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introduction to time series and forecasting second edition
Peter J. Brockwell
Richard A. Davis
This book is aimed at the reader who wishes to gain a working knowledge of time
series and forecasting methods as applied in economics, engineering and the natural
and social sciences. Unlike our earlier book, Time Series: Theory and Methods, referred
to in the text as TSTM, this one requires only a knowledge of basic calculus,
matrix algebra and elementary statistics at the level (for example) of Mendenhall,
Wackerly and Scheaffer (1990). It is intended for upper-level undergraduate students
and beginning graduate students.
The emphasis is on methods and the analysis of data sets. The student version
of the time series package ITSM2000, enabling the reader to reproduce most of the
calculations in the text (and to analyze further data sets of the reader’s own choosing),
is included on the CD-ROM which accompanies the book. The data sets used in the
book are also included. The package requires an IBM-compatible PC operating under
Windows 95, NT version 4.0, or a later version of either of these operating systems.
The program ITSM can be run directly from the CD-ROM or installed on a hard disk
as described at the beginning of Appendix D, where a detailed introduction to the
package is provided.
Very little prior familiarity with computing is required in order to use the computer
package. Detailed instructions for its use are found in the on-line help files which
are accessed, when the program ITSM is running, by selecting the menu option
Help>Contents and selecting the topic of interest. Under the heading Data you
will find information concerning the data sets stored on the CD-ROM. The book can
also be used in conjunction with other computer packages for handling time series.
Chapter 14 of the book by Venables and Ripley (1994) describes how to perform
many of the calculations using S-plus.
There are numerous problems at the end of each chapter, many of which involve
use of the programs to study the data sets provided.
To make the underlying theory accessible to a wider audience, we have stated
some of the key mathematical results without proof, but have attempted to ensure
that the logical structure of the development is otherwise complete. (References to
proofs are provided for the interested reader.)
viii Preface
Since the upgrade to ITSM2000 occurred after the first edition of this book
appeared, we have taken the opportunity, in this edition, to coordinate the text with
the new software, to make a number of corrections pointed out by readers of the first
edition and to expand on several of the topics treated only briefly in the first edition.
Appendix D, the software tutorial, has been rewritten in order to be compatible
with the new version of the software.
Some of the other extensive changes occur in (i) Section 6.6, which highlights
the role of the innovations algorithm in generalized least squares and maximum
likelihood estimation of regression models with time series errors, (ii) Section 6.4,
where the treatment of forecast functions for ARIMA processes has been expanded
and (iii) Section 10.3, which now includes GARCH modeling and simulation, topics
of considerable importance in the analysis of financial time series. The new material
has been incorporated into the accompanying software, to which we have also added
the option Autofit. This streamlines the modeling of time series data by fitting
maximum likelihood ARMA(p, q) models for a specified range of (p, q) values and
automatically selecting the model with smallest AICC value.
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