时间序列预测：Third Edition

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"时间序列预测" 《时间序列预测》是一本由Peter J. Brockwell和Richard A. Davis合作编写的统计学专业书籍，现在已经更新到了第三版。这本书是Springer Texts in Statistics系列的一部分，由R. DeVeaux、S. Fienberg和I. Olkin等人主编。该系列图书在Springer出版社的官方网站上可以找到更多相关信息。时间序列分析是一种统计方法，用于研究和预测按时间顺序排列的数据集。在本书中，作者深入探讨了时间序列模型和预测技术，包括ARIMA（自回归积分滑动平均模型）和REGARIMA（回归ARIMA），以及Holt-Winters方法。这些模型在经济学、金融、气象学、工程学等多个领域都有广泛应用。 ARIMA模型是时间序列分析中的核心工具，它结合了自回归（AR）、差分（I，即整合）和滑动平均（MA）三个部分，能够处理非平稳时间序列数据，使其转化为平稳过程，从而进行预测。ARIMA模型通过参数调整，可以捕捉数据中的趋势、季节性和随机波动。 REGARIMA模型是ARIMA模型的扩展，它引入了外部解释变量，使得预测不仅基于过去的观测值，还可以考虑其他因素的影响，如经济指标或政策变化，提高了预测的准确性和解释性。 Holt-Winters方法则是一种适用于具有趋势和季节性的时间序列的预测模型。它分为三步：平滑趋势、平滑季节性和外推预测。这种方法特别适合处理有明显季节模式的数据，如零售销售、电力消耗等。书中还可能涵盖了时间序列的建模步骤，包括数据检查、模型选择、诊断检验、模型验证和预测。此外，作者可能还会讨论现代时间序列分析的其他方法，如状态空间模型、季节性分解趋势循环不规则（STL）等。通过对时间序列预测的深入学习，读者将能够理解和应用这些技术来解决实际问题，比如预测股票价格、分析气候变化趋势、优化库存管理等。这本书对于统计学、数据分析和决策科学的学生以及专业人士来说，都是极有价值的参考资料。

Introduction

1.1 Examples of Time Series

1.2 Objectives of Time Series Analysis

1.3 Some Simple Time Series Models

1.4 Stationary Models and the Autocorrelation Function

1.5 Estimation and Elimination of Trend and Seasonal Components

1.6 Testing the Estimated Noise Sequence

In this chapter we introduce some basic ideas of time series analysis and stochastic

processes. Of particular importance are the concepts of stationarity and the autocovari-

ance and sample autocovariance functions. Some standard techniques are described

for the estimation and removal of trend and seasonality (of known period) from

an observed time series. These are illustrated with reference to the data sets in

Section 1.1. The calculations in all the examples can be carried out using the time

series package ITSM, the professional version of which is av ailable at http://extras.

springer.com. The data sets are contained in files with names ending in .TSM. For

example, the Australian red wine sales are filed as WINE.TSM. Most of the topics

cov ered in this chapter will be developed more fully in later sections of the book. The

reader who is not already familiar with random variables and random vectors should

first read Appendix A, where a concise account of the required background is given.

1.1 Examples of Time Series

A time series is a set of observations x

, each one being recorded at a specific time t.

A discrete-time time series (the type to which this book is primarily devoted) is one

in which the set T

of times at which observations are made is a discrete set, as is the

case, for example, when observations are made at fixed time intervals. Continuous-

time time series are obtained when observations are recorded continuously over some

time interval, e.g., when T

=[0, 1].

P.J. Brockwell, R.A. Davis, Introduction to Time Series and Forecasting,

Springer Te xts in Statistics, DOI 10.1007/978-3-319-29854-2_1

1.2 Objectives of Time Series Analysis 5

Figure 1-6

Strikes in the

U.S.A., 1951–1980

(thousands)

1950 1960 1970 1980

3.5 4.0 4.5 5.0 5.5 6.0

1.2 Objectives of Time Series Analysis

The examples considered in Section 1.1 are an extremely small sample from the

multitude of time series encountered in the fields of engineering, science, sociology,

and economics. Our purpose in this book is to study techniques for drawing inferences

from such series. Before we can do this, however, it is necessary to set up a hypothetical

probability model to represent the data. After an appropriate family of models has

been chosen, it is then possible to estimate parameters, check for goodness of fit to

the data, and possibly to use the fitted model to enhance our understanding of the

mechanism generating the series. Once a satisfactory model has been developed, it

may be used in a variety of ways depending on the particular field of application.

The model may be used simply to provide a compact description of the data. We

may, for example, be able to represent the accidental deaths data of Example 1.1.3 as

the sum of a specified trend, and seasonal and random terms. For the interpretation

of economic statistics such as unemployment figures, it is important to recognize

the presence of seasonal components and to remove them so as not to confuse

them with long-term trends. This process is known as seasonal adjustment.Other

applications of time series models include separation (or filtering) of noise from signals

as in Example 1.1.4, prediction of future v alues of a series such as the red wine

sales in Example 1.1.1 or the population data in Example 1.1.5, testing hypotheses

such as global warming using recorded temperature data, predicting one series from

observations of another, e.g., predicting future sales using advertising expenditure data,

and controlling future values of a series by adjusting parameters. Time series models

are also useful in simulation studies. For e xample, the performance of a reservoir

depends heavily on the random daily inputs of water to the system. If these are modeled

as a time series, then we can use the fitted model to simulate a large number of

independent sequences of daily inputs. Knowing the size and mode of operation

of the reservoir, we can determine the fraction of the simulated input sequences that

cause the reservoir to run out of water in a given time period. This fraction will then be

an estimate of the probability of emptiness of the reservoir at some time in the given

period.

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