CRC.The Analysis of Time Series An Introduction, Sixth Edition

Preface to the Sixth Edition My aim in writing this text has been to provide an accessible book, which is wide-ranging and up-to-date and which covers both theory and practice. Enough theory is given to introduce essential concepts and make the book mathematically interesting. In addition, practical problems are addressed and worked examples are included so as to help the reader tackle the analysis of real data. The book can be used as a text for an undergraduate or a postgraduate course in time series, or it can be used for sel f-tuition by research workers. The positive feedback I have received over the years (plus healthy sales figures!) has encouraged me to continue to update, revise and improve the material. However, I do plan that this should be the sixth, and final edition! The book assumes a knowledge of basic probability theory and elementary statistical inference. A reasonable level of mathematics is required, though I have glossed over some mathematical difficulties, especially in the advanced Sections 3.4.8 and 3.5, which the reader is advised to omit at a first reading. In the sections on spectral analysis, the reader needs some familiarity with Fourier analysis and Fourier transforms, and I have helped the reader here by providing a special appendix on the latter topic. I am lucky in that I enjoy the rigorous elegance of mathematics as well as the very different challenge of analysing real data. I agree with David Williams (2001, Preface and p. 1) that “common sense and scientific insight are more important than Mathematics” and that “intuition is much more important than rigour”, but I also agree that this should not be an excuse for ignoring mathematics. Practical ideas should be backed up with theory whenever possible. Throughout the book, my aim is to teach both concepts and practice. In the process, I hope to convey the notion that Statistics and Mathematics are both fascinating, and I will be delighted if you agree. Although intended as an introductory text on a rather advanced topic, I have nevertheless provided appropriate references to further reading and to more advanced topics, especially in Chapter 13. The references are mainly to comprehensible and readily accessible sources, rather than to the original attributive references. This should help the reader to further the study of any topics that are of particular interest. One difficulty in writing any textbook is that many practical problems contain at least one feature that is ‘nonstandard’ in some sense. These cannot all be envisaged in a book of reasonable length. Rather the task of an author, such as myself, is to introduce generally applicable concepts and models, while making clear that some versatility may be needed to solve problems in practice. Thus the reader must always be prepared to use common sense when tackling real problems. Example 5.1 is a typical situation where common sense has to be applied and also reinforces the recommendation that the first step in any timeseries analysis should be to plot the data. The worked examples in Chapter 14 also include candid comments on practical difficulties in order to complement the general remarks in the main text. The first 12 chapters of the sixth edition have a similar structure to the fifth edition, although substantial revision has taken place. The notation used is mostly unchanged, but I note that the h-step-ahead forecast of the variable XN+h, made at time N, has been changed from to to better reflect modern usage. Some new topics have been added, such as Section 2.9 on Handling Real Data and Section 5.2.6 on Prediction Intervals. Chapter 13 has been completely revised and restructured to give a brief introduction to a variety of topics and is primarily intended to give readers an overview and point them in the right direction as regards further reading. New topics here include the aggregation of time series, the analysis of time series in finance and discrete-valued time series. The old Appendix D has been revised and extended to become a new Chapter 14. It gives more practical advice, and, in the process reflects the enormous changes in computing practice that have taken place over the last few years. The references have, of course, been updated throughout the book. I would like to thank Julian Faraway, Ruth Fuentes Garcia and Adam Prowse for their help in producing the graphs in this book. I also thank Howard Grubb for providing Figure 14.4. I am indebted to many other people, too numerous to mention, for assistance in various aspects of the preparation of the current and earlier editions of the book. In particular, my colleagues at Bath have been supportive and helpful over the years. Of course any errors, omissions or obscurities which remain are my responsibility and I will be glad to hear from any reader who wishes to make constructive comments. I hope you enjoy the book and find it helpful. Chris Chatfield Department of Mathematical Sciences University of Bath Bath, Avon, BA2 7AY, U.K. e-mail: cc@maths.bath.ac.uk f-tuition by research workers. The positive feedback I have received over the years (plus healthy sales figures!) has encouraged me to continue to update, revise and improve the material. However, I do plan that this should be the sixth, and final edition! The book assumes a knowledge of basic probability theory and elementary statistical inference. A reasonable level of mathematics is required, though I have glossed over some mathematical difficulties, especially in the advanced Sections 3.4.8 and 3.5, which the reader is advised to omit at a first reading. In the sections on spectral analysis, the reader needs some familiarity with Fourier analysis and Fourier transforms, and I have helped the reader here by providing a special appendix on the latter topic. I am lucky in that I enjoy the rigorous elegance of mathematics as well as the very different challenge of analysing real data. I agree with David Williams (2001, Preface and p. 1) that “common sense and scientific insight are more important than Mathematics” and that “intuition is much more important than rigour”, but I also agree that this should not be an excuse for ignoring mathematics. Practical ideas should be backed up with theory whenever possible. Throughout the book, my aim is to teach both concepts and practice. In the process, I hope to convey the notion that Statistics and Mathematics are both fascinating, and I will be delighted if you agree. Although intended as an introductory text on a rather advanced topic, I have nevertheless provided appropriate references to further reading and to more advanced topics, especially in Chapter 13. The references are mainly to comprehensible and readily accessible sources, rather than to the original attributive references. This should help the reader to further the study of any topics that are of particular interest. One difficulty in writing any textbook is that many practical problems contain at least one feature that is ‘nonstandard’ in some sense. These cannot all be envisaged in a book of reasonable length. Rather the task of an author, such as myself, is to introduce generally applicable concepts and models, while making clear that some versatility may be needed to solve problems in practice. Thus the reader must always be prepared to use common sense when tackling real problems. Example 5.1 is a typical situation where common sense has to be applied and also reinforces the recommendation that the first step in any timeseries analysis should be to plot the data. The worked examples in Chapter 14 also include candid comments on practical difficulties in order to complement the general remarks in the main text. The first 12 chapters of the sixth edition have a similar structure to the fifth edition, although substantial revision has taken place. The notation used is mostly unchanged, but I note that the h-step-ahead forecast of the variable XN+h, made at time N, has been changed from to to better reflect modern usage. Some new topics have been added, such as Section 2.9 on Handling Real Data and Section 5.2.6 on Prediction Intervals. Chapter 13 has been completely revised and restructured to give a brief introduction to a variety of topics and is primarily intended to give readers an overview and point them in the right direction as regards further reading. New topics here include the aggregation of time series, the analysis of time series in finance and discrete-valued time series. The old Appendix D has been revised and extended to become a new Chapter 14. It gives more practical advice, and, in the process reflects the enormous changes in computing practice that have taken place over the last few years. The references have, of course, been updated throughout the book. I would like to thank Julian Faraway, Ruth Fuentes Garcia and Adam Prowse for their help in producing the graphs in this book. I also thank Howard Grubb for providing Figure 14.4. I am indebted to many other people, too numerous to mention, for assistance in various aspects of the preparation of the current and earlier editions of the book. In particular, my colleagues at Bath have been supportive and helpful over the years. Of course any errors, omissions or obscurities which remain are my responsibility and I will be glad to hear from any reader who wishes to make constructive comments. I hope you enjoy the book and find it helpful. Chris Chatfield Department of Mathematical Sciences University of Bath Bath, Avon, BA2 7AY, U.K. e-mail: cc@maths.bath.ac.uk