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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
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- 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|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 $A R(1)$ model. The prevalence of the 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 $\mathrm{AR}(1)$ 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.
Most of the 13 climate indices in Table $5.1$ do not show any response to the global warming in the form of a trend; the reason for this feature is not clear. In seven cases, the names include the term “oscillation,” that is, regularly repeating deviations from some equilibrity level. Visually, none of those time series contains oscillations. The presence of oscillations can also be seen from the spectral density and/or from the roots of the characteristic equation corresponding to a given AR model: at least, some of the roots must be complex-valued and the damping coefficient should not be too large. For example, the Antarctic Oscillation (or the Antarctic Oscillation Index) is defined as the difference of mean zonal atmospheric pressure at sea level between $40^{\circ} \mathrm{S}$ and $65^{\circ} \mathrm{S}$ and can be regarded as similar to NAO (Gong and Wang 1999). The optimal model for both NAO and AAO time series is a white noise, that is, a sequence of identically distributed and mutually independent random variables; it cannot contain oscillations and hardly carries any useful probabilistic information. The AR orders 0 and 1 exclude the presence of oscillations in respective time series because their spectral densities are frequency independent when $p=0$ or decrease monotonically with growing frequency when $p=1$. Oscillations may exist in time series whose AR orders exceed 1. In this case, there are six such indices: AMO, SOI, NINO3.4, GPCC, MEI, and TPI. (This TPI time series differs from the time series analyzed in Chap. 4.)
统计代写|时间序列分析作业代写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 $\mathrm{AMO}$ 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. $14 .$
The predictability criterion used by Hasselmann (1976) in his Eq. (6.3) can be given as
$$
s^{2}=\delta^{2} /\left(\varepsilon^{2}+\delta^{2}\right)
$$
where $\delta^{2}$ and $\varepsilon^{2}$ are the variances of the predictable and unpredictable parts of the time series (signal and noise, according to $\mathrm{K}$. Hasselmann). In our notations, $\varepsilon^{2}$ coincides with $\sigma_{a}^{2}$ and $\delta^{2}=\sigma_{x}^{2}-\sigma_{a}^{2}$. Therefore, $s^{2}=r_{e}^{2}(1)$. In Hasselmann’s opinion, the statistical predictability criterion for stationary climate systems generally does not exceed $0.5$ and actually is always much less than unity. The results in Table $5.1$ agree with that statement but spatial averaging seems to lead to more complicated models and to better statistical predictability (Table 5.2). All these time series successfully pass the test for Gaussianity.
统计代写|时间序列分析作业代写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. $5.4 \mathrm{a}$ ). 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.
The AR spectral estimates of $\mathrm{QBO}$ at all other levels are given in Fig. 5.5. In all seven cases (including the $10 \mathrm{~Pa}$ level in Fig. 5.4), the frequency of the major spectral peak is found at $f=0.432$ cpy. A tenfold increase in the frequency resolution from $0.012$ cpy to $0.0012$ cpy showed that the period of oscillation determined through the frequency of the maximum spectral density in all seven estimates varies by less than $2 \%$ and stays between $27.7$ and $28.1$ months. The average over the seven spectral estimates frequency of the spectral peak corresponds to the average period equal to $27.99$ month. This very clear-cut stability can be regarded as another distinctive property of the QBO phenomenon.
According to the model suggested by Holton and Lindzen (1972), the QuasiBiennial Oscillation is forced by vertically propagating planetary waves with periods of $5-15$ days. This explanation means that at altitudes where $\mathrm{QBO}$ occurs the equatorial stratosphere works as a filter that transforms the upward propagation of this high-frequency noise into a downward moving oscillation whose frequency is up to two orders of magnitude lower that the frequency of the forcing.
As seen from these descriptions and from the figures, the QBO system has a complicated structure and it should be studied as a multivariate random process. This will be done in Chap. 10 .
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|Properties of Climate Indices
在气候时间尺度上，Dobrovolski 在基础工作中总结了大量地球物理时间序列（约 3000 个）的基本统计特性(2000)处理标量气候数据的随机模型。那本书中的时间序列包括地表温度、大气压力、降水、海平面和在各个站观测到的其他一些地球物理变量；该数据集包括 195 个时间序列的平均海表温度5∘×5∘正方形。大多数时间序列最好用白噪声或马尔可夫过程近似（Dobrovolski 2000，第 135 页）。白噪声模型 AR(0) 可以公正地看作是一种R(1)模型。最近在 Privalsky 和 Yushkov (2018) 中注意到了在没有大尺度空间平均的情况下获得的气候时间序列的 AR(1) 模型的流行，但在 Dobrovolski 中给出的结果(2000)是基于更大的观察基础。
在本节中，我们将通过首先研究一些经常用作气候指标或指数的地球物理时间序列来补充现有信息；它们的名称通常包含术语“振荡”或“指数”。列表见表 5.1，数据来源见本章附录。在所有情况下，价值Δ吨是一年。连同最佳的 AR 订单p对于时间序列，该表包含统计可预测性标准 (3.7) 的值：r和(1)=1−σ一种2/σX2， 在哪里σX2和σ一种2是时间序列方差及其创新序列的方差。
表中数据来源见本章附录：表中第一栏数字与附录中数字一致。
表 5.1 中的时间序列有两个共同的特征：它们都可以看作是高斯的，除了一个例外，它们都具有低
统计可预测性。这意味着它们呈现类似于白噪声的随机过程的样本记录；也就是说，它们在时域中的行为是非常不规则的，因此，它们都不包含物理学中所理解的振荡。例外是大西洋多年代际振荡的相对较高的可预测性。因此，从低最优 AR 阶数和低可预测性来看，有人可能会说，尽管大多数时间序列的最优模型不是一种R(1)他们的行为与气候变率的马尔可夫特征以及自回归系数的值显着小于 1 的假设并不矛盾。
表中 13 个气候指数中的大部分5.1不以趋势的形式表现出对全球变暖的任何反应；此功能的原因尚不清楚。在七种情况下，名称中包含“振荡”一词，即定期重复偏离某个平衡水平。从视觉上看，这些时间序列中没有一个包含振荡。振荡的存在也可以从谱密度和/或给定 AR 模型对应的特征方程的根中看出：至少，一些根必须是复值并且阻尼系数不应该太大. 例如，南极涛动（或南极涛动指数）被定义为海平面平均纬向大气压力之间的差异40∘小号和65∘小号并且可以被视为类似于NAO（Gong和Wang 1999）。NAO 和 AAO 时间序列的最优模型是白噪声，即一系列同分布且相互独立的随机变量；它不能包含振荡，并且几乎不携带任何有用的概率信息。AR 阶数 0 和 1 排除了相应时间序列中存在的振荡，因为它们的频谱密度在以下情况下与频率无关p=0或随着频率的增加单调减少，当p=1. AR阶数超过1的时间序列中可能存在振荡。在这种情况下，有六个这样的指数：AMO、SOI、NINO3.4、GPCC、MEI和TPI。（这个 TPI 时间序列不同于第 4 章中分析的时间序列。）
统计代写|时间序列分析作业代写time series analysis代考|Properties of Time Series of Spatially Averaged Surface Temperature
除ENSO相关现象外，地球物理时间序列分析结果见表5.1不与马尔可夫气候行为的假设相矛盾（Hasselmann 1976）。在表中的 13 个时间序列中5.1, 7 的阶数不高于 1 ，可以认为是对假设的确认。其他 6 个样本的可预测性较低，与其余 7 个时间序列的可预测性差别不大。AMO 的可预测性优于所有其他情况，对于实际应用来说可能已经足够高了。AMO 时间序列与表中其他时间序列的不同之处在于它是通过对北大西洋大片区域的 SST 进行平均获得的；因此，可以假设相对较高的光谱密度下降率和较高的可预测性标准r和(1)≈0.62为了一种米这可能是该平均的结果。
通过对全球大部分地区进行平均获得的数据可以更好地表征全球气候。AMO 时间序列只是这种平均的一个具体示例，但我们有九个时间序列来显示整个地球、其半球以及海洋和陆地部分的表面温度。这些时间序列已在 Privalsky 和 Yushkov (2018) 中进行了分析，发现与该工作中研究的其他时间序列相比，它们具有更复杂的结构和更高的可预测性。
上述出版物中使用的数据包括东英吉利大学给出的完整时间序列；大部分时间序列始于 1850 年。数据文件的作者表明，十九世纪的覆盖程度很差。遵循 Dobrovolski 中给出的示例(2000)，我们将从 1920 年开始研究相同的时间序列，那时观测的覆盖率通常会增加到50%全球、半球和海洋数据更高。
表中给出的结果5.2确认先前的结论之一：全球大部分地区的年平均表面温度最好用具有 AR 阶的相对复杂的模型来描述p=3或者p=4和相对较高的统计可预测性。整个南半球及其陆地的结果遵循马尔可夫模型，统计可预测性较低；他们同意我们从戈达德空间研究所 (GISS) 提供的数据中获得的结果。根据南半球的 GISS 数据（附录中的#14），自回归顺序p=1和标准r和(1)≈0.55.
数据集显示，全球尺度和北半球（包括其海洋和陆地）的空间平均产生时间序列，其属性
与表中显示的有很大差异5.1个别气候指数。最优 AR 阶数增加到四个，可预测性标准增加到0.82对于北半球海洋。从 1920 年开始的时间序列南半球温度变化的原因尚不清楚，但可能与由全球、陆地和陆地时间序列组成的三元系统的统计特性的变化有关时间序列。例如，可预测性标准r和(1)对于整个时间序列是0.74（Privalsky 和 Yushkov 2018）和0.44对于从 1920 年开始的时间序列。在第 1 章中给出了更详细的变化描述。14.
Hasselmann (1976) 在他的方程式中使用的可预测性标准。(6.3) 可以表示为
s2=d2/(e2+d2)
在哪里d2和e2是时间序列的可预测和不可预测部分的方差（信号和噪声，根据ķ. 哈塞尔曼）。在我们的符号中，e2恰逢σ一种2和d2=σX2−σ一种2. 所以，s2=r和2(1). 在 Hasselmann 看来，静止气候系统的统计可预测性标准通常不超过0.5实际上总是比统一少得多。表中的结果5.1同意这一说法，但空间平均似乎会导致更复杂的模型和更好的统计可预测性（表 5.2）。所有这些时间序列都成功地通过了高斯性检验。
统计代写|时间序列分析作业代写time series analysis代考|Quasi-Biennial Oscillation
气候光谱中的“没有显着尖峰的规则”至少有一个例外，它得到了数十年直接观测的支持。至少有一个大气过程——准双年振荡，或 QBO——不遵循这一规则。QBO 现象存在于海拔约 16 度的赤道平流层。ķ米到50 ķ米, 其特点是西风和东风的准周期性变化。振荡周期约为 28 个月，对应的频率约为0.43cp。它在 1950 年代被发现并在许多出版物中进行了研究，特别是在 Holton 和 Lindzen (1972) 中提出了 QBO 的物理模型。在 Baldwin 等人 (2001) 对 QBO 研究的评论中，QBO 被称为“一个由传播波驱动的连贯、振荡平均流的迷人例子，其周期与产生的振荡无关。” Anstey 和 Shepherd (2014) 讨论了 QBO 对气候的一些影响。
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）)应该在与问乙这作为标量和双变量（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磷一种; 这些级别对应于从31 ķ米到18 ķ米.
如果研究的目标是分析问乙这作为标量随机过程，数据可以在采样间隔内获取Δ吨=6几个月甚至一年。由于 QBO 在每月采样率下的统计可预测性也将在第 1 章中进行研究。6、采样间隔Δ吨=1本节也采用月份。示例问乙这变化如图 5.3 所示。
基本统计特征问乙这如表 5.3 所示。平均风速为东风（负），低于20H磷一种水平在最低水平向东转。方差从10H磷一种大约水平10%到15H磷一种和20H磷一种然后逐渐向下减少一个数量级。这些事实是众所周知的（例如，Baldwin et al. 2001）。最优 AR 模型的订单来自p=11到p=29; 这样的阶数对于单独的时域分析来说太高了。
频谱的典型形状显示了一个几乎周期性的时间随机函数F≈0.43cpy (图.5.4一种）。最大值非常窄并且完全支配了光谱，因此只有当比例尺沿两个轴都是对数时才能看到更详细的图片（图 5.4b）。这似乎是一个绝对
气候时间尺度上的独特现象。在较高的频率下，频谱密度下降得相当快，而所有其他峰值在统计上都是不显着的。考虑到这一点，频谱将以不超过 1 cpy 的频率显示如下。
的 AR 谱估计问乙这图 5.5 给出了所有其他级别的情况。在所有七种情况下（包括10 磷一种图 5.4 中的水平），主要频谱峰值的频率位于F=0.432cp。频率分辨率提高十倍0.012复制到0.0012cpy 表明，在所有七个估计中，通过最大频谱密度的频率确定的振荡周期变化小于2%并停留在27.7和28.1个月。频谱峰值的七个频谱估计频率的平均值对应于平均周期等于27.99月。这种非常明确的稳定性可以被视为 QBO 现象的另一个独特属性。
根据 Holton 和 Lindzen (1972) 提出的模型，准双年振荡是由垂直传播的行星波推动的，周期为5−15天。这种解释意味着在海拔高度问乙这赤道平流层作为过滤器起作用，将这种高频噪声的向上传播转换为向下移动的振荡，其频率比强迫的频率低两个数量级。
从这些描述和图中可以看出，QBO 系统具有复杂的结构，应该将其作为多元随机过程来研究。这将在第 1 章中完成。10.
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，工具箱允许您学习和应用专业技术。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。