Spectral Analysis and Time Series. Volumes I and II in 1 book. (Probability and Mathematical Statistics) [Paperback]

M. B. Priestley (Author)

Book Description

Publication Date: February 11, 1983 | ISBN-10: 0125649223 | ISBN-13: 978-0125649223

A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering", state-space filtering", "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first section-Volume 1-deals with single (univariate) series, while the second-Volume 2-treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control.

Editorial Reviews

From the Back Cover

Electric signals, stress and vibration records, seismographic traces and economic index stress all exhibit irregular patterns of vibration over time, and one of the main objectives of time series analysis is to describe the statistical properties of these irregularities by means of mathematical models. Such models can provide considerable insight into the basic structure of the series and form one of the major tools used for forecasting future behaviour on the basis of past values.

A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering", state-space filtering", "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first section-Volume 1-deals with single (univariate) series, while the second-Volume 2-treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control.

The reader is assumed to have knowledge of mathematics to at least first degree standard, although an advanced level of statistical knowledge is not necessary, as the book contains its own treatment of relevant topics in probability theory and statistical inference. The book will appeal to professional mathematical statisticians, in particular, and will also provide physicists, oceanographers, economists, and electrical engineers with a compact account of this subject.

Product Details

• Paperback: 890 pages
• Publisher: Academic Press (February 11, 1983)
• Language: English
• ISBN-10: 0125649223
• ISBN-13: 978-0125649223
• Product Dimensions: 9 x 6 x 1.6 inches
• Shipping Weight: 3.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #145,946 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

5.0 out of 5 stars Wonderful Intermediate-Level Treatment, June 20, 2006

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Paul Thurston (New York, NY USA) - See all my reviews
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This review is from: Spectral Analysis and Time Series. Volumes I and II in 1 book. (Probability and Mathematical Statistics) (Paperback)

The author has assembled a wonderfully accessible study of time series analysis from the point of view of spectral theory. This book really bridges the gap between Brockwell & Davis' elementary text Introduction to Time Series and Forecasting and their advanced text Time Series: Theory and Methods.
The book is logically partitioned into two volumes: Volume I (Chapters 1-8) considers spectral methods for time series, while Volume II (Chapters 9-11) extends the results to multivariate time series.

Priestly tries to keep the prerequisites to a minimum, but the reader is well advised to do a little background preparation before jumping in to this book. For the required material in mathematical analysis of Fourier series, I recommend Rudin's Real and Complex Analysis. Although Priestly provide a brief introduction to probability theory, I'd recommend a more solid grounding, as can be found in Chung's A Course in Probability Theory. The elementary text by Brockwell & Davis Introduction to Time Series and Forecasting presents the needed material on time series analysis.

In Chapter 1, Priestly sets up the motivation for considering spectral analysis of stationary time series, and gives four practical reasons for the use of spectral methods.

The reader will find a brief, 70 page overview of probability theory in Chapter 2. If the terms don't look familiar on a quick scan of this chapter, you'll want to get more detail from Chung's text before proceeding with Priestly.

Chapter 3 introduces stochastic processes and time series. Stationary time series are defined, as is the auto-covariance and autocorrelation function. ARMA(p,q) models are introduced and some basic results are established about these models.

The core results from spectral analysis are given in Chapter 4. The two main results are the Wiener-Khintchine Theorem (characterized those functions which can be the autocorrelation function of a stationary process), and the Spectral Representation Theorem for Stationary Processes.

Chapter 5 gives a really nice treatment of ARMA(p,q) model specification and estimation. The author motivates the well-known conditional maximum likelihood techniques for estimating coefficients, and gives really insight into the development of methods of order estimation using the information criterion ala Akaike (i.e. AIC) and Schwartz.

The next section consists discuss spectral estimation and consists of Chapters 6, 7, and 8. Chapter 6 tackles the theoretical issues surrounding estimated the spectral density of a stationary process. The author does a good job explaining the shortcomings of the periodogram as an estimator, as well as the need for tapering or 'windowing'. Chapter 7 continues along this theme by giving empirical guidance for selecting windowing schemes. Chapter 8 discusses the thorny problem of posed by processes containing both a continuous and a discrete spectrum.

The last part of the book comprised Volume II and extends the results of the first volume to cover the case of multivariate time series. Applications considered in this volume include problems of filtering and prediction. In the last chapter of the book, Priestly presents some of his own research on "evolutionary spectra" which is an attempt to extend the analysis to non-stationary processes.

The book is written in monograph style; as such there are no formal exercises. However, the author gives lots of examples using real-world datasets. Working through the examples serves to reinforce the reading. The author states several theorems, but usually prefers to justify these results with a heuristic argument. On occasion, a formal proof is given, but there are no end-of-proof markers (e.g. QED). The reader must take care to determine where the proof ends and the discussion resumes.

3 of 4 people found the following review helpful:

4.0 out of 5 stars Needs more examples but still very good., January 8, 2001

By 

Michael Quigley (San Francisco, CA USA) - See all my reviews
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This review is from: Spectral Analysis and Time Series. Volumes I and II in 1 book. (Probability and Mathematical Statistics) (Paperback)

I thought James D. Hamiltons book Time Serives Aanlysis was better. It was easier to understand and covered more material, including VAR models and State Space. Still this was and is an excellent book, and it goes into details about multivariate statistics that are not contained in Hamilton's book. I have the same complaint about this book as Hamilton's. Not enough examples. I compare these two books to those of Hosmer and Lemeshow's Applied Logistic Regression where there were nurmerous examples and problems to solve based on data they had provided.

Michael Quigley Director, Statistical Model and Data Mining Wells Fargo Bank

3 of 5 people found the following review helpful:

4.0 out of 5 stars Theoretical, January 19, 2001

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Steve Uhlig (Berlin, Germany) - See all my reviews
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This review is from: Spectral Analysis and Time Series. Volumes I and II in 1 book. (Probability and Mathematical Statistics) (Paperback)

This book covers almost all possible aspects of spectral analysis of time series. The problem is that it is almost exclusively theoretical. It should not be used for learning spectral analysis but rather as a reference book. There are very few practical examples but when looking for a proof or an abstract presentation of a particular concept, this book should allow you to understand the theory that lies behind... However, a very good treatment of spectral analysis and very broad coverage of the subject...