时间序列分析及其在R语言中的应用第四版

Time

Series

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"Time Series Analysis and its Applications with R Examples 4th ed" 本书是时间序列分析领域经典教材的第四版，涵盖了时间域和频率域方法的均衡和综合处理，伴随着理论。书中使用非平凡数据进行了许多示例，解决了发现自然和人为气候变化、评估功能磁共振成像实验中的疼痛感知、监测核试验禁止条约等问题。本书旨在作为研究生水平的教科书，适用于物理、生物和社会科学领域的研究生，也可以作为统计学研究生的教科书。部分内容也可以作为本科生的入门课程。理论和方法论被分开，以便在不同水平上进行讲解。此外，本书还涵盖了经典方法，如时间序列回归、ARIMA 模型、频谱分析和状态空间模型，以及现代发展，如分类时间序列分析、多变量频谱方法、长记忆系列、非线性模型、重采样技术、GARCH 模型、ARMAX 模型、随机 volatility 模型、Wavelet 分析和 Markov 链 Monte Carlo 积分方法。本版还包括每个数值示例的 R 代码，以及附录 R，提供了数据集和 R 脚本的参考，以及基本 R 命令和 R 时间序列教程。另外，在书籍网站上还提供了一个额外的文件，用于下载所有数据集和脚本，以便轻松加载到 R。时间序列分析是统计学和数据科学中的一门重要学科，旨在研究和分析时间序列数据。时间序列数据是指随着时间变化的数据，例如股票价格、气候数据、生理信号等。本书涵盖了时间序列分析的基本概念和方法，包括时间序列的定义、时间序列的特征、时间序列的模型、时间序列的预测等。时间序列分析有很多实际应用，例如金融预测、气候预测、医疗健康预测等。本书还涵盖了时间序列分析在这些领域的应用，例如使用时间序列分析来预测股票价格、气候变化、疾病预测等。本书是时间序列分析领域的经典教材，涵盖了时间序列分析的基本概念和方法，以及在不同领域的应用。通过阅读本书，读者可以掌握时间序列分析的基本知识和技能，并应用于实际问题中。时间序列分析的重要性在于其广泛的应用前景，例如： * 金融预测：使用时间序列分析来预测股票价格、货币汇率等金融指标。 * 气候预测：使用时间序列分析来预测气候变化、天气预报等。 * 医疗健康预测：使用时间序列分析来预测疾病发生、医疗健康趋势等。 * 生产预测：使用时间序列分析来预测生产过程、生产计划等。此外，时间序列分析还可以应用于其他领域，例如交通预测、能源预测、环境监测等。本书是时间序列分析领域的经典教材，涵盖了时间序列分析的基本概念和方法，以及在不同领域的应用。通过阅读本书，读者可以掌握时间序列分析的基本知识和技能，并应用于实际问题中。

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1.1 The Nature of Time Series Data 7

Cortex

020406080100120

−0.6 −0.2 0.2 0.6

Cortex

BOLD

Thalamus & Cerebellum

020406080100120

−0.6 −0.2 0.2 0.6

BOLD

Time (1 pt = 2 sec)

Fig. 1.6. fMRI data from various locations in the cortex, thalamus, and cerebellum; n = 128

points, one observation taken every 2 s

recording station. The recording instruments in Scandinavia are observing earth-

quakes and mining explosions with one of each shown in Fig. 1.7. The general

problem of interest is in distinguishing or discriminating between waveforms gen-

erated by earthquakes and those generated by explosions. Features that may be

important are the rough amplitude ratios of the ﬁrst phase P to the second phase S,

which tend to be smaller for earthquakes than for explosions. In the case of the

two events in Fig. 1.7, the ratio of maximum amplitudes appears to be somewhat

less than .5 for the earthquake and about 1 for the explosion. Otherwise, note a

subtle diﬀerence exists in the periodic nature of the S phase for the earthquake.

We can again think about spectral analysis of variance for testing the equality of

the periodic components of earthquakes and explosions. We would also like to be

able to classify future P and S components from events of unknown origin, leading

to the time series discriminant analysis developed in Chap. 7.

To plot the data as in this example, use the following commands in R:

par(mfrow=c(2,1))

plot(EQ5, main="Earthquake")

plot(EXP6, main="Explosion")

1.2 Time Series Statistical Models 9

It is conventional to display a sample time series graphically by plotting the values

of the random variables on the vertical axis, or ordinate, with the time scale as the

abscissa. It is usually convenient to connect the values at adjacent time periods to

reconstruct visually some original hypothetical continuous time series that might

have produced these values as a discrete sample. Many of the series discussed in

the previous section, for example, could have been observed at any continuous point

in time and are conceptually more properly treated as continuous time series.The

approximation of these series by discrete time parameter series sampled at equally

spaced points in time is simply an acknowledgment that sampled data will, for the

most part, be discrete because of restrictions inherent in the method of collection.

Furthermore, the analysis techniques are then feasible using computers, which are

limited to digital computations. Theoretical developments also rest on the idea that a

continuous parameter time series should be speciﬁed in terms of ﬁnite-dimensional

distribution functions deﬁned over a ﬁnite number of points in time. This is not to

say that the selection of the sampling interval or rate is not an extremely important

consideration. The appearance of data can be changed completely by adopting an

insuﬃcient sampling rate. We have all seen wheels in movies appear to be turning

backwards because of the insuﬃcient number of frames sampled by the camera. This

phenomenon leads to a distortion called aliasing (see Sect. 4.1).

The fundamental visual characteristic distinguishing the diﬀerent series shown

in Example 1.1–Example 1.7 is their diﬀering degrees of smoothness. One possible

explanation for this smoothness is that it is being induced by the supposition that

adjacent points in time are correlated, so the value of the series at time t,say,

, depends in some way on the past values x

t−1

, x

t−2

,.... This model expresses a

fundamental way in which we might think about generating realistic-looking time

series. To begin to develop an approach to using collections of random variables to

model time series, consider Example 1.8.

Example 1.8 White Noise (3 Flavors)

A simple kind of generated series might be a collection of uncorrelated random

variables, w

, with mean 0 and ﬁnite variance σ

. The time series generated from

uncorrelated variables is used as a model for noise in engineering applications,

where it is called white noise; we shall denote this process as w

∼ wn(0,σ

).The

designation white originates from the analogy with white light and indicates that

all possible periodic oscillations are present with equal strength.

We will sometimes require the noise to be independent and identically dis-

tributed (iid) random variables with mean 0 and variance σ

. We distinguish this

by writing w

∼ iid(0,σ

) or by saying white independent noise or iid noise.

A particularly useful white noise series is Gaussian white noise, wherein the w

are independent normal random variables, with mean 0 and variance σ

;ormore

succinctly, w

∼ iid N(0,σ

). Figure 1.8 shows in the upper panel a collection of

500 such random variables, with σ

= 1, plotted in the order in which they were

drawn. The resulting series bears a slight resemblance to the explosion in Fig. 1.7

but is not smooth enough to serve as a plausible model for any of the other experi-

1.2 Time Series Statistical Models 11

A linear combination of values in a time series such as in (1.1) is referred to,

generically, as a ﬁltered series; hence the command

filter in the following code

for Fig. 1.8.

w = rnorm(500,0,1)

# 500 N(0,1) variates

v = filter(w, sides=2, filter=rep(1/3,3))

# moving average

par(mfrow=c(2,1))

plot.ts(w, main="white noise")

plot.ts(v, ylim=c(-3,3), main="moving average")

The speech series in Fig. 1.3 and the Recruitment series in Fig. 1.5,aswellas

some of the MRI series in Fig. 1.6, diﬀer from the moving average series because one

particular kind of oscillatory behavior seems to predominate, producing a sinusoidal

type of behavior. A number of methods exist for generating series with this quasi-

periodic behavior; we illustrate a popular one based on the autoregressive model

considered in Chap. 3.

Example 1.10 Autoregressions

Suppose we consider the white noise series w

of Example 1.8 as input and calculate

the output using the second-order equation

= x

t−1

− .9x

t−2

+ w

(1.2)

successively for t = 1, 2,...,500. Equation (1.2) represents a regression or predic-

tion of the current value x

of a time series as a function of the past two values of the

series, and, hence, the term autoregression is suggested for this model. A problem

with startup values exists here because (1.2) also depends on the initial conditions

and x

−1

, but assuming we have the values, we generate the succeeding values by

substituting into (1.2). The resulting output series is shown in Fig. 1.9, and we note

the periodic behavior of the series, which is similar to that displayed by the speech

series in Fig. 1.3. The autoregressive model above and its generalizations can be

used as an underlying model for many observed series and will be studied in detail

in Chap. 3.

As in the previous example, the data are obtained by a ﬁlter of white noise.

The function

filter uses zeros for the initial values. In this case, x

= w

,and

= x

+ w

= w

+ w

, and so on, so that the values do not satisfy (1.2). An easy

ﬁx is to run the ﬁlter for longer than needed and remove the initial values.

w = rnorm(550,0,1)

# 50 extra to avoid startup problems

x = filter(w, filter=c(1,-.9), method="recursive")[-(1:50)]

# remove first 50

plot.ts(x, main="autoregression")

Example 1.11 Random Walk with Drift

A model for analyzing trend such as seen in the global temperature data in Fig. 1.2,

is the random walk with drift model given by

= δ + x

t−1

+ w

(1.3)

for t = 1, 2,..., with initial condition x

= 0, and where w

is white noise. The

constant δ is called the drift,andwhenδ = 0, (1.3) is called simply a random walk.

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时间序列分析及其在R语言中的应用第四版

Time.Series.Analysis.With.Applications.in.R-Jonathan

Time Series Analysis and Its Application-时间序列

Time Series Analysis and Its Applications

#ifdef CONFIG_FLUORIDE_EXAMPLES_HD_KEYBOARD

如何导入set_seed, convert_ext_examples, convert_cls_examples

有关时间序列预测的文献

ModuleNotFoundError: No module named 'pos_neg_examples_generator'

def file_based_convert_examples_to_features( examples, label_list, max_seq_length, tokenizer, output_file):pytorch实现

You must specify either total_examples or total_words, for proper learning-rate and progress calculations. If you've just built the vocabulary using the same corpus, using the count cached in the model is sufficient: total_examples=model.corpus_count.

aurix_code_examples

mnist.train.num_examples / batch_size

ERROR: Could not find a version that satisfies the requirement tensorflow_examples (from versions: none) ERROR: No matching distribution found for tensorflow_examples

No module named 'tensorflow_examples'

model = model.to("cuda:0") # 从测试集中挑选4个样本 test_examples = dev_dataset["document"][:4] inputs = tokenizer( test_examples, padding="max_length", truncation=True, max_length=max_input_length, return_tensors="pt", )这是什么意思

for i in range(0, num_examples, batch_size):

batch_indices = torch.tensor(indices[i: min(i + batch_size, num_examples)])什么意思

num_inputs=2 num_examples=1000 ture_w=[2,-3.4] ture_b=[4.2] features=np.random.normal(scale=1,size=(num_examples,num_inputs)) labels=ture_w[0]*features[:0]+ture_w[1]*features[:1]+ture_b labels+=np.random.normal(scale=0.01,size=labels.shape)

for i in range(0,num_examples,batch_size): batch_indices = torch.tensor(indices[i:min(i+batch_size,num_examples)]) yield features[batch_indices],labels[batch_indices]

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num_inputs=2 num_examples=1000 ture_w=[2,-3.4] ture_b=[4.2] features=np.random.normal(scale=1,size=(num_examples,num_inputs)) labels=ture_w[0]features[:0]+ture_w[1]features[:1]+ture_b labels+=np.random.normal(scale=0.01,size=labels.shape)