### 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

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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。

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## 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。