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《Forecasting Principles and Practice 2e》是Rob J Hyndman和George Athanasopoulos两位作者合著的，由澳大利亚莫纳什大学发布的一部在线教科书，旨在为读者提供全面的预测方法介绍，并使读者能够合理地使用这些方法。尽管本书不会对每种预测方法背后的理论细节进行深入探讨，但每章末尾的参考文献将补充很多细节信息。本书有三个主要的目标受众：一是在商务活动中发现自己需要进行预测，却没有正式接受过这方面培训的人；二是本科学生，特别是学习商务相关专业的学生；三是攻读MBA学位并选修预测课程的学生。本书也是莫纳什大学三年级学生攻读商务或商业学士学位时使用的一门课程。本书的大多数章节仅假定读者熟悉基础统计和高中代数。但也有少数几个章节需要具备矩阵知识，这在书中会有明确标注。每个章节的末尾，作者提供了“进一步阅读”的列表，这包括了更高级或更详细地探讨该主题的推荐教科书。在没有合适教科书的情况下，会建议相关领域的期刊文章以提供更多信息。本书通篇使用R语言，并且旨在使学生学会如何使用R进行预测。 R语言是一种免费且在几乎每种操作系统上都可用的工具，非常适合进行统计分析，不仅仅是预测。本书中所有使用R语言的示例都假定用户已经加载了fpp2包，这个包在CRAN（Comprehensive R Archive Network）上可用，使用library(fpp2)命令即可载入。这将自动加载其他几个包，包括forecast和ggplot2，以及书中所使用的所有数据。fpp2包至少需要forecast包的8.0版本和ggplot2包的2.0.0版本。在本书中，所有的图形制作都将使用ggplot2包。如果读者希望学习如何修改图形，或者创建与书中示例不同的自定义ggplot2图形，可以阅读ggplot2的书籍（Wickham 2016）或参加相关的在线课程。通过这样的内容编排，本书不仅仅提供了一个预测的实用工具箱，也为希望深入了解统计学和预测理论的读者提供了进一步学习的路径。总体来看，《Forecasting Principles and Practice 2e》涵盖了预测方法的广泛主题，从基础到进阶，满足了不同层次读者的需求。此外，它还特别强调了使用R语言进行预测实践的重要性，使得学生在学习理论的同时，能够通过实际操作增强理解和应用能力。通过学习这本教材，学生和专业人士都可以在预测领域中获得扎实的基础知识，并在实际工作中应用这些知识解决实际问题。

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Forecasting: Principles and Practice

Rob J Hyndman and George Athanasopoulos

Monash University, Australia

From: http://otexts.org/fpp2/

Preface

Welcome to our online textbook on forecasting.

This textbook is intended to provide a comprehensive introduction to

forecasting methods and to present enough information about each

method for readers to be able to use them sensibly. We don’t attempt to

give a thorough discussion of the theoretical details behind each method,

although the references at the end of each chapter will fill in many of

those details.

The book is written for three audiences: (1) people finding themselves

doing forecasting in business when they may not have had any formal

training in the area; (2) undergraduate students studying business;

(3) MBA students doing a forecasting elective. We use it ourselves for a

third-year subject for students undertaking a Bachelor of Commerce or a

Bachelor of Business degree at Monash University, Australia.

For most sections, we only assume that readers are familiar with

introductory statistics, and with high-school algebra. There are a couple

of sections that also require knowledge of matrices, but these are

flagged.

At the end of each chapter we provide a list of “further reading”. In

general, these lists comprise suggested textbooks that provide a more

advanced or detailed treatment of the subject. Where there is no suitable

textbook, we suggest journal articles that provide more information.

We use R throughout the book and we intend students to learn how to

forecast with R. R is free and available on almost every operating system.

It is a wonderful tool for all statistical analysis, not just for forecasting. See

the Using R appendix for instructions on installing and using R.

All R examples in the book assume you have loaded the fpp2 package,

available on CRAN, using library(fpp2). This will automatically load

several other packages including forecast and ggplot2, as well as all the

data used in the book. The fpp2 package requires at least version 8.0 of the forecast package and version 2.0.0 of the ggplot2 package.

We will use the ggplot2 package for all graphics. If you want to learn how to modify the graphs, or create your own ggplot2 graphics that are different from

the examples shown in this book, please either read the ggplot2 book (Wickham 2016), or do the ggplot2 course on the DataCamp online learning

platform.

There is also a DataCamp course based on this book which provides an introduction to some of the ideas in Chapters 2, 3, 7 and 8, plus a brief glimpse at

a few of the topics in Chapters 9 and 11.

The book is different from other forecasting textbooks in several ways.

It is free and online, making it accessible to a wide audience.

It uses R, which is free, open-source, and extremely powerful software.

The online version is continuously updated. You don’t have to wait until the next edition for errors to be removed or new methods to be discussed. We

will update the book frequently.

There are dozens of real data examples taken from our own consulting practice. We have worked with hundreds of businesses and organizations

helping them with forecasting issues, and this experience has contributed directly to many of the examples given here, as well as guiding our general

philosophy of forecasting.

We emphasise graphical methods more than most forecasters. We use graphs to explore the data, analyse the validity of the models fitted and

present the forecasting results.

Changes in the second edition

The most important change in edition 2 of the book is that we have restricted our focus to time series forecasting. That is, we no longer consider the

problem of cross-sectional prediction. Instead, all forecasting in this book concerns prediction of data at future times using observations collected in the

past.

We have also simplified the chapter on exponential smoothing, and added new chapters on dynamic regression forecasting, hierarchical forecasting and

practical forecasting issues. We have added new material on combining forecasts, handling complicated seasonality patterns, dealing with hourly, daily

and weekly data, forecasting count time series, and we have many new examples. We have also revised all existing chapters to bring them up-to-date

with the latest research, and we have carefully gone through every chapter to improve the explanations where possible, to add newer references, to add

more exercises, and to make the R code simpler.

Helpful readers of the earlier versions of the book let us know of any typos or errors they had found. These were updated immediately online. No doubt we

have introduced some new mistakes, and we will correct them online as soon as they are spotted. Please continue to let us know about such things.

Please note

This second edition is now almost complete, although we still plan to change a few of the examples. The print version should be available on Amazon by

March 2018.

We have used the latest v8.3 of the forecast package in preparing this book. The current CRAN version is 8.2, and a few examples will not work if you

have v8.2. To install v8.3, use

# install.packages("devtools")

devtools::install_github("robjhyndman/forecast")

Happy forecasting!

Rob J Hyndman and George Athanasopoulos

December 2017

Bibliography

Wickham, Hadley. 2016. ggplot2: Elegant Graphics for Data Analysis. 2nd ed. Springer.

Chapter 1 Getting started

Forecasting has fascinated people for thousands of years, sometimes being considered a sign of divine inspiration, and sometimes being seen as a

criminal activity. The Jewish prophet Isaiah wrote in about 700 BC

Tell us what the future holds, so we may know that you are gods.

(Isaiah 41:23)

One hundred years later, in ancient Babylon, forecasters would foretell the future based on the distribution of maggots in a rotten sheep’s liver. By 300 BC,

people wanting forecasts would journey to Delphi in Greece to consult the Oracle, who would provide her predictions while intoxicated by ethylene

vapours. Forecasters had a tougher time under the emperor Constantine, who issued a decree in AD357 forbidding anyone “to consult a soothsayer, a

mathematician, or a forecaster May curiosity to foretell the future be silenced forever.” A similar ban on forecasting occurred in England in 1736 when

it became an offence to defraud by charging money for predictions. The punishment was three months’ imprisonment with hard labour!

The varying fortunes of forecasters arise because good forecasts can seem almost magical, while bad forecasts may be dangerous. Consider the

following famous predictions about computing.

I think there is a world market for maybe five computers. (Chairman of IBM, 1943)

Computers in the future may weigh no more than 1.5 tons. (Popular Mechanics, 1949)

There is no reason anyone would want a computer in their home. (President, DEC, 1977)

The last of these was made only three years before IBM produced the first personal computer. Not surprisingly, you can no longer buy a DEC computer.

Forecasting is obviously a difficult activity, and businesses that do it well have a big advantage over those whose forecasts fail.

In this book, we will explore the most reliable methods for producing forecasts. The emphasis will be on methods that are replicable and testable, and

have been shown to work.

1.1 What can be forecast?

Forecasting is required in many situations: deciding whether to build another power generation plant in the next five years requires forecasts of future

demand; scheduling staff in a call centre next week requires forecasts of call volumes; stocking an inventory requires forecasts of stock requirements.

Forecasts can be required several years in advance (for the case of capital investments), or only a few minutes beforehand (for telecommunication

routing). Whatever the circumstances or time horizons involved, forecasting is an important aid to effective and efficient planning.

…

Some things are easier to forecast than others. The time of the sunrise tomorrow morning can be forecast very precisely. On the other hand, tomorrow’s

lotto numbers cannot be forecast with any accuracy. The predictability of an event or a quantity depends on several factors including:

1. how well we understand the factors that contribute to it;

2. how much data are available;

3. whether the forecasts can affect the thing we are trying to forecast.

For example, forecasts of electricity demand can be highly accurate because all three conditions are usually satisfied. We have a good idea of the

contributing factors: electricity demand is driven largely by temperatures, with smaller effects for calendar variation such as holidays, and economic

conditions. Provided there is a sufficient history of data on electricity demand and weather conditions, and we have the skills to develop a good model

linking electricity demand and the key driver variables, the forecasts can be remarkably accurate.

On the other hand, when forecasting currency exchange rates, only one of the conditions is satisfied: there is plenty of available data. However, we have a

very limited understanding of the factors that affect exchange rates, and forecasts of the exchange rate have a direct effect on the rates themselves. If

there are well-publicized forecasts that the exchange rate will increase, then people will immediately adjust the price they are willing to pay and so the

forecasts are self-fulfilling. In a sense, the exchange rates become their own forecasts. This is an example of the “efficient market hypothesis”.

Consequently, forecasting whether the exchange rate will rise or fall tomorrow is about as predictable as forecasting whether a tossed coin will come down

as a head or a tail. In both situations, you will be correct about 50% of the time, whatever you forecast. In situations like this, forecasters need to be aware

of their own limitations, and not claim more than is possible.

Often in forecasting, a key step is knowing when something can be forecast accurately, and when forecasts will be no better than tossing a coin. Good

forecasts capture the genuine patterns and relationships which exist in the historical data, but do not replicate past events that will not occur again. In this

book, we will learn how to tell the difference between a random fluctuation in the past data that should be ignored, and a genuine pattern that should be

modelled and extrapolated.

Many people wrongly assume that forecasts are not possible in a changing environment. Every environment is changing, and a good forecasting model

captures the way in which things are changing. Forecasts rarely assume that the environment is unchanging. What is normally assumed is that the way in

which the environment is changing will continue into the future. That is, a highly volatile environment will continue to be highly volatile; a business with

fluctuating sales will continue to have fluctuating sales; and an economy that has gone through booms and busts will continue to go through booms and

busts. A forecasting model is intended to capture the way things move, not just where things are. As Abraham Lincoln said, “If we could first know where

we are and whither we are tending, we could better judge what to do and how to do it”.

Forecasting situations vary widely in their time horizons, factors determining actual outcomes, types of data patterns, and many other aspects.

Forecasting methods can be very simple, such as using the most recent observation as a forecast (which is called the “naïve method”), or highly complex,

such as neural nets and econometric systems of simultaneous equations. Sometimes, there will be no data available at all. For example, we may wish to

forecast the sales of a new product in its first year, but there are obviously no data to work with. In situations like this, we use judgmental forecasting,

discussed in Chapter 4. The choice of method depends on what data are available and the predictability of the quantity to be forecast.

1.2 Forecasting, planning and goals

Forecasting is a common statistical task in business, where it helps to inform decisions about the scheduling of production, transportation and personnel,

and provides a guide to long-term strategic planning. However, business forecasting is often done poorly, and is frequently confused with planning and

goals. They are three different things.

Forecasting

is about predicting the future as accurately as possible, given all of the information available, including historical data and knowledge of any future

events that might impact the forecasts.

Goals

are what you would like to have happen. Goals should be linked to forecasts and plans, but this does not always occur. Too often, goals are set

without any plan for how to achieve them, and no forecasts for whether they are realistic.

Planning

is a response to forecasts and goals. Planning involves determining the appropriate actions that are required to make your forecasts match your

goals.

Forecasting should be an integral part of the decision-making activities of management, as it can play an important role in many areas of a company.

Modern organizations require short-term, medium-term and long-term forecasts, depending on the specific application.

Short-term forecasts

are needed for the scheduling of personnel, production and transportation. As part of the scheduling process, forecasts of demand are often also

required.

Medium-term forecasts

are needed to determine future resource requirements, in order to purchase raw materials, hire personnel, or buy machinery and equipment.

Long-term forecasts

are used in strategic planning. Such decisions must take account of market opportunities, environmental factors and internal resources.

An organization needs to develop a forecasting system that involves several approaches to predicting uncertain events. Such forecasting systems require

the development of expertise in identifying forecasting problems, applying a range of forecasting methods, selecting appropriate methods for each

problem, and evaluating and refining forecasting methods over time. It is also important to have strong organizational support for the use of formal

forecasting methods if they are to be used successfully.

1.3 Determining what to forecast

In the early stages of a forecasting project, decisions need to be made about what should be forecast. For example, if forecasts are required for items in a

manufacturing environment, it is necessary to ask whether forecasts are needed for:

1. every product line, or for groups of products?

2. every sales outlet, or for outlets grouped by region, or only for total sales?

3. weekly data, monthly data or annual data?

It is also necessary to consider the forecasting horizon. Will forecasts be required for one month in advance, for 6 months, or for ten years? Different types

of models will be necessary, depending on what forecast horizon is most important.

How frequently are forecasts required? Forecasts that need to be produced frequently are better done using an automated system than with methods that

require careful manual work.

It is worth spending time talking to the people who will use the forecasts to ensure that you understand their needs, and how the forecasts are to be used,

before embarking on extensive work in producing the forecasts.

Once it has been determined what forecasts are required, it is then necessary to find or collect the data on which the forecasts will be based. The data

required for forecasting may already exist. These days, a lot of data are recorded, and the forecaster’s task is often to identify where and how the required

data are stored. The data may include sales records of a company, the historical demand for a product, or the unemployment rate for a geographical

region. A large part of a forecaster’s time can be spent in locating and collating the available data prior to developing suitable forecasting methods.

1.4 Forecasting data and methods

The appropriate forecasting methods depend largely on what data are available.

If there are no data available, or if the data available are not relevant to the forecasts, then qualitative forecasting methods must be used. These methods

are not purely guesswork—there are well-developed structured approaches to obtaining good forecasts without using historical data. These methods are

discussed in Chapter 4.

Quantitative forecasting can be applied when two conditions are satisfied:

1. numerical information about the past is available;

2. it is reasonable to assume that some aspects of the past patterns will continue into the future.

There is a wide range of quantitative forecasting methods, often developed within specific disciplines for specific purposes. Each method has its own

properties, accuracies, and costs that must be considered when choosing a specific method.

Most quantitative prediction problems use either time series data (collected at regular intervals over time) or cross-sectional data (collected at a single

point in time). In this book we are concerned with forecasting future data, and we concentrate on the time series domain.

Time series forecasting

Examples of time series data include:

Daily IBM stock prices

Monthly rainfall

Quarterly sales results for Amazon

Annual Google profits

Anything that is observed sequentially over time is a time series. In this book, we will only consider time series that are observed at regular intervals of

time (e.g., hourly, daily, weekly, monthly, quarterly, annually). Irregularly spaced time series can also occur, but are beyond the scope of this book.

When forecasting time series data, the aim is to estimate how the sequence of observations will continue into the future. Figure 1.1 shows the quarterly

Australian beer production from 1992 to the second quarter of 2010.

Figure 1.1: Australian quarterly beer production: 1992Q1–2010Q2, with two years of forecasts.

The blue lines show forecasts for the next two years. Notice how the forecasts have captured the seasonal pattern seen in the historical data and

replicated it for the next two years. The dark shaded region shows 80% prediction intervals. That is, each future value is expected to lie in the dark shaded

region with a probability of 80%. The light shaded region shows 95% prediction intervals. These prediction intervals are a very useful way of displaying the

uncertainty in forecasts. In this case the forecasts are expected to be very accurate, and hence the prediction intervals are quite narrow.

The simplest time series forecasting methods use only information on the variable to be forecast, and make no attempt to discover the factors that affect

its behaviour. Therefore they will extrapolate trend and seasonal patterns, but they ignore all other information such as marketing initiatives, competitor

activity, changes in economic conditions, and so on.

Time series models used for forecasting include ARIMA models, exponential smoothing and structural models. These models are discussed in Chapters

6, 7 and 8.

Predictor variables and time series forecasting

Predictor variables can also be used in time series forecasting. For example, suppose we wish to forecast the hourly electricity demand (ED) of a hot

region during the summer period. A model with predictor variables might be of the form

The relationship is not exact—there will always be changes in electricity demand that cannot be accounted for by the predictor variables. The “error” term

on the right allows for random variation and the effects of relevant variables that are not included in the model. We call this an “explanatory model”

because it helps explain what causes the variation in electricity demand.

Because the electricity demand data form a time series, we could also use a time series model for forecasting. In this case, a suitable time series

forecasting equation is of the form

where is the present hour, is the next hour, is the previous hour, is two hours ago, and so on. Here, prediction of the future is based

on past values of a variable, but not on external variables which may affect the system. Again, the “error” term on the right allows for random variation and

the effects of relevant variables that are not included in the model.

There is also a third type of model which combines the features of the above two models. For example, it might be given by

These types of mixed models have been given various names in different disciplines. They are known as dynamic regression models, panel data models,

longitudinal models, transfer function models, and linear system models (assuming that is linear). These models are discussed in Chapter 9.

An explanatory model is very useful because it incorporates information about other variables, rather than only historical values of the variable to be

forecast. However, there are several reasons a forecaster might select a time series model rather than an explanatory model. First, the system may not be

understood, and even if it was understood it may be extremely difficult to measure the relationships that are assumed to govern its behaviour. Second, it is

necessary to know or forecast the future values of the various predictors in order to be able to forecast the variable of interest, and this may be too

ED=