ hourly observations.

统计代写|时间序列分析作业代写time series analysis代考|Example of AR Analysis in Time and Frequency

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 $\operatorname{AR}(p)$ 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 $\operatorname{AR}(3)$ 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.

The characteristic equation of the $\operatorname{AR}(3)$ model of TPI given with Eq. (4.11) is
$$
1-0.46 B+0.29 B^{2}-0.15 B^{3}=0
$$
and it has a pair of complex-conjugated roots $[(-0.05+1.81 i),(-0.05-1.81 i)]$ where $i=\sqrt{-1}$. The roots correspond to the natural frequency $f_{e} \approx 0.25 \mathrm{cpy}$. An estimate of the spectrum such as shown in Fig. 4.10a and/or b must be included into analysis of any time series. In this case, the spectrum diminishes with frequency almost monotonically and contains a shelf at frequencies close to $0.25$ cpy.

The above described steps are normally required for analysis of any stationary time series.

统计代写|时间序列分析作业代写time series analysis代考|Research activities

Abstract Research activities at all stages of analysis constitute preliminary steps for the most important task-time series forecasting. One of such stages includes efforts to understand statistical properties of the processes that are being studied including probability density functions, spectral densities, and the degree of statistical predictability. Climate is often regarded as a Markov process with a small parameter, which means a slowly and monotonically decreasing spectral density without any oscillations and/or quasi-periodic phenomena. Many climatic time series and indices including $\mathrm{AO}$ and $\mathrm{AAO}$, NAO, PDO, AMO, and PNA behave in agreement with that Markov model or even with white noise. The climate indices related to ENSO behave in a different manner: their spectra are nonmonotonic and contain a smooth maximum at about $0.2$ cpy. Yet, none of them contains regular oscillations and their predictability stays low. The annual surface temperature for 1920-2018 averaged over large parts of the globe generally does not follow the Markov model, and its predictability is relatively high. Some other oscillatory processes are studied as well, including a version of $\mathrm{AAO}$ and $\mathrm{MJO}$ – a bivariate random process whose scalar components are shown to possess some statistical predictability.

The final and most important stage of analysis of time series generated by stationary random processes is forecasting. It consists of two parts: determining the achievable quality of forecasting, that is, measuring statistical predictability, and performing the forecast, which means constructing a forecast formula and calculating the future trajectory of the time series with respective confidence intervals.

In order to understand the results of prediction one needs to know what features of the time series have led to its specific forecasts and forecast error variances. This information is implicitly contained in the most essential statistical moment of any stationary time series: its spectral density. If the prediction error variance at the unit lead time coincides with the time series variance, the spectral density will be independent of frequency – a white noise. This random process is unpredictable. If the spectrum is concentrated at low frequencies, the predictability improvement occurs due to the ability to forecast long-term variations of the time series at relatively short lead times. If the spectrum contains a peak whose area composes a significant

part of the total area under the spectral density curve, the better predictability occurs due to the presence of a quasi-periodic or cyclic, component.

Thus, time series analysis must provide a time domain model of the time series and an estimate of the spectral density corresponding to it. This chapter contains results of analysis of time series obtained from observations, mostly at climatic time scales. Specifically, the tasks here are to describe typical time domain models of different types of climatic time series and to characterize the behavior of their spectral densities.

Essentially, Sects. $5.1$ and $5.2$ can be regarded as an attempt to sum up information about the typical behavior of climate as a stationary random process starting from its first stochastic model suggested by Hasselmann (1976) in the form of a Markov process. The early estimates of climate spectra used in particular, to verify the model, include publications by Privalsky $(1976,1977)$ and by Frankingnoul and Hasselmann (1977). The other goal is to see if the concept of low statistical predictability of respective climate models agrees with observation data. The task of time series forecasting will be discussed and illustrated with examples in Chap. 6 .

统计代写|时间序列分析作业代写time series analysis代考|Frequency Resolution of Autoregressive Spectral

时间序列分析代写

统计代写|时间序列分析作业代写time series analysis代考|Frequency Resolution of Autoregressive Spectral

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:光谱曲线中极值点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。

根据定义,线性规则随机过程不包含任何严格的周期性分量。此功能可能会导致对为常规过程设计的参数时间序列分析检测彼此接近的频率处的尖峰的能力产生一些疑问,例如,当数据包含谐波振荡时。实际上,自回归光谱分析在这方面的能力非常高,仅在一个条件下:获得准确的结果需要有足够的数据进行分析。(当然,此要求适用于所有非参数光谱分析方法,例如 Blackman 和 Tukey’s、MTM、Welch’s 等)

地球系统内具有完全已知频率的谐波振荡的一个独特情况是潮汐。潮汐成分的频率可以从天文学中准确得知;幅度由观察确定。频域中的自回归分析为估计包含在潮汐现象时间序列中的谐波振荡频率提供了一种方便的工具。如果在海平面观测中正确确定了频率,人们可能希望在任何其他固定数据中也能正确确定频率。
下面的示例旨在通过分析码头 9414317 站的海平面时间序列来验证最大熵谱分析如何准确地确定潮汐成分的频率221/2,美国旧金山,使用105从 2000 年 1 月 28 日开始的每小时海平面观测。数据源是附录中的#3。部分记录(约 50 天)如图 4.7 所示。潮汐显然占主导地位。

通过对整个长度时间序列进行自回归谱分析来确定主要潮汐成分的频率105 H, AR 顺序p=104, 和频谱估计的频率分辨率10−6CpH. 日潮的结果如图 1 所示。4.8并在表 4.2 中。

从表中可以看出,成分股期间的估计误差不超过0.022%. 整个日潮范围的平均误差为0.0077%. 这不是印刷错误。它证明了自回归光谱分析确实允许人们获得对潮汐成分周期的非常准确的估计,因此也可以对任何其他周期性或准周期性成分进行非常准确的估计。只要有足够的可靠数据,这种说法就是正确的。用较短的时间序列可以获得很好的估计,例如一年的每小时数据,分辨率仍然很高,但没有时间序列包含的时候那么高105每小时观察。

统计代写|时间序列分析作业代写time series analysis代考|Example of AR Analysis in Time and Frequency

以年代际太平洋涛动的三极子指数 (TPI) 的年度值为例,考虑时间序列分析的整个过程(Henley 等人,2015 年)。时间序列如图所示。4.9从 1854 年延伸到2018(ñ=165); 它与其他厄尔尼诺-南方涛动指数密切相关,但在某些方面有所不同。数据源取自本章附录中的网站#5。时间序列不包含任何统计上显着的趋势,并且它的行为允许人们在没有任何进一步分析的情况下假设它可以被视为平稳随机过程的样本。高斯性检验表明,该时间序列的概率密度函数可视为正态。

时间序列已通过拟合在时域中进行了分析和⁡(p)订单型号来自p=0通过p=16(时间序列长度的十分之一)。本书中使用的五个订单选择标准中的三个选择了订单p=3 :
X吨≈0.46X吨−1−0.29X吨−2+0.15X吨−3+一种吨
所有估计的 AR 系数的 RMS 误差大约等于0.08使得系数在置信水平上具有统计显着性0.9本书中使用。

平均值和标准差的估计是X¯≈−0.15和σ^X≈0.61. 用模型(4.11)表示的 TPI 时间序列的平均值和方差估计值的相应置信区间为[−0.25,

−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获得的和⁡(3)模型(4.11)。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.

创新序列方差σ一种2≈0.31和可预测性(持久性)标准r和(1)=1−σ一种2/σX2等于0.17意味着不可预测的创新序列一种吨在三极子指数的时间序列中起主导作用。这个时间序列非常接近白噪声序列,其预测误差的方差会很大。

的特征方程和⁡(3)用方程式给出的 TPI 模型。(4.11) 是
1−0.46乙+0.29乙2−0.15乙3=0
它有一对复共轭根[(−0.05+1.81一世),(−0.05−1.81一世)]在哪里一世=−1. 根对应于固有频率F和≈0.25Cp是. 如图 4.10a 和/或 b 所示的频谱估计必须包含在任何时间序列的分析中。在这种情况下,频谱几乎单调地随频率递减,并且在频率接近于0.25cp。

分析任何平稳时间序列通常都需要上述步骤。

统计代写|时间序列分析作业代写time series analysis代考|Research activities

摘要 分析各个阶段的研究活动构成了最重要的任务时间序列预测的初步步骤。其中一个阶段包括努力了解正在研究的过程的统计特性,包括概率密度函数、谱密度和统计可预测性程度。气候通常被视为具有小参数的马尔可夫过程,这意味着光谱密度缓慢且单调递减,没有任何振荡和/或准周期性现象。许多气候时间序列和指数,包括一种这和一种一种这、NAO、PDO、AMO 和 PNA 的行为与该马尔可夫模型甚至与白噪声一致。与 ENSO 相关的气候指数以不同的方式表现:它们的光谱是非单调的,并且在大约0.2cp。然而,它们都不包含有规律的振荡,而且它们的可预测性仍然很低。1920-2018年全球大部分地区的年平均地表温度一般不遵循马尔可夫模型,其可预测性较高。还研究了其他一些振荡过程,包括一种一种这和米Ĵ这– 一个双变量随机过程,其标量分量被证明具有某种统计可预测性。

平稳随机过程生成的时间序列分析的最后也是最重要的阶段是预测。它由两部分组成:确定可实现的预测质量,即衡量统计可预测性,以及执行预测,即构建预测公式并计算具有相应置信区间的时间序列的未来轨迹。

为了理解预测的结果,需要知道时间序列的哪些特征导致了其特定的预测和预测误差方差。这些信息隐含在任何平稳时间序列中最重要的统计时刻:它的谱密度。如果单位提前期的预测误差方差与时间序列方差一致,则谱密度将与频率无关——白噪声。这个随机过程是不可预测的。如果频谱集中在低频,则由于能够在相对较短的前置时间内预测时间序列的长期变化,因此可预测性提高。如果光谱包含一个峰,其面积构成显着

谱密度曲线下总面积的一部分,由于准周期性或循环分量的存在,出现更好的可预测性。

因此,时间序列分析必须提供时间序列的时域模型和与之对应的谱密度估计。本章包含从观测获得的时间序列分析结果,主要是在气候时间尺度上。具体来说,这里的任务是描述不同类型气候时间序列的典型时域模型,并描述其光谱密度的行为。

本质上,教派。5.1和5.2可以看作是从哈塞尔曼(1976)提出的马尔可夫过程形式的第一个随机模型开始,将有关气候典型行为的信息总结为平稳随机过程的尝试。特别是用于验证模型的气候光谱的早期估计包括 Privalsky 的出版物(1976,1977)以及 Frankingnoul 和 Hasselmann (1977)。另一个目标是看看各自气候模型的低统计可预测性的概念是否与观测数据一致。时间序列预测的任务将在第 1 章中通过示例进行讨论和说明。6.

统计代写|时间序列分析作业代写time series analysis代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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。

随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

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。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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