时间序分析和预测第二版：线性回归分析和时间序分析方法

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"线性回归分析—教科书" 本资源主要介绍了线性回归分析的基本概念、方法和应用，涵盖了线性回归模型、残差分析、多重共线性等方面的内容。下面是本资源的知识点总结：一、线性回归分析的基本概念 * 线性回归分析是一个统计学方法，用于研究自变量和因变量之间的关系。 * 线性回归模型的数学表达式为：Y = β0 + β1X + ε，其中Y为因变量，X为自变量，β0为截距，β1为斜率，ε为随机误差项。二、线性回归模型的参数估计 * 线性回归模型的参数估计可以使用最小二乘法（Ordinary Least Squares, OLS）或最大似然估计法等方法。 * 参数估计的结果可以用来描述自变量和因变量之间的关系，例如斜率（slope）和截距（intercept）。三、残差分析 * 残差分析是指对线性回归模型的残差项进行分析，以了解模型的拟合程度和预测能力。 * 残差分析可以用于检测模型的假设是否成立，例如检测残差是否服从正态分布。四、多重共线性 * 多重共线性是指自变量之间存在高度相关性的情况，这可能会导致线性回归模型的参数估计不稳定。 * 多重共线性可以通过对自变量进行变换或选择合适的模型来解决。五、线性回归分析在数据分析中的应用 * 线性回归分析广泛应用于各种领域，例如经济学、金融学、生物学、医学等。 * 线性回归分析可以用于预测连续型变量的值，例如预测股票价格、预测患者的治疗效果等。六、相关统计概念 * 统计学中的相关概念，例如协方差、相关系数、F统计量等。 *这些概念在线性回归分析中扮演着重要的角色，例如协方差可以用于计算斜率的标准误差。七、时序分析和预测 * 时序分析是指对时间序列数据进行分析，以了解数据的模式和趋势。 * 时序分析可以用于预测未来事件的发生，例如预测股票价格、预测天气等。八、数据分析和大数据 * 数据分析是指对数据进行收集、清洁、变换和分析，以了解数据的特征和模式。 * 大数据是指大量的结构化或非结构化数据，需要使用特殊的分析工具和方法来处理。本资源提供了线性回归分析的基础知识和应用，涵盖了线性回归模型、残差分析、多重共线性等方面的内容，为读者提供了一个系统的了解线性回归分析的机会。

xiv PREFACE

Department of the Treasury (http://www.treas.gov/ofces/domestic-

nance/debt-management/interest-rate/). The time series data library

created by Rob Hyndman at Monash University (http://www-personal.

buseco.monash.edu.au/∼hyndman/TSDL/index.htm) and the time series

data library at the Mathematics Department of the University of York

(http://www.york.ac.uk/depts/maths/data/ts/) also contain many excellent

data sets. Some of these sources provide links to other data. Data sets and

other materials related to this book can be found at ftp://ftp.wiley.com/

public/scitechmed/ timeseries.

We would like to thank the many individuals who provided feedback

and suggestions for improvement to the rst edition. We found these sug-

gestions most helpful. We are indebted to Clifford Long who generously

provided the R codes he used with his students when he taught from the

book. We found his codes very helpful in putting the end-of-chapter R code

sections together. We also have placed a premium in the book on bridging

the gap between theory and practice. We have not emphasized proofs or

technical details and have tried to give intuitive explanations of the mate-

rial whenever possible. The result is a book that can be used with a wide

variety of audiences, with different interests and technical backgrounds,

whose common interests are understanding how to analyze time-oriented

data and constructing good short-term statistically based forecasts.

We express our appreciation to the individuals and organizations who

have given their permission to use copyrighted material. These materials

are noted in the text. Portions of the output contained in this book are

printed with permission of Minitab Inc. All material remains the exclusive

D C. M

C L. J

M K

THE NATURE AND USES OF FORECASTS 3

series plot. The rate variable is collected at equally spaced time periods, as

is typical in most time series and forecasting applications. Many business

applications of forecasting utilize daily, weekly, monthly, quarterly, or

annual data, but any reporting interval may be used. Furthermore, the data

may be instantaneous, such as the viscosity of a chemical product at the

point in time where it is measured; it may be cumulative, such as the total

sales of a product during the month; or it may be a statistic that in some

way reects the activity of the variable during the time period, such as the

daily closing price of a specic stock on the New York Stock Exchange.

The reason that forecasting is so important is that prediction of future

events is a critical input into many types of planning and decision-making

processes, with application to areas such as the following:

1. Operations Management. Business organizations routinely use fore-

casts of product sales or demand for services in order to schedule

production, control inventories, manage the supply chain, determine

stafng requirements, and plan capacity. Forecasts may also be used

to determine the mix of products or services to be offered and the

locations at which products are to be produced.

2. Marketing. Forecasting is important in many marketing decisions.

Forecasts of sales response to advertising expenditures, new promo-

tions, or changes in pricing polices enable businesses to evaluate

their effectiveness, determine whether goals are being met, and make

adjustments.

3. Finance and Risk Management. Investors in nancial assets are inter-

ested in forecasting the returns from their investments. These assets

include but are not limited to stocks, bonds, and commodities; other

investment decisions can be made relative to forecasts of interest

rates, options, and currency exchange rates. Financial risk man-

agement requires forecasts of the volatility of asset returns so that

the risks associated with investment portfolios can be evaluated and

insured, and so that nancial derivatives can be properly priced.

4. Economics. Governments, nancial institutions, and policy organi-

zations require forecasts of major economic variables, such as gross

domestic product, population growth, unemployment, interest rates,

ination, job growth, production, and consumption. These forecasts

are an integral part of the guidance behind monetary and scal pol-

icy, and budgeting plans and decisions made by governments. They

are also instrumental in the strategic planning decisions made by

business organizations and nancial institutions.

4 INTRODUCTION TO FORECASTING

5. Industrial Process Control. Forecasts of the future values of criti-

cal quality characteristics of a production process can help deter-

mine when important controllable variables in the process should be

changed, or if the process should be shut down and overhauled. Feed-

back and feedforward control schemes are widely used in monitoring

and adjustment of industrial processes, and predictions of the process

output are an integral part of these schemes.

6. Demography. Forecasts of population by country and regions are

made routinely, often stratied by variables such as gender, age,

and race. Demographers also forecast births, deaths, and migration

patterns of populations. Governments use these forecasts for planning

policy and social service actions, such as spending on health care,

retirement programs, and antipoverty programs. Many businesses

use forecasts of populations by age groups to make strategic plans

regarding developing new product lines or the types of services that

will be offered.

These are only a few of the many different situations where forecasts

are required in order to make good decisions. Despite the wide range of

problem situations that require forecasts, there are only two broad types of

forecasting techniques—qualitative methods and quantitative methods.

Qualitative forecasting techniques are often subjective in nature and

require judgment on the part of experts. Qualitative forecasts are often

used in situations where there is little or no historical data on which to base

the forecast. An example would be the introduction of a new product, for

which there is no relevant history. In this situation, the company might use

the expert opinion of sales and marketing personnel to subjectively estimate

product sales during the new product introduction phase of its life cycle.

Sometimes qualitative forecasting methods make use of marketing tests,

surveys of potential customers, and experience with the sales performance

of other products (both their own and those of competitors). However,

although some data analysis may be performed, the basis of the forecast is

subjective judgment.

Perhaps the most formal and widely known qualitative forecasting tech-

nique is the Delphi Method. This technique was developed by the RAND

Corporation (see Dalkey [1967]). It employs a panel of experts who are

assumed to be knowledgeable about the problem. The panel members are

physically separated to avoid their deliberations being impacted either by

social pressures or by a single dominant individual. Each panel member

responds to a questionnaire containing a series of questions and returns the

information to a coordinator. Following the rst questionnaire, subsequent

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