The IMA Volumes in Mathematics and its Applications

Transcription

1 The IMA Volumes in Mathematics and its Applications Volume 139 Series Editors Douglas N. Arnold Fadil Santosa Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo

2 Institute for Mathematics and its Applications (IMA) The Institute for Mathematics and its Applications was established by a grant from the National Science Foundation to the University of Minnesota in The primary mission of the IMA is to foster research of a truly interdisciplinary nature, establishing links between mathematics of the highest caliber and important scientific and technological problems from other disciplines and industry. To this end, the IMA organizes a wide variety of programs, ranging from short intense workshops in areas of exceptional interest and opportunity to extensive thematic programs lasting a year. IMA Volumes are used to communicate results of these programs that we believe are of particular value to the broader scientific community. The full list of IMA books can be found at the Web site of the Institute for Mathematics and its Applications: umn.edu/ springer / full-list-volumes.html. Douglas N. Arnold, Director of the IMA ********** IMA ANNUAL PROGRAMS Statistical and Continuum Approaches to Phase Transition Mathematical Models for the Economics of Decentralized Resource Allocation Continuum Physics and Partial Differential Equations Stochastic Differential Equations and Their Applications Scientific Computation Applied Combinatorics Nonlinear Waves Dynamical Systems and Their Applications Phase Transitions and Free Boundaries Applied Linear Algebra Control Theory and its Applications Emerging Applications of Probability Waves and Scattering Mathematical Methods in Material Science Mathematics of High Performance Computing Emerging Applications of Dynamical Systems Mathematics in Biology Continued at the back

3 David R. Brillinger Enders Anthony Robinson Frederic Paik Schoenberg Editors Time Series Analysis and Applications to Geophysical Systems With 94 Illustrations Springer

4 David R. Brillinger Department of Statistics University of California, Berkeley 367 Evens Hall Berkeley, CA USA Enders Anthony Robinson Department of Earth and Environmental Engineering Henry Krumb School of Mines Columbia University 918 Seeley Mudd Building th Street New York, NY USA earl Frederic Paik Schoenberg Department of Statistics University of California, Los Angeles 8142 Math-Science Building Los Angeles, CA USA frederic@stat.ucla.edu Series Editors: Douglas N. Arnold Fadil Santosa Institute for Mathematics and its Applications University of Minnesota Minneapolis, MN USA Mathematics Subject Classification (2000): 62MIO, 62M15, 62M20, 60G35, 86A15, 86AI0, 86A05, 86A22, 86A32, 86A40, 86A60, 62H12, 94A12, 94A13, 60G15, 60G25, 60G60, 62HII, 62M30, 93EIO, 93EII, 60K35. Library of Congress Cataloging-in-Publication Data On file. ISBN DOl / ISBN (ebook) 2004 Springer-Verlag New York, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, LLC, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Authorization to photocopy items for internai or personal use, or the internal or personal use of specific clients, is granted by Springer-Verlag New York, LLC, provided that the appropriate fee is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, USA (Telephone: (508) ), stating the ISBN number, the title of the book, and the first and last page numbers of each article copied. The copyright owner's consent does not include copying for general distribution, promotion, new works, or resale. In these cases, specific written permission must first be obtained from the publisher I SPIN Springer-Verlag is part of Springer Science+Business Media springeroniine.com

5 FOREWORD 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 annual program on " Mathematics in the Geosciences." We would like to thank David R. Brillinger (Department of Statistics, University of California, Berkeley), Enders Anthony Robinson (Department of Earth and Environmental Engineering, Columbia University), and Frederic 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

6 PREFACE This volume contains a collection of papers that were presented during 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, 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. The Workshop brought together 28 scientists from around the world and from various scientific backgrounds: many were specialists in the statistical analysis of time series; others were geophysicists, geologists, or climatologists with mainly subject matter expertise. The main goals of this Workshop were to engage discussion between these groups in order to facilitate the application of recent methodological advances in time series analysis to the most important geophysical problems. Before other matters, we extend our sincerest thanks for making the Workshop a success to Robert Shumway, who not only presented but also served as the local organizer of the Workshop with very little advanced notice, and by all accounts did a superb job. The idea for this workshop, and more generally for the IMA Thematic Year on Mathematics in the Geosciences, was Bill Newman's, and we thank Bill for all his help and for asking us to get involved. We also thank the IMA staff, especially Patricia V. Brick for her enormous help 'in coordinating and overseeing these proceedings and preparing this book for publication, as well as Alison Givand, Willard Miller, and Douglas N. Arnold for their helpful assistance and supervision. We also thank the authors for their contributions. Univariate and multivariate time series methods are critical in the analysis and identification of dynamical properties in a wide range of geophysical systems. While traditional approaches are based on the spectral analysis of random processes, more recent developments incorporate ideas from the ergodic theory of dynamical systems. The interaction of these two approaches provides unique opportunities for the application of time series methods to the geosciences. Much of the path connecting time series and geophysics was paved by John Tukey, who unfortunately died in the year preceding this workshop. Tukey made giant strides in applying concepts such as robust estimation, spectral analysis, and exploratory data analysis to geophysics, and the works in these Proceedings build upon his great contributions. The early interest of Tukey in geophysics goes back to the "Symposium on Autocorrelation Analysis applied to Physical Problems" held at Woods Hole, MA in June Tukey's paper entitled "The sampling theory of power spectrum estimates" was the high point of this meeting. This paper appears as pages in The Collected Works of John W. Thkey, Volume I (1984), vii

7 viii PREFACE Wadsworth, Belmont, CA. Before Tukey's work, the power spectra computed from empirical autocorrelation functions were too erratic to be of any use in formulating physical hypotheses. Not only did Tukey show correctly how to compute power spectra from empirical data, but he also laid the statistical framework for the analysis of short time series, as opposed to the very long ones envisaged by others. The works in this volume deal with theoretical and methodological issues as well as real geophysical applications, and are written with both statistical and geophysical audiences in mind. They cover a wide range of important geophysical applications, including the investigation and prediction of climatic variations and the interpretation of seismic signals. The first four papers deal with the interpretation of seismic signals. Robert H. Shumway, Jessie L. Bonner, and Delaine T. Reiter extend univariate cepstral methods to the problem of deconvolving seismic phases in a multivariate seismic arrays in order to determine the source depth of the seismic event. Genshiro Kitagawa, Tetsuo Takanami, and Norio Matsumoto fit a state space model with time-varying parameters and assess its implications on arrival time estimation, detection of coseismic contamination and spectral changes, and other problems. Enders Robinson suggests a method for obtaining a more refined estimate of a seismic signal in a layered system. Hernando Ombao, Jungeun Heo, and David Stoffer propose fitting piecewise stationary AR models as a way of decoding seismic signals in real time. The next four papers deal with temperature data. T. Subba Rao and E.P. Tsolaki perform tests and spectral analysis on global climatic data and present nonstationary time series models that explain observed climatic trends and temperature anomalies. Wei Biao Wu similarly investigates global warming trends but from quite a different perspective, namely that of testing whether temperature levels are constant versus isotonic alternatives. T. Subba Rao and Ana Monica Costa Antunes fit space-time ARMA models to data on monthly mean temperatures at various sites in the United Kingdom, and investigate the forecasting performance of the models. Donald B. Percival, James E. Overland, and Harold O. Mofjeld inspect the fit of an autoregressive model, a fractionally differenced model, and a square wave signal plus noise model to a North Pacific climatic index, and conclude that although the three models provide very different predictions, current data are insufficient to discriminate adequately between the models. The final five papers deal with an assortment of important time series problems and applications. Marc G. Genton and Keith R. Thompson apply a skew-elliptical time series model to hourly sea-level data in Atlantic Canada in order to estimate the risk of flooding. Zhongjie Xie suggests a method for identifying hidden periodicities in spatial time series data and applies the results to data on permeability in Chinese oil fields. T. Ozaki, J.C. Jimenez, H. Peng, and V. Haggan-Ozaki propose using an innovation

8 PREFACE ix approach with nonlinear models generally, and radial basis function models in particular, for the description of nonlinear time series data, and illustrate the implications of their results on a variety of different processes including models for the NOx decomposition from thermal power plants. Many geophysical processes appear to be characterized by non-gaussian noise, though the assumption of Gaussianity is typically assumed in conventional time series methods. Hence the importance of Murray Rosenblatt's discussion of the estimation and prediction of linear non-gaussian time series models as well as Winston C. Chow and Edward J. Wegman's treatment of, and proposed estimators for, stochastic differential equation models with fractional Gaussian noise. David R. Brillinger Department of Statistics University of California, Berkeley Enders Anthony Robinson Department of Earth and Environmental Engineering Krumb School of Mines Columbia University Frederic Paik Schoenberg Department of Statistics University of California, Los Angeles

9 CONTENTS Foreword... v Preface... vii INTERPRETATION OF SEISMIC SIGNALS Nonparametric deconvolution of seismic depth phases... 1 Robert H. Shumway, Jessie L. Bonner, and Delaine T. Reiter State space approach to signal extraction problems in seismology Genshiro Kitagawa, Tetsuo Takanami, and N orio Matsumoto Improved signal transmission through randomization Enders A. Robinson Online analysis of seismic signals Hernando Ombao, Jungeun Heo, and David Stoffer TEMPERATURE DATA Nonstationary time series analysis of monthly global temperature anomalies T. Subba Rao and E.P. Tsolaki A test for detecting changes in mean Wei Biao Wu Spatio-temporal modelling of temperature time series: a comparative study T. Subba Rao and Ana Monica Costa Antunes Modeling North Pacific climate time series Donald B. Percival, James E. Overland, and Harold O. Mofjeld xi

10 xii CONTENTS ASSORTMENT OF IMPORTANT TIME SERIES PROBLEMS AND ApPLICATIONS Skew-elliptical time series with application to flooding risk Marc G. Genton and Keith R. Thompson Hidden periodicities analysis and its application in geophysics Zhongjie Xie The innovation approach to the identification of nonlinear causal models in time series analysis T. Ozaki, J. C. Jimenez, H. Peng, and V.H. Ozaki Non-Gaussian time series models Murray Rosenblatt Modeling continuous time series driven by fractional Gaussian noise Winston C. Chow and Edward J. Wegman List of workshop participants