Table Of ContentNonlinear Filters
2nd Edition
Springer-Verlag Berlin Heidelberg GmbH
Hisashi Tanizaki
Nonlinear Filters
Estimation and Applications
Second Revised and Enlarged Edition
With 18 Figures
and 45 Tables
Springer
Associate Professor
Hisashi Tanizaki
Kobe University
Faculty of Economics
Rokkodai, Nadaku
Kobe 657, Japan
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Tanlzakl, Hlsashl:
Nonlinear filters : estimation and applications / Hisashi
Tanizaki. - 2. rev. and enl. ed. - Berlin ; Heidelberg; New
York; Barcelona; Budapest; Hong Kong; London; Milan ;
Paris ; Santa Clara; Singapore; Tokyo : Springer. 1996
ISBN 978-3-642-08253-5 ISBN 978-3-662-03223-7 (eBook)
DOI 10.1007/978-3-662-03223-7
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© Springer-Verlag Berlin Heidelberg 1993, 1996
Originally published by Springer-Verlag Berlin Heidelberg New York in 1996
Softcover reprint of the hardcover 2nd edition 1996
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To My Wife Miyuki
Preface
Preface to Second Edition
This book is a revision of Nonlinear Filters: Estimation and Applications,
(Lecture Notes in Economics and Mathematical Systems, No.400), which was
published from Springer-Verlag in 1993.
Compared with the first edition, I have made a substantial revision in the
second edition.
First, titles in the following chapters, sections, terms and so on are
changed as follows.
The First Edition The Second Edition
Chapter 3 Chapter 3
Nonlinear Filters based on Taylor ==> Traditional Nonlinear Filters
Series Expansion
Chapter 4 Chapter 4
Nonlinear Filters based on Density =* Density-Based Nonlinear Filters
Approximation
Section 4.3 Section 4.3
Numerical Density Approximation =* Numerical Integration Filter
by Piecewise Linear Functions:
Modified Kitagawa Estimator
Section 4.4 Section 4.4
Simulation-based Density Estimator =* Importance Sampling Filter
Chapter 5 Chapter 5
Comparison of Nonlinear Filters: =* Monte-Carlo Experiments
Monte-Carlo Experiments
Chapter 6 Chapter 6
An Application of Nonlinear ==> Application of Nonlinear Filters
Filters: Estimation of Permanent
Consumption
Monograph =* Book
VIII Preface
Thus, the most appropriate title is taken or the title is made short.
Second, new contents are briefly summarized as follows.
• Section 2.3.3 Minimum Mean Square Linear Estimator
As the third derivation method of the Kalman filter, I put this section.
This section is not utilized for the proceeding chapters but it is added as
a survey of the standard Kalman filter.
• Appendix A2.2 Conditional Normal Distribution
The derivation method under normality assumption is discussed in Sec
tion 2.3.1. Lemmas and Proofs used in Section 2.3.1 are summarized in
this appendix.
• Section 4.5 Density-based Monte-Carlo Filter
This nonlinear filter is one of the recent new nonlinear filters.
• Section 4.6 Rejection Sampling Filter
The rejection sampling filter is also one of the recent topics, where a
recursive algorithm of random draws from filtering densities is derived.
• Appendix A4.5 Density-Based Monte-Carlo Filter
For the filtering estimates by the density-based Monte-Carlo filter, the
asymptotic properties are discussed.
• Appendix A4.6 Rejection Sampling
Random number generation by rejection sampling is discussed in a gen
eral form.
• Appendix A5.1 On Initial Value of State-Variable
In the Kalman filter algorithm, the filtering estimates are recursively
obtained given the initial value. We analyze how the filtering estimates
are sensitive to the initial value.
• Appendix A5.3 On Random Draws by Importance Sampling
Monte-Carlo integration with importance sampling is utilized to the non
linear filter in Section 4.4, where random draws have to be generated from
the importance density. We discuss about the random draws generated
from the importance density.
• Appendix A5.4 Rejection Sampling
Using rejection sampling, random draws are generated by a computer.
Precision of random draws are examined.
• Chapter 7 Prediction and Smoothing
The density-based filtering algorithms discussed in Chapter 4 are ex
tended to prediction and smoothing.
Moreover, the following chapters are substantially revised.
• Chapter 5 Monte-Carlo Experiments
I changed a functional form of the nonlinear measurement and transition
equations in some simulation studies.
Preface to Second Edition IX
• Chapter 6 Application of Nonlinear Filters
In the first edition, only the U.S. data are used. In the second edition,
the same type of state-space model is estimated for Japan, U.S., U.K.,
France, Spain, Italy, Canada and Germany. I focus on estimation of the
unknown parameters and estimation of a ratio of per capita permanent
consumption relative to per capita total consumption for the above coun
tries.
Thus, the second edition is substantially changed compared with the first
edition.
Finally, I am grateful to the editor Dr. Werner A. Mueller, who gave me
a chance to revise the monograph.
March,1996
Author: Hisashi Tanizaki
Associate Professor
Faculty of Economics, Kobe University
Rokkodai, Nadaku, Kobe 657, Japan
E-mail: tanizaki@kobe-u.ac.jp
Preface to First Edition
Acknowledgements
Originally, this monograph is a revision of my Ph.D. dissertation (" Nonlinear
Filters: Estimation and Applications, " December, 1991) at the University of
Pennsylvania. In writing the dissertation, many people took care of me in
different ways.
In particular, Professor Roberto S. Mariano was very patient as my main
thesis advisor, and he gave me many useful suggestions and comments. I wish
to thank him for recommending me this line of research and giving me the
suggestions and comments. Also, I would like to acknowledge the support of
NSF grant SES 9011917 in Professor Roberto S. Mariano's supervision of the
thesis.
Professor Marc Nerlove supported me financially during my staying in
the U.S. in spite of my trouble with English. I would like to acknowledge
the support of NSF grant SES 5-25056. Professor Francis X. Diebold has
stimulated me through his studies. Although the dissertation was not directly
related to their research, their work significantly affected me and will influence
my future research. I am grateful to them for that.
Moreover, I do not forget to thank the classmates in the Graduate Pro
gram in Economics who had been encouraging me since I started studying
at the University. Especially, I got many " invisible things " from Michael
Blackman, Celia Chen, Haria Fornari and Til Schuermann (in alphabetical
order) and asked them to correct my English.
Also, I am grateful to Jun Sato and Shinichi Suda (the same year Japanese
Ph.D. students in Economics) and Suminori Tokunaga (Japanese Ph.D.
student in Regional Science) for helping me. I could not continue to study
there without them. When I was depressed just after coming to the U.S.,
they encouraged me.
Furthermore, I wish to thank Professors Mitsuo Saito, Kazuo Ogawa,
Toshihisa Toyoda and Kazuhiro Ohtani. When I was in Japan before going to
the U.S., I learned a lot of things under them at Kobe University. Especially,
Professor Mistuo Saito, who was my main advisor in Japan, recommended
that I continue to study econometrics at the University of Pennsylvania.
And I am grateful to Shinichi Kitasaka, who was one of my classmates at
Kobe University, for his suggestions and comments. Moreover, I have been
stimulated by Shigeyuki Hamori's passion for research. He was one of my
classmates at Kobe University, and he studied economics at Duke University
at the same time that I was at the University of Pennsylvania. I am grateful
to him for his valuable suggestions and advice.
Also, I wish to say " Thanks" to my parents. They have not understood
what I have done, but they supported me with regard to everything. Thus,
I believe that I could finish the dissertation thanks to all the professors and
all the friends who know me.
