By Graham Weedon Cambridge University Press, New York, 2003 ISBN 0-521-62001-5 US $70.00, hardcover, 259 p

1 This book provides a very useful and well illustrated introduction to time series analysis and its application to the determination of cyclic behaviour of environmental variables. The author has succeeded admirably in summarizing the main methods used in the examination of quantitative records of ancient environmental change. The book is well-organized and clearly written with a minimum of jargon. The Table of Contents allows easy search for sections cross-referenced in the text. The author has included an index at the end of the book which also makes for easy searching. At the end of each of the six chapters, a brief summary of key issues addressed is presented in point form, an excellent idea for an introductory book. I especially liked the use of bold type-face for terms relating to time series analysis, particularly appropriate for an introductory text. Both the author and the editors are to be commended on production of a remarkably well-edited book.

2 Weedon demonstrates the applicability of time series analysis to a wide temporal range of palaeoenvironmental data ranging from annual to Milankovitch cycles. The overall balance in the examples presented is quite appropriate to the author's stated aim of encouraging new researchers to venture into the field of cyclostratigraphy and time series analysis. Weedon has drawn extensively on his own experience which, in some respects, strengthens his presentation through personal familiarity with his own time series data and its interpretation. This reviewer would have preferred a somewhat more varied use of examples in order to expose the reader to a broader range of applications using different data sets.

3 Chapter 1 provides a rather brief history of cyclostratigraphy, followed by an introduction to time series analysis. Weedon's synthetic time series (Figures 1.6 and 1.7) are particularly instructive. The author demonstrates the progressive increase in the graphic visual complexity of perfectly ordered, relatively simple time series in which several cycles are present, and their resolution into simple line spectra with time series analysis. The key bullet at the end of the chapter highlights the ability of spectral analysis to detect multiple regular cycles.

4 In Chapter 2, the author addresses the construction of time series in cyclostratigraphy. The reader progresses through a concise and very useful section in which discrete- and continuous-signal records are clearly and succinctly described. Three conditions fundamental to the construction of meaningful time series follow and should not be disregarded by those who seriously intend to undertake such an exercise. The chapter ends with a brief discussion of sampling, sample intervals, and aliasing related to sampling procedures. The use of irregularly spaced data is briefly discussed, almost at the level of an aside, and does not sufficiently acquaint the novice with viable alternatives that allow this procedure.

5 Chapter 3 deals with spectral estimation; it presents a variety of methods for doing spectral analysis of time series with examples of outputs. Preliminary discussion highlights time series that require pre-processing. The determination of statistical significance of spectral peaks completes the chapter. Here the author has, as promised in his preface, kept mathematics to a minimum. Chapter 4 continues in a partially similar vein, but here less familiar methods of time series analysis such as phase spectra, complex demodulation, wavelet analysis and singular spectrum analysis are presented. Much of this chapter deals with methods that allow follow-up analysis after a time series has yielded spectral indications of potentially significant periodicities.

6 In Chapter 5, Weedon deals with practical considerations and offers a cautionary perspective on environmental cyclicity, its invariable distortion in real stratigraphic records, and limitations on the interpretation of such cyclic signatures. Here synthetic time series, simplified in a mathematical context but still graphically realistic, provide an especially useful illustration of the author's points. This chapter is perhaps the most enlightening for the uninitiated reader. One suspects that Weedon has avoided overt criticism of certain techniques that deal with sediment accumulation rate distortions of natural time series. He cites instances where methods have been shown to give results "other than expected". Such restraint may be appropriate for a general text, but this lack of emphasis does not serve the target audience well.

7 Weedon finishes strong with Chapter 6 in which he links environmental processes to the cyclostratigraphic record, beginning with an admission that the mechanism through which this is done remains controversial in many instances. Perhaps fewer pages could have been used to address the climate spectrum but this might simply reflect new emphasis in this field in very small scale cyclicity in the stratigraphic record.

8 With the publication of this introductory book, Weedon has achieved his stated objective of providing a text on methods and concepts in cyclostratigraphy and time series analysis for students and those new to the field. Any disappointment I felt with the text no doubt reflects slightly different personal views, no fault of the author. My only criticism is in Weedon's hesitation to highlight in more detail some of the contentious issues in methodology and in the interpretation of spectral results, an effort that would have served the reader well. For example, Weedon could have usefully addressed very current research where orbital versus radiometric time-scale estimations are dramatically at odds and remain unresolved. The dramatic successes in the development of astronomical time scales receive lots of emphasis, and appropriately so. Why not some of the controversial issues which should be cautionary eye-openers for the neophyte?