This IMA Volume in Mathematics and its Applications TIME SERIES ANALYSIS AND APPLICATIONS TO GEOPHYSICAL SYSTEMS contains papers presented at a very successful workshop on the same title. The event which was held on November 12-15, 2001 was an integral part of the IMA 2001-2002 annual program on " Mathematics in the Geosciences. " We would like to thank David R. Brillinger (Department of Statistics, Uni versity of California, Berkeley), Enders Anthony Robinson (Department of Earth and Environmental Engineering, Columbia University), and Fred eric Paik Schoenberg (Department of Statistics, University of California, Los Angeles) for their superb role as workshop organizers and editors of the proceedings. We are also grateful to Robert H. Shumway (Department of Statistics, University of California, Davis) for his help in organizing the four-day event. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a collection of papers that were presented dur ing the Workshop on Time Series Analysis and Applications to Geophysical Systems at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota from November 12-15, 2001. This was part of the IMA Thematic Year on Mathematics in the Geosciences, and was the last in a series of four Workshops during the Fall Quarter dedicated to Dynamical Systems and Ergodic Theory.

Part of a two volume set based on a recent IMA program of the same name. The goal of the program and these books is to develop a community of statistical and other scientists kept up-to-date on developments in this quickly evolving and interdisciplinary field. Consequently, these books present recent material by distinguished researchers. Topics discussed in Part I include nonlinear and non- Gaussian models and processes (higher order moments and spectra, nonlinear systems, applications in astronomy, geophysics, engineering, and simulation) and the interaction of time series analysis and statistics (information model identification, categorical valued time series, nonparametric and semiparametric methods). Self-similar processes and long-range dependence (time series with long memory, fractals, 1/f noise, stable noise) and time series research common to engineers and economists (modeling of multivariate and possibly non-stationary time series, state space and adaptive methods) are discussed in Part II.

Time Series Analysis in Seismology: Practical Applications provides technical assistance and coverage of available methods to professionals working in the field of seismology. Beginning with a thorough review of open problems in geophysics, including tectonic plate dynamics, localization of solitons, and forecasting, the book goes on to describe the various types of time series or punctual processes obtained from those systems. Additionally, the book describes a variety of methods and techniques relating to seismology and includes a discussion of future developments and improvements. Time Series Analysis in Seismology offers a concise presentation of the most recent advances in the analysis of geophysical data, particularly with regard to seismology, making it a valuable tool for researchers and students working in seismology and geophysics. Presents the necessary tools for time series analysis as it relates to seismology in a compact and consistent manner Includes a discussion of technical resources that can be applied to time series data analysis across multiple disciplines Describes the methods and techniques available for solving problems related to the analysis of complex data sets Provides exercises at the end of each chapter to enhance comprehension

A modern and accessible guide to the analysis of introductory time series data Featuring an organized and self-contained guide, Time Series Analysis provides a broad introduction to the most fundamental methodologies and techniques of time series analysis. The book focuses on the treatment of univariate time series by illustrating a number of well-known models such as ARMA and ARIMA. Providing contemporary coverage, the book features several useful and newlydeveloped techniques such as weak and strong dependence, Bayesian methods, non-Gaussian data, local stationarity, missing values and outliers, and threshold models. Time Series Analysis includes practical applications of time series methods throughout, as well as: Real-world examples and exercise sets that allow readers to practice the presented methods and techniques Numerous detailed analyses of computational aspects related to the implementation of methodologies including algorithm efficiency, arithmetic complexity, and process time End-of-chapter proposed problems and bibliographical notes to deepen readers’ knowledge of the presented material Appendices that contain details on fundamental concepts and select solutions of the problems implemented throughout A companion website with additional data fi les and computer codes Time Series Analysis is an excellent textbook for undergraduate and beginning graduate-level courses in time series as well as a supplement for students in advanced statistics, mathematics, economics, finance, engineering, and physics. The book is also a useful reference for researchers and practitioners in time series analysis, econometrics, and finance. Wilfredo Palma, PhD, is Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. He has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. He is the author of Long-Memory Time Series: Theory and Methods, also published by Wiley.

This book provides an essential appraisal of the recent advances in technologies, mathematical models and computational software used by those working with geodetic data. It explains the latest methods in processing and analyzing geodetic time series data from various space missions (i.e. GNSS, GRACE) and other technologies (i.e. tide gauges), using the most recent mathematical models. The book provides practical examples of how to apply these models to estimate seal level rise as well as rapid and evolving land motion changes due to gravity (ice sheet loss) and earthquakes respectively. It also provides a necessary overview of geodetic software and where to obtain them.

'Handbook of Statistics' is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with volume 30 dealing with time series.

The enormous progress over the last decades in our understanding of the mechanisms behind the complex system “Earth” is to a large extent based on the availability of enlarged data sets and sophisticated methods for their analysis. Univariate as well as multivariate time series are a particular class of such data which are of special importance for studying the dynamical p- cesses in complex systems. Time series analysis theory and applications in geo- and astrophysics have always been mutually stimulating, starting with classical (linear) problems like the proper estimation of power spectra, which hasbeenputforwardbyUdnyYule(studyingthefeaturesofsunspotactivity) and, later, by John Tukey. In the second half of the 20th century, more and more evidence has been accumulated that most processes in nature are intrinsically non-linear and thus cannot be su?ciently studied by linear statistical methods. With mat- matical developments in the ?elds of dynamic system’s theory, exempli?ed by Edward Lorenz’s pioneering work, and fractal theory, starting with the early fractal concepts inferred by Harold Edwin Hurst from the analysis of geoph- ical time series,nonlinear methods became available for time seriesanalysis as well. Over the last decades, these methods have attracted an increasing int- est in various branches of the earth sciences. The world’s leading associations of geoscientists, the American Geophysical Union (AGU) and the European Geosciences Union (EGU) have reacted to these trends with the formation of special nonlinear focus groups and topical sections, which are actively present at the corresponding annual assemblies.