Statistics for Engineering and Physical Science

Akaike/Kitagawa: The Practice of Time Series Analysis.

Hawkins/Olwell: Cumulative Sum Charts and Charting for Quality Improvement.

Statistics for Engineering and Physical Science

Series Editors P. Green, J.F. Lawless, V. Nair

Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Singapore Tokyo

Hirotugu Akaike Genshiro Kitagawa Editors

The Practice of Time Series Analysis

, Springer

Hirotugu Akaike Genshiro Kitagawa The Institute of Statistical Mathematics Minato-ku, Tokyo Japan

Series Editors P. Green Department of Mathematics University of Bristol Bristol B58 1 TW England

V. Nair Department of Statistics University of Michigan Ann Arbor, MI 48109 USA

J.P. Lawless Department of Statistics University of Waterloo Waterloo, Ontario, N2L 3G 1 Canada

Library of Congress Cataloging-in-Publication Data The practice of time series analysis / Hirotugu Akaike, Genshiro

Kitagawa, editors. p. cm. - (Statistics for engineering and physical science)

Includes bibliographical references and index.

ISBN-13: 978-1-4612-7439-1 e-ISBN-13: 978-1-4612-2162-3 DOl: 10.1007/978-1-4612-2162-3

1. Engineering-Statistical methods. 2. Time-series analysis. I. Akaike, Hirotugu, 1927- . II. Kitagawa, G. (Genshiro), 1948-

III. Series. TA340.P72 1998 519.5'5-dc21 98-31331

Printed on acid-free paper.

© 1999 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1999

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, Inc., 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 of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Production managed by Lesley Poliner; manufacturing supervised by Jacqui Ashri. Camera-ready copy prepared by the authors using LATEX.

987654321

Preface to the English Version

This book is aimed at presenting examples of the successful application of time series analysis and control in various fields such as engineering, earth science, medi­cal science, biology, and economics. The development of statistical science seriously depends on the accumulation of successful experiences of the solution of concrete real problems. Once a statistical method finds a new application it often encourages further applications in other areas of research.

The examples included in this book are related to various stages of the practical application of the time series analysis. We hope that the examples will be helpful to the readers in finding solutions to their own problems.

The original version of this book was published in Japanese, in two volumes in 1994 and 1995, respectively, by Asakura Publishing Company, to whom we are grateful for giving permission to publish this English version. Thanks are also due to Mr. Tom Nishikawa, representative of Technical Translator's Agency, for preparing the first draft of the English translations of most of the chapters and to Mrs. Setsuko Ono for her efforts in inputting, proof reading and laying out the text in lffi.TEX,

Hirotugu Akaike Genshiro Kitagawa Tokyo, Japan July 1998

Preface

Due to the introduction of the information criterion AIC and development of prac­tical use of Bayesian modeling, the method of time analysis is now showing remarkable progress. In attempting the study of a new field the actual phenomenon is rarely so simple as to allow direct applications of existing methods of analysis or models. The real thrill of the statistical analysis lies in the process of developing a new model depending on the purpose and the characteristics of the object of the research. The purpose of this book ist.o introduce the readers to successful applications of the meth­ods of time series analysis in a variety of fields, such as engineering, earth science, medical science, biology, and economics.

The editors have been aware of the importance of cooperative research in sta­tistical science and carried out various cooperative research projects in the area of time series analysis. The Institute of Statistical Mathematics was reorganized as an inter-university research institute in 1985 and the activities of the Institute have been organized to promote the cooperative researches as its central activity. This book is composed of the outcomes of cooperative researches developed within this environ­ment and contains the results ranging from the pioneering realizations of statistical control to the latest consequences of time series modeling.

The initial process of the research of the control of cement kilns discussed in this book revealed the crucial importance of the model selection and lead to the introduc­tion of the information criterion AIC. The method of analysis and control of dynamic systems established by this research found applications in various fields. The expan­sion of the fields of application encouraged the development of new statistical methods and lead to the practical application of Bayesian models. Several results obtained by the utilization of Bayesian models are included in this book.

Results at various stages of the development of the time series analysis are shown to enable the readers to closely observe an ideal form of the development of statistical science where the theory and application help each other. It is hoped that the readers will learn how the authors of this book have solved the problems by developing their own ideas and will properly use the acquired knowledge as an aid in undertaking

viii Preface

researches in further wider areas of applications. The publication of this book was planned as one of the activities to celebrate the

50th anniversary of the Institute of Statistical Mathematics. We are very grateful to professor Kunio Tanabe, chairman of the publication committee, who enthusiastically encouraged the publication of this book. We are also deeply thankful to Professor Takashi Nakamura of the institute for his help in preparing the style file by Jb..TEX. Special thanks are due to Mrs. Setsuko Ono who efficiently performed the work of inputting and editing of some of the material in Jb..TEX. It is by the efforts of these people that the publication was made possible within a very short period of time of about one year after the initial planning of the book.

Hirotugu Akaike Genshiro Kitagawa Tokyo, Japan March 1994

The Structure of This Book and General References

The contents of the chapters of this book can be roughly classified by the subject and the model used as follows.

Control Engineering Earth Medical Economics SCIence biological

AR model 1,4,12 6, 13, 14 2, 15, 16 17

Bayes model 7 19,20 9

State space model 11, 21, 22 10 3,18

Other 8 5

(Numbers denote chapters)

The readers are supposed to have basic knowledge on the time series analysis. The references explicitly cited within the text are shown in the references of each chapter. The basic general references of this book are as follows:

l. Akaike, H. and Nakagawa, T. (1988), Statistical Analysis and Control of Dy­namic Systems, Kluwer Academic Pub., Dordrecht. (Original Japanese version was published in 1972 by Saiensu-Sha, Tokyo).

2. Kitagawa, G. and Gersch, W. (1996), Smoothness Priors Analysis of Time Se­ries, Springer-Verlag, New York.

3. Sakamoto, Y. Ishiguro, M. and Kitagawa, G. (1986), Akaike Information Crite­rion Statistics, D. Reidel Pub., Dordrecht.

x The Structure of This Book and General References

Most of the necessary computer software are published in the following TIMSAC (Time Series Analysis and .control Program Package) series with source code and numerical examples.

4. TIMSAC. (Included in the above reference 1.)

5. TIMSAC-74, TIMSAC-78, TIMSAC-84: Computer Science Monograph, The Institute of Statistical Mathematics, Nos. 5 (1975) & 6 (1976), No. 11 (1979), Nos. 22 & 23 (1985).

Contents

Preface to the English Version

Preface

The Structure of This Book and General References

1 Control of Boilers for Thermoelectric Power Plants by Means of a Statistical Model

Hideo Nakamum

1.1 Introduction··························· 1.2 Problems in Controlling Multivariable System . . . . . . . . 1.3 System Analysis and Control by Means of Statistical Model 1.4 Practical Procedure for Optimal Controller Design· 1.5 Application Results at Actual Plants 1.6 Closing Remarks .................. .

2 Feedback Analysis of a Living Body by a Multivariate Autoregressive Model

Takao Wada

v

vii

ix

1

1 2 4 6

13 15

19

2.1 Introduction······························· 19 2.2 Body Liquid Control and Feedback . . . . . . . . . . . . . . . . .. 20 2.3 Example of the Relative Power Contribution and Impulse Response 23 2.4 Using an Autoregressive Model for Feedback Analysis 25 2.5 Obtaining the Power Contribution· . . . . . . . . . 26 2.6 State Equation and Impulse Response· . . . . . . . 27 2.7 Impulse Response of the Closed and Open Systems 29 2.8 Confirmation by a Virtual Feedback System 31 2.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . 34

xii Contents

3 Factor Decomposition of Economic Time Series Fluctuations - Economic and Statistical Models in Harmony 37

Kosei Fukuda

3.1 Introduction·························· 3.2 Modell (Model with Stochastic Components Only) .... 3.3 Model 2 (the Model Including Deterministic Components) 3.4 Model 3 (the Model by Which Macroeconomic Policy

Effect can Also be Measured) .. 3.5 Has Fine Tuning been Successful? .. . 3.6 Is Prediction Ability Available? ... . 3.7 Conclusions and Subjects in the Future

4 The Statistical Optimum Control of Ship Motion and a Marine Main Engine

Kohei Ohtsu

37 38 42

46 50 52 53

57

4.1 Introduction······························ 57 4.2 Outline of the Control of the Motion of the Hull and Main Engine 58 4.3 Statistical Model of Ship Motions and Its Control . 60 4.4 Design of Optimum Autopilot System Based on the

Control-Type Autoregressive Model 62 4.5 Noise-Adaptive Control System . . . . . . . . . . . 68 4.6 Rudder-Roll Control System . . . . . . . . . . . . . 71 4.7 Application to the Marine Main Engine Governor System . 72 4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 High Precision Estimation of Seismic Wave Arrival Times

Tetsuo Takanami

79

5.1 Introduction······················ 79 5.2 Locally Stationary AR Model . . . . . . . . . . . . 80 5.3 Automatic Division of a Locally Stationary Interval 83 5.4 Precision Estimation of Seismic Wave Arrival Times . 85 5.5 Application: Earthquake Location and Velocity Structure Determina-

tion from Precise Arrival Time Estimates . 86 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92

6 Analysis of Dynamic Characteristics of a Driver-Vehicle System

Hitoshi Soma

95

6.1 Introduction····························· 95 6.2 Dynamics of Automobile under Lateral-Wind Disturbance .. . 96 6.3 Application of Multivariate AR Model to Driver-Vehicle System 102 6.4 Dynamics of Driver-Vehicle System under Lateral-Wind· 106 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Contents Xlll

7 Estimation of Directional Wave Spectra Using Ship Motion Data 115

Toshio Iseki

7.1 Introduction························ 7.2 Cross-spectrum Analysis by a Multivariate AR Model· 7.3 Relation Between the Directional Wave Spectrum and

the Ship Motions . . . . . . . . . . . . . . . . . . . . . 7.4 Estimation of the Directional Wave Spectrum Using a

Bayesian Model . . . . . . . . . . . . . . . . . 7.5 Results of the Tank Test Using a Model Ship· 7.6 Conclusions .................. .

8 Control of Filature Production Process

Akinori Shimazaki

8.1 Dropping-end Control and Gap Process . 8.2 Size Control of Raw Silk .. 8.3 Dwell Time in a Black Box· ...... .

9 Application to Pharmacokinetic Analysis

Akifumi Yafune

9.1 Introduction······················· 9.2 Pharmacokinetic Model· ............... . 9.3 Monte Carlo Estimation of Maximum Log Likelihood 9.4 Example······· 9.5 Concluding Remarks ............... .

10 State Space Modeling of Switching Time Series

Fumiyasu Komaki

10.1 Introduction· ....................... . 10.2 Time Series Data with Pulses and the Existing Methods 10.3 The State Space Model for Time Series with Pulses 10.4 Conclusions ........................ .

11 Time Varying Coefficient AR and VAR Models

Xing-Qi Jiang

11.1 Introduction . . . . . . . . . . . . . . . 11.2 Time Varying Coefficient AR Models . 11.3 Time Varying Coefficient VAR Models 11.4 An Example of Seismic Data Analysis·

115 116

120

122 124 128

131

131 137 144

153

153 154 155 157 160

163

163 164 166 172

175

175 176 180 183

XIV Contents

12 Statistical Control of Cement Process 193

Yoshitaka Yagiham

12.1 Introduction . . . . . . . . . . . . . . . . . . . 193 12.2 Cement Plant . . . . . . . . . . . . . . . . . . 194 12.3 Identification and Control of the Kiln Process 196 12.4 Collection and Identification of the Data under the On-line Control 204 12.5 Optimal Production Level and Pursuit Control· 204 12.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

13 Analysis of a Human/2-Wheeled-Vehicle System by ARdock 209

Makio Ishiguro and Takao Oya

13.1 Introduction· ..... . 13.2 Data· ......... . 13.3 AR Model and ARdock . 13.4 Numerical Results· . . . 13.5 Analysis of the Hands-Free Steering 13.6 The Optimum Control ....... .

14 Vibration Data Analysis of Automobiles

Shinzi Yamakawa

14.1 Preface· ......................... . 14.2 Road Surface Input-Wear of Component Material and

Riding Comfort . . . . . . . . . . . . . . . . . . . . . . 14.3 Separation of Correlated Power Components in a

Multiple Input System by Means of Power Contributions 14.4 Decision of Continuity of Data Properties· ...... . 14.5 Identification of Nonlinear Vibration System Through

Bispectral Analysis . . . . . . . . . . . . . . . . . . . 14.6 Continuous Measurement of Time-variant Spectrum· 14.7 Afterword ....................... .

15 Auto-Regressive Spectral Analysis of RR-Interval Time Series in Healthy Fetus and Newborn Infants

Teruyuki Ogawa

15.1 Introduction· ..... 15.2 Subjects and Methods 15.3 Results . . . 15.4 Discussion . 15.5 Conclusions

209 211 214 215 222 225

229

229

230

232 235

236 240 243

247

247 247 253 256 258

Contents

16 Information Processing Mechanisms in the Mammalian Brain: Analysis of Spatio-Temporal Neural Response in the Auditory Cortex

Kohyu Fukunishi

xv

263

16.1 Introduction· . . . . . . . . . . . . . . . . . . . . . . . . . . 263 16.2 Instrumentation of and Information Processing in the Brain 264 16.3 Optical Multipoint Observation in

the Mammalian Auditory Cortex . . . . . . . 265 16.4 Spatio-Temporal Neural Activity Observation 266 16.5 Functional Modules in the Auditory Cortex 270 16.6 Pattern Time Series Analysis ....... 272 16.7 Neural Correlation of and Neural Binding 273 16.8 Evaluation of Cortical Neural Binding· . . 274 16.9 Characteristics of Stationary Stochastic Response 279 16.10 Conclusions . . . . . . . . . . . . . . . . . . . . . 280

17 Time Series Analysis of Financial Asset Price Fluctuations 285

Hiroshi Tsuda

17.1 17.2 17.3 17.4

Introduction Nonstationary Nature of Financial Asset Prices Multivariate Analysis of the Time Series Model Conclusion . . . . . . . . . . . . . . . . . . . .

18 Dynamic Analysis of Economic Time Series

Sadao Naniwa

18.1 Introduction· ....................... . 18.2 Trend of the Economic Time Series and the Fluctuation

Around the Trend· . . . . . . . . . . . . . . . . . . 18.3 Analysis of Abrupt Change of Trend .. . . . . . . 18.4 Analysis of the Economic System by a Multivariate

Nonstationary Time Series Model 18.5 Conclusions . . . . . . . . . . . . . . . . . . . . . .

19 Processing of Time Series Data Obtained by Satellites

Tomoyuki Higuchi

19.1 Introduction . . . . . . . . . . . . . . . . . . . . 19.2 Problems to be Dealt With· . . . . . . . . . . . 19.3 Approach by a Bayesian Model-Simple Model· 19.4 Example of a Simple Model 19.5 Point Noise Source Model 19.6 Conclusions ........ .

283 283 288 297

299

299

300 304

307 311

313

313 314 316 321 322 326

XVI

20 Analysis of Earth Tides Data

Yoshiaki Tamura

20.1 What are Earth Tides? . . . . . . . . 20.2 Analysis Model ........... . 20.3 Tidal Analysis Program BAYTAP-G 20.4 Focal Points in the Analysis 20.5 Concluding Remarks ........ .

21 Detection of Groundwater Level Changes Related to Earthquakes

Norio Matsumoto

21.1 Introduction . 21.2 Observation Data ... 21.3 Data Analysis Method 21.4 Analysis of Actual Data 21.5 Conclusions . . . . . . .

22 Processing of Missing Observations and Outliers in Time Series

Genshiro Kitagawa

22.1 Missing Observations and Outliers· 22.2 Processing of Missing Observations 22.3 Processing of Outliers· 22.4 Conclusions ............ .

23 Mental Preparation for Time Series Analysis

Hirotugu Akaike

23.1 Introduction· ................ . 23.2 Time Series Analysis and Statistical Science 23.3 Prediction and Expectation ........ . 23.4 Ultimate Truth and Models ........ . 23.5 Evaluation of a Model and Information Criterion 23.6 Confirmation of Validity 23.7 Conclusions ...... .

Appendix

Index

Contents

327

327 329 334 337 338

341

341 342 342 346 350

353

353 355 360 364

367

367 367 368 368 369 370 371

373

381

Contributors

Hirotugu Akaike 1-7-14-204 Toride, Toride, 302 Japan.

Kosei Fukuda Economic Planning Agency, 3-1-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8970 Japan.

Kohyu Fukunishi Advanced Research laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395 Japan. (Present address: Department of Electronic Engineering, Graduate School of Engineering, Osaka University, Yamada-Oka 2-1, Suita 565-0871 Japan. E-mail: fukunisi@ele.eng.osaka-u.ac.jp)

Tomoyuki Higuchi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan. E-mail: higuchi@ism.ac.jp.

Toshio Iseki Tokyo University of Mercantile Marine, 2-1-6 Etchujima, Koto-ku, Tokyo 135-8533 Japan. E-mail: iseki@ipc.tosho-u.ac.jp.

Makio Ishiguro The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan. E-mail: ishiguro@ism.ac.jp.

Xing-Qi Jiang Department of Economics, Asahikawa University, 3-jo 23-Chome, Nagayama, Asahikawa, Hokkaido 079-8501 Japan. E-mail: jiang@asahikawa-u.ac.jp.

Genshiro Kitagawa The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan. E-mail: kitagawa@ism.ac.jp.

Fumiyasu Komaki Department of Mathematical Engineering and Information Physics, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 Japan. E-mail: komaki@stat.t.u-tokyo.ac.jp.

Norio Matsumoto Geological Survey of Japan. 1-1-3 Higashi, Tsukuba, Ibaraki 305-8567 Japan. E-mail: norio@gsj.go.jp

xviii Contributors

Hideo Nakamura 6-18-6 Minamiga-oka, Ohnojo-shi, Fukuoka-ken 816-0964 Japan.

Sadao Naniwa Kansai University of International Studies, 1-18 Aoyama, Shijimi­cho, Miki-shi, Hyogo Japan. E-mail: naniwa@kuins.ac.jp.

Teruyuki Ogawa Professor Emiritus of Pediatics, Oita Medical University, School of Medicine, Midorigaoka 5-13-7, Oita 870-1172 Japan. http://www.lukaster@oec­net.or.jp.

Kohei Ohtsu Tokyo University of Mercantile Marine, 2-1-6 Etyujima, Koto-ku, Tokyo 135-8533 Japan. E-mail: ohtsu@ipc.tosho-u.ac.jp.

Takio Oya Meiji University, 1-1-1 Higasi-Mita, Tama-ku, Kawasaki-shi 214-0034 Japan.

Akinori Shimazaki 691-2 Kokubu, Ueda-shi, Nagano-ken 386-0016 Japan.

Hitoshi Soma Japan Automobile Research Institute, 2530 Karima, Tsukuba, Ibaraki 305-0822 Japan. E-mail: hsoma@jari.or.jp

Tetsuo Takanami Institute of Seismological and Volcanology, Graduate School of Science, Hokkaido University, Kita 10-jyou, Nishi 8-choume, Kita-ku, Sapporo 060-0810 Japan. E-mail: ttaka@eos.hokudai.ac.jp.

Yoshiaki Tamura National Astronomical Observatory, Division of Earth Rotation, Mizusawa Astrogeodynamics Observatory, Mizusawa, Iwate-ken 023-0861 Japan. E-mail: tamura@miz.nao.ac.jp.

Hiroshi Tsuda NLI Research Institute, 1-1-1 Yurakucho, Chiyoda-ku, Tokyo 100 Japan. E-mail: tsuda@nli-research.co.jp

Akifumi Yafune Bio-Iatric Center, The Kitasato Institute, 5-9-1, Shirokane Minato­ku, Tokyo 108-8642 Japan.

Yoshitaka Yagihara System Sogo Kaihatsu Co. Ltd., 4-8-17 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan.

Shinzi Yamakawa Kogakuin University, 1-24-2 Nishi-Shinjyuku, Shinjyuku-ku, Tokyo 160-0023 Japan. E-mail: yamakawa@cc.kogakuin.ac.jp.

Takao Wada Former director of the Inaki Hospital. (Dr. Wada passed away on November 7, 1997.)